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He tries to break free of narrow specialization and cross the boundaries between scientific disciplines. Expeditions beyond economics’ borders and its connection to history, philosophy, psychology, and ancient myths are not only refreshing, but necessary for understanding the world of the twenty-first century.

Reality is spun from stories, not from material. Zdeněk Neubauer

Before it was emancipated as a field, economics lived happily within subsets of philosophy—ethics, for example—miles away from today’s concept of economics as a mathematical-allocative science that views “soft sciences” with a scorn born from positivistic arrogance. But our thousand-year “education” is built on a deeper, broader, and oftentimes more solid base. It is worth knowing about.

The study of the history of a certain field is not, as is commonly held, a useless display of its blind alleys or a collection of the field’s trials and errors (until we got it right), but history is the fullest possible scope of study of a menu that the given field can offer.

History of thought helps us to get rid of the intellectual brainwashing of the age, to see through the intellectual fashion of the day, and to take a couple of steps back.

“The separation between the history of a science, its philosophy, and the science itself dissolves into thin air, and so does the separation between science and non-science; differences between the scientific and unscientific are vanishing.”

we seek to chart the development of the economic ethos. We ask questions that come before any economic thinking can begin—both philosophically and, to a degree, historically. The area here lies at the very borders of economics—and often beyond. We may refer to this as protoeconomics (to borrow a term from protosociology) or, perhaps more fittingly, metaeconomics (to borrow a term from metaphysics).

stories; Adam Smith believed. As he puts it in The Theory of Moral Sentiments, “the desire of being believed, or the desire of persuading, of leading and directing other people, seems to be one of the strongest of all our natural desires.”

“The human mind is built to think in terms of narratives … in turn, much of human motivation comes from living through a story of our lives, a story that we tell to ourselves and that creates a framework of our motivation. Life could be just ‘one damn thing after another’ if it weren’t for such stories. The same is true for confidence in a nation, a company, or an institution. Great leaders are foremost creators of stories.”

contrary to what our textbooks say, economics is predominantly a normative field. Economics not only describes the world but is frequently about how the world should be (it should be effective, we have an ideal of perfect competition, an ideal of high-GDP growth in low inflation, the effort to achieve high competitiveness …). To this end, we create models, modern parables,

I will try to show that mathematics, models, equations, and statistics are just the tip of the iceberg of economics; that the biggest part of the iceberg of economic knowledge consists of everything else; and that disputes in economics are rather a battle of stories and various metanarratives than anything else.

That is the reason for this book: to look for economic thought in ancient myths and, vice versa, to look for myths in today’s economics.

is a paradox that a field that primarily studies values wants to be value-free. One more paradox is this: A field that believes in the invisible hand of the market wants to be without mysteries.

The History of Animal Spirits: Dreams Never Sleep

The more important elements of a culture or field of inquiry such as economics are found in fundamental assumptions that adherents of all the various systems within the epoch unconsciously presuppose. Such assumptions appear so obvious that people do not know what they are assuming, because no other way of putting things has ever occurred to them, as the philosopher Alfred Whitehead notes in Adventures of Ideas.

I argue that economic questions were with mankind long before Adam Smith. I argue that the search for values in economics did not start with Adam Smith but culminated with him.

We should go beyond economics and study what beliefs are “behind the scenes,” ideas that have often become the dominant yet unspoken assumptions in our theories. Economics is surprisingly full of tautologies that economists are predominantly unaware of. I

argue that economics should seek, discover, and talk about its own values, although we have been taught that economics is a value-free science. I argue that none of this is true and that there is more religion, myth, and archetype in economics than there is mathematics.

In a way, this is a study of the evolution of both homo economicus and, more importantly, the history of the animal spirits within him. This book tries to study the evolution of the rational as well as the emotional and irrational side of human beings.

I argue that his most influential contribution to economics was ethical. His other thoughts had been clearly expressed long before him, whether on specialization, or on the principle of the invisible hand of the market. I try to show that the principle of the invisible hand of the market is much more ancient and developed long before Adam Smith. Traces of it appear even in the Epic of Gilgamesh, Hebrew thought, and in Christianity, and it is expressly stated by Aristophanes and Thomas Aquinas.

This is not a book on the thorough history of economic thought. The author aims instead to supplement certain chapters on the history of economic thought with a broader perspective and analysis of the influences that often escape the notice of economists and the wider public.

Progress (Naturalness and Civilization)

The Economy of Good and Evil

from his beginnings, man has been marked as a naturally unnatural creature, who for unique reasons surrounds himself with external possessions. Insatiability, both material and spiritual, are basic human metacharacteristics, which appear as early as the oldest myths and stories.

the Hebrews, with linear time, and later the Christians gave us the ideal (or amplified the Hebrew ideal) we now embrace. Then the classical economists secularized progress. How did we come to today’s progression of progress, and growth for growth’s sake?

The Need for Greed: The History of Consumption and Labor

Metamathematics From where did economics get the concept of numbers as the very foundation of the world?

mathematics at the core of economics, or is it just the icing of the cake, the tip of the iceberg of our field’s inquiry?

idea that we can manage to utilize our natural egoism, and that this evil is good for something, is an ancient philosophical and mythical concept. We will also look into the development of the ethos of homo economicus, the birth of “economic man.”

All of economics is, in the end, economics of good and evil. It is the telling of stories by people of people to people. Even the most sophisticated mathematical model is, de facto, a story, a parable, our effort to (rationally) grasp the world around us.

Masters of the Truth

Originally, truth was a domain of poems and stories, but today we perceive truth as something much more scientific, mathematical. Where does one go (to shop) for the truth? And who “has the truth” in our epoch?

Our animal spirits (something of a counterpart to rationality) are influenced by the archetype of the hero and our concept of what is good.

The entire history of ethics has been ruled by an effort to create a formula for the ethical rules of behavior. In the final chapter we will show the tautology of Max Utility, and we will discuss the concept of Max Good.

The History of the Invisible Hand of the Market and Homo Economicus

We understand “economics” to mean a broader field than just the production, distribution, and consumption of goods and services. We consider economics to be the study of human relations that are sometimes expressible in numbers, a study that deals with tradables, but one that also deals with nontradables (friendship, freedom, efficiency, growth).

When we mention economics in this book, we mean the mainstream perception of it, perhaps as best represented by Paul Samuelson.

By the term homo economicus, we mean the primary concept of economic anthropology. It comes from the concept of a rational individual, who, led by narrowly egotistical motives, sets out to maximize his benefit.

the Epic of Gilgamesh bears witness to the opposite—despite the fact that the first written clay fragments (such as notes and bookkeeping) of our ancestors may have been about business and war, the first written story is mainly about great friendship and adventure.

is a story of nature and civilization, of heroism, defiance, and the battle against the gods, and evil; an epic about wisdom, immortality, and also futility.

Even today we live in Gilgamesh’s vision that human relations—and therefore humanity itself—are a disturbance to work and efficiency; that people would perform better if they did not “waste” their time and energy on nonproductive things.

But it is in friendship where—often by-the-way, as a side product, an externality—ideas and deeds are frequently performed or created that together can altogether change the face of society.19 Friendship can go against an ingrained system in places where an individual does not have the courage to do so himself or herself.

started with Babylonians—rural nature becomes just a supplier of raw materials, resources (and humans the source of human resources). Nature is not the garden in which humans were created and placed, which they should care for and which they should reside in, but becomes a mere reservoir for natural (re)sources.

To be human seems to be somewhere in between, or both of these two. We

The entire history of culture is dominated by an effort to become as independent as possible from the whims of nature.39 The more developed a civilization is, the more an individual is protected from nature and natural influences and knows how to create around him a constant or controllable environment to his liking.

The epic captures one of the greatest leaps in the development of the division of labor. Uruk itself is one of the oldest cities of all, and in the epic it reflects a historic step forward in specialization—in the direction of a new social city arrangement. Because of the city wall, people in the city can devote themselves to things other than worrying about their own safety, and they can continue to specialize more deeply.

“The chief thing which the common-sense individual wants is not satisfactions for the wants he had, but more, and better wants.”47

If a consumer buys something, theoretically it should rid him of one of his needs—and the aggregate of things they need should be decreased by one item. In reality, though, the aggregate of “I want to have” expands together with the growing aggregate of “I have.”

the Old Testament, this relationship is perceived completely differently. Man (humanity) is created in nature, in a garden. Man was supposed to care for the Garden of Eden and live in harmony with nature and the animals. Soon after creation, man walks naked and is not ashamed, de facto the same as the animals. What is characteristic is that man dresses (the natural state of creation itself is not enough for him), and he (literally and figuratively) covers52 himself—in shame after the fall.53

Nature is where one goes to hunt, collect crops, or gather the harvest. It is perceived as the saturator of our needs and nothing more. One goes back to the city to sleep and be “human.” On the contrary, evil resides in nature. Humbaba lives in the cedar forest, which also happens to be the reason to completely eradicate it.

Symbolically, then, we can view the entire issue from the standpoint of the epic in the following way: Our nature is insufficient, bad, evil, and good (humane) occurs only after emancipation from nature (from naturalness), through culturing and education. Humanity is considered as being in civilization.

The city was frequently (at least in older Jewish writings) a symbol of sin, degeneration, and decadence—nonhumanity. The Hebrews were originally a nomadic nation, one that avoided cities. It is no accident that the first important city57 mentioned in the Bible is proud Babylon,58 which God later turns to dust.

is enough, for example, to read the Book of Revelation to see how the vision of paradise developed from the deep Old Testament period, when paradise was a garden. John describes his vision of heaven as a city—paradise is in New Jerusalem, a city where the dimensions of the walls(!) are described in detail, as are the golden streets and gates of pearl.

Hebrews later also chose a king (despite the unanimous opposition of God’s prophets) and settled in cities, where they eventually founded the Lord’s Tabernacle and built a temple for Him. The city of Jerusalem later gained an illustrious position in all of religion.

this time Christianity (as well as the influence of the Greeks) does not consider human naturalness to be an unambiguous good, and it does not have such an idyllic relationship to nature as the Old Testament prophets.

If a tendency toward good is not naturally endowed in people, it must be imputed from above through violence or at least the threat of violence.

If we were to look at human naturalness as a good, then collective social actions need a much weaker ruling hand. If people themselves have a natural tendency (propensity) toward good, this role does not have to be supplied by the state, ruler, or, if you wish, Leviathan.

How does this affect economics?

us return for the last time to the humanization of the wild Enkidu, which is a process we can perceive with a bit of imagination as the first seed of the principle of the market’s invisible hand, and therefore the parallels with one of the central schematics of economic thinking.

Sometimes it is better to “harness the devil to the plow” than to fight with him. Instead of summoning up enormous energy in the fight against evil, it is better to use its own energy to reach a goal we desire; setting up a mill on the turbulent river instead of futile efforts to remove the current. This is also how Saint Prokop approached it in one of the oldest Czech legends.

Enkidu caused damage and it was impossible to fight against him. But with the help of a trap, trick, this evil was transformed into something that greatly benefited civilization.

By culturing and “domesticating” Enkidu, humanity tamed the uncontrollable wild and chaotic evil

Enkidu devastated the doings (the external, outside-the-walls) of the city. But he was later harnessed and fights at the side of civilization against nature, naturalness, the natural state of things.

A similar story (reforming something animally wild and uncultivated in civilizational achievement) is used by Thomas Aquinas in his teachings. Several centuries later, this idea is fully emancipated in the hands of Bernard Mandeville and his Fable of the Bees: or, Private Vices, Publick Benefits. The economic and political aspects of this idea are—often incorrectly—ascribed to Adam Smith.

Here the individual does not try anymore to maximize his goods or profits, but what is important is writing his name in human memory in the form of heroic acts or deeds.

immortality, one connected with letters and the cult of the word: A name and especially a written name survives the body.”77

After this disappointment, he comes to the edge of the sea, where the innkeeper Siduri lives. As tonic for his sorrow, she offers him the garden of bliss, a sort of hedonistic fortress of carpe diem, where a person comes to terms with his mortality and at least in the course of the end of his life maximizes earthly pleasures, or earthly utility.

In the second stage, after finding his friend Enkidu, Gilgamesh abandons the wall and sets out beyond the city to maximalize heroism. “In his (…) search of immortal life, Gilgamesh

The hero refuses hedonism in the sense of maximizing terrestrial pleasure and throws himself into things that will exceed his life. In the blink of an eye, the epic turns on its head the entire utility maximization role that mainstream economics has tirelessly tried to sew on people as a part of their nature.81

today remember Gilgamesh for his story of heroic friendship with Enkidu, not for his wall, which no longer reaches monumental heights.

the eleventh and final tablet, Gilgamesh again loses what he sought. Like Sisyphus, he misses his goal just before the climax

The very existence of questions similar to today’s economic ones can be considered as the first observation. The first written considerations of the people of that time were not so different from those today. In other words: The epic is understandable for us, and we can identify with it.

We have also been witnesses to the very beginnings of man’s culturing—a great drama based on a liberation and then a distancing from the natural state.

Let us take this as a memento in the direction of our restlessness, our inherited dissatisfaction and the volatility connected to it. Considering that they have lasted five thousand years and to this day we find ourselves in harmony with a certain feeling of futility, perhaps these characteristics are inherent in man.

with the phenomenon of the creation of the city, we have seen how specialization and the accumulation of wealth was born, how holy nature was transformed into a secular supplier of resources, and also how humans’ individualistic ego was emancipated.

For small acts (hunting together, work in a factory), small love is enough: Camaraderie. For great acts, however, great love is necessary, real love: Friendship. Friendship that eludes the economic understanding of quid pro quo. Friendship gives. One friend gives (fully) for the other. That is friendship for life and death,

less a civilized, city person is dependent on nature, the more he or she is dependent on the rest of society. Like Enkidu, we have exchanged nature for society; harmony with (incalculable) nature for harmony with (incalculable) man.

human nature good or evil? To this day these questions are key for economic policy: If we believe that man is evil in his nature, therefore that a person himself is dog eat dog (animal), then the hard hand of a ruler is called for. If we believe that people in and of themselves, in their nature, gravitate toward good, then it is possible to loosen up the reins and live in a society that is more laissez-faire.

For a concept of historical progress, for the undeification of heroes, rulers, and nature, mankind had to wait for the Hebrews.

Because nature is not undeified, it is beyond consideration to explore it, let alone intervene in it (unless a person was a two-thirds god like Gilgamesh). It

As early as the “dark” ages, the Jews commonly used economic tools that were in many ways ahead of their time and that later became key elements of the modern economy:

Gilgamesh’s story ends where it began. There is a consistency in this with Greek myths and fables: At the end of the story, no progress occurs, no essential historic change; the story is set in indefinite time, something of a temporal limbo.

For a nation originally based on nomadism, where did this Jewish business ethos come from? And can the Hebrews truly be considered as the architects of the values that set the direction of our civilization’s economic thought?

PROGRESS: A SECULARIZED RELIGION One of the things the writers of the Old Testament gave to mankind is the idea and notion of progress. The Old Testament stories have their development; they change the history of the Jewish nation and tie in to each other. The Jewish understanding of time is linear—it has a beginning and an end.

The observance of God’s Commandments in Judaism leads not to some ethereal other world, but to an abundance of material goods (Genesis 49:25–26, Leviticus 26:3–13, Deuteronomy 28:1–13) (…) There are no accusing fingers pointed at

There are no echoes of asceticism nor for the cleansing and spiritual effect of poverty. It is fitting therefore, that the founders of Judaism, the Patriarchs Abraham, Isaac and Jacob, were all wealthy men.12

about due to a linear understanding of history. If history has a beginning as well as an end, and they are not the same point, then exploration suddenly makes sense in areas where the fruits are borne only in the next generation.

however, the idea of progress itself underwent major changes, and today we perceive it very differently. As opposed to the original spiritual conceptions, today we perceive progress almost exclusively in an economic or scientific-technological sense.

Because care for the soul has today been replaced by care for external things,

This is why we must constantly grow, because we (deep down and often implicitly) believe that we are headed toward an (economic) paradise on Earth.

Only since the period of scientific-technological revolution (and at a time when economics was born as an independent field) is material progress automatically assumed.

Jewish thought is the most grounded, most realistic school of thought of all those that have influenced our culture.17 An abstract world of ideas was unknown to the Jews. To this day it is still forbidden to even depict God, people, and animals in symbols, paintings, statues, and drawings.

economists have become key figures of great importance in our time (Kacířské eseje o filosofii dějin [Heretical Essays in the Philosophy of History]). They are expected to perform interpretations of reality, give prophetic services (macroeconomic forecasts), reshape reality (mitigate the impacts of the crisis, speed up growth), and, in the long run, provide leadership on the way to the Promised Land—paradise on Earth.

REALISM AND ANTIASCETICISM Aside from ideas of progress, the Hebrews brought another very fundamental contribution to our culture: The desacralization of heroes, nature, and rulers.

Voltaire writes: “It certain fact is, that in his public laws he [Moses] never so much as once made mention of a life to come, limiting all punishments and all rewards to the present life.”21

As opposed to Christianity, the concept of an extraterrestrial paradise or heaven was not developed much in Hebrew thought.19 The paradise of the Israelites—Eden—was originally placed on Earth at a given place in Mesopotamia20 and at a given time,

The Hebrews consider the world to be real—not just a shadow reflection of a better world somewhere in the cloud of ideas, something the usual interpretation of history ascribes to Plato. The soul does not struggle against the body and is not its prisoner, as Augustine would write later.

The land, the world, the body, and material reality are for Jews the paramount setting for divine history, the pinnacle of creation. This idea is the conditio sine qua non of the development of economics, something of an utterly earthly making,

The mythology of the hero-king was strongly developed in that period, which Claire Lalouette summarizes into these basic characteristics: Beauty (a perfect face, on which it is “pleasant to look upon,” but also “beauty,” expressed in the Egyptian word nefer, not only means aesthetics, but contains moral qualities as well),

THE HERO AND HIS UNDEIFICATION: THE DREAM NEVER SLEEPS The concept of the hero is more important than it might appear. It may be the remote origin of Keynes’s animal spirits, or the desire to follow a kind of internal archetype that a given individual accepts as his own and that society values.

This internal animator of ours, our internal mover, this dream, never sleeps and it influences our behavior—including economic behavior—more than we want to realize.

Anthropology knows several archetypes of heroes. The Polish-born American anthropologist Paul Radin examined the myths of North American Indians and, for example, in his most influential book, The Trickster, he describes their four basic archetypes of heroes.

The Torah’s heroes (if that term can be used at all) frequently make mistakes and their mistakes are carefully recorded in the Bible—maybe precisely so that none of them could be deified.32

the Hebrew heroes correspond most to the Tricksters, the Culture Bearers, and the Twins. The divine muscleman, that dominant symbol we think of when we say hero, is absent here.

Undeification, however, does not mean a call to pillage or desecration; man was put here to take care of nature (see the story of the Garden of Eden or the symbolism of the naming of the animals). This protection and care of nature is also related to the idea of progress

For the heroes who moved our civilization to where it is today, the heroic archetypes of the cunning trickster, culture bearer, and sufferer are rather more appropriate.

the Old Testament strongly emphasizes the undeification of nature.37 Nature is God’s creation, which speaks of divinity but is not the domain of moody gods

in an Old Testament context, the pharaoh was a mere man (whom one could disagree with, and who could be resisted!).

RULERS ARE MERE MEN In a similar historical context, the Old Testament teachings carried out a similar desacralization of rulers, the so-called bearers of economic policy.

Ultimately the entire idea of a political ruler stood against the Lord’s will, which is explicitly presented in the Torah. The Lord unequivocally preferred the judge as the highest form of rule—an

The needs of future generations will have to be considered; after all humankind are the guardians of God’s world. Waste of natural resources, whether privately owned or nationally owned is forbidden.”39

Politics lost its character of divine infallibility, and political issues were subject to questioning. Economic policy could become a subject of examination.

44 God first creates with the word and then on individual days He divides light from darkness, water from dry land, day from night, and so forth—and He gives order to things.45 The world is created orderly— it is wisely, reasonably put together. The way of the world is put together at least partially46 decipherably by any other wise and reasonable being who honors rational rules.

THE PRAISE OF ORDER AND WISDOM: MAN AS A PERFECTER OF CREATION The created world has an order of sorts, an order recognizable by us as people,

From the very beginning, when God distances Himself from the entire idea, there is an anticipation that there is nothing holy, let alone divine, in politics. Rulers make mistakes, and it is possible to subject them to tough criticism—which frequently occurs indiscriminately through the prophets in the Old Testament.

Hebrew culture laid the foundations for the scientific examination of the world.

Examining the world is therefore an absolutely legitimate activity, and one that is even requested by God—it is a kind of participation in the Creator’s work.51 Man is called on to understand himself and his surroundings and to use his knowledge for good.

The Book of Proverbs emphasizes specifically several times that it was wisdom that was present at the creation of the world. Wisdom personified calls out:

The last act, final stroke of the brush of creation, naming of the animals—this act is given to a human, it is not done by God, as one would expect. Man was given the task of completing the act of creation that the Lord began:

MAN AS A FINISHER OF CREATION The creation of the world, as it is explained in Jewish teachings, is described in the Book of Genesis. Here God (i) creates, (ii) separates, and (iii) names [my emphasis]:

Naming is a symbolic expression. In Jewish culture (and also in our culture to this day), the right to name meant sovereign rights and belonged, for example, to explorers (new places), inventors (new principles), or parents (children)—that is, to those who were there at the genesis, at the origin. This right was handed over by God to mankind.

The Naming itself (the capital N is appropriate) traditionally belongs to the crowning act of the Creator and represents a kind of grand finale of creation, the last move of the brush to complete the picture—a signature of the master.

Without naming, reality does not exist; it is created together with language. Wittgenstein tightly names this in his tractatus—the limits of our language are the limits of our world.53

Reality is not a given; it is not passive. Perceiving reality and “facts” requires man’s active participation. It is man who must take the last step, an act (and we

A real-ization act on our part represents the creation of a construct, the imputation of sense and order (which is beautifully expressed by the biblical act of naming, or categorization, sorting, ordering).

God connects man with the task of guarding and protecting the Garden of Eden, and thus man actually cocreates the cultural landscape. The Czech philosopher Zdeněk Neubauer also describes this: “Such is reality, and it is so deep that it willingly crystallizes into worlds. Therefore I profess that reality is a creation and not a place of occurrence for objectively given phenomena.”61

The Jews believed the exact opposite. The world is created by a good God, and evil appears in it as a result of immoral human acts. Evil, therefore, is induced by man.66 History unwinds according to the morality of human acts.

GOOD AND EVIL IN US: A MORAL EXPLANATION OF WELL-BEING We have seen that in the Epic of Gilgamesh, good and evil are not yet addressed systematically on a moral level.

the epic, good and evil are not envisaged morally—they are not the result of an (a)moral act. Evil was not associated with free moral action or individual will.

Hebrew thought, on the other hand, deals intensively with moral good and evil. A moral dimension touches the core of its stories.65

discrepancy between savings and investment, and others are convinced of the monetary essence

The entire history of the Jewish nation is interpreted and perceived in terms of morality. Morality has become, so to speak, a mover and shaker of Hebrew history.

sunspots. The Hebrews came up with the idea that morals were behind good and bad years, behind the economic cycle. But we would be getting ahead of ourselves. Pharaoh’s Dream: Joseph and the First Business Cycle To

It is the Pharaoh’s well-known dream of seven fat and seven lean cows, which he told to Joseph, the son of Jacob. Joseph interpreted the dream as a macroeconomic prediction of sorts: Seven years of abundance were to be followed by seven years of poverty, famine, and misery.

Self-Contradicting Prophecy Here, let’s make several observations on this: Through taxation74 on the level of one-fifth of a crop75 in good years to save the crop and then open granaries in bad years, the prophecy was de facto prevented (prosperous years were limited and hunger averted—through a predecessor of fiscal stabilization).

The Old Testament prophesies therefore were not any deterministic look into the future, but warnings and strategic variations of the possible, which demanded some kind of reaction. If the reaction was adequate, what was prophesied would frequently not occur at all.

If the threat is anticipated, it is possible to totally or at least partially avoid it. Neither Joseph nor the pharaoh had the power to avoid bounty or crop failure (in this the dream interpretation was true and the appearance of the future mystical), but they avoided the impacts and implications of the prophecy (in this the interpretation of the dream was “false”)—famine did not ultimately occur in Egypt, and this was due to the application of reasonable and very intuitive economic policy.

Let us further note that the first “macroeconomic forecast” appears in a dream.

back to Torah: Later in this story we will notice that there is no reason offered as to why the cycle occurs (that will come later). Fat years will simply come, and then lean years after them.

Moral Explanation of a Business Cycle That is fundamentally different from later Hebrew interpretations, when the Jewish nation tries to offer reasons why the nation fared well or poorly. And those reasons are moral.

Only in recent times have some currents of economics again become aware of the importance of morals and trust in the form of measuring the quality of institutions, the level of justice, business ethics, corruption, and so forth, and examining their influence on the economy,

it is not within the scope of this book to answer that question; justice has been done to the question if it manages to sketch out the main contours of possible searches for answers.

THE ECONOMICS OF GOOD AND EVIL: DOES GOOD PAY OFF? This is probably the most difficult moral problem we could ask.

Inquiring about the economics of good and evil, however, is not that easy. Where would Kant’s “moral dimension of ethics” go if ethics paid? If we do good for profit, the question of ethics becomes a mere question of rationality.

He remains righteous, even if his only reward is death. What economic advantage could he have from that?

morals cannot be considered in the economic dimension of productivity and calculus. The role of the Hebrews was to do good, whether it paid off or not. If good (outgoing) is rewarded by incoming goodness, it is a bonus,99 not a reason to do outgoing good. Good and reward do not correlate to each other.

This reasoning takes on a dimension of its own in the Old Testament. Good (incoming) has already happened to us. We must do good (outgoing) out of gratitude for the good (incoming) shown to us in the past.

So why do good? After all, suffering is the fate of many biblical figures. The answer can only be: For good itself. Good has the power to be its own reward. In this sense, goodness gets its reward, which may or may not take on a material dimension.

the Hebrews offered an interesting compromise between the teachings of the Stoics and Epicureans. We will go into it in detail later, so only briefly

constraint. It calls for bounded optimalization (with limits). A kind of symbiosis existed between the legitimate search for one’s own utility (or enjoyment of life) and maintaining rules, which are not negotiable and which are not subject to optimalization.

In other words, clear (exogenously given) rules exist that must be observed and cannot be contravened. But within these borders it is absolutely possible, and even recommended, to increase utility.

To Love the Law The Jews not only had to observe the law (perhaps the word covenant would be more appropriate), but they were to love it because it was good.

the principle of doing good (outgoing) on the basis of a priori demonstrated good (incoming) was also taken over by the New Testament. Atonement itself is based on an a priori principle; all our acts are preceded by good.

THE SHACKLES OF THE CITY Owing to the Hebrew’s liberation from Egyptian slavery, freedom and responsibility become the key values of Jewish thought.

Laws given by God are binding for Jews, and God is the absolute source of all values,

The Hebrew ideal is represented by the paradise of the Garden of Eden, not a city.116 The despised city civilization or the tendency to see in it a sinful and shackling way of life appears in glimpses and allusions in many places in the Old Testament.

The nomadic Jewish ethos is frequently derived from Abraham, who left the Chaldean city of Ur on the basis of a command:

This way of life had understandably immense economic impacts. First, such a society lived in much more connected relationships, where there was no doubt that everyone mutually depended on each other. Second, their frequent wanderings meant the inability to own more than they could carry; the gathering up of material assets did not have great weight—precisely because the physical weight (mass) of things was tied to one place.

One of Moses’s greatest deeds was that he managed to explain to his nation once and for all that it is better to remain hungry and liberated than to be a slave with food “at no cost.”

SOCIAL WELFARE: NOT TO ACT IN THE MANNER OF SODOM

regulations is developed in the Old Testament, one we hardly find in any other nation of the time. In Hebrew teachings, aside from individual utility, indications of the concept of maximalizing utility societywide appear for the first time as embodied in the Talmudic principle of Kofin al midat S´dom, which can be translated as “one is compelled not to act in the manner of Sodom” and to take care of the weaker members of society.

In a jubilee year, debts were to be forgiven,125 and Israelites who fell into slavery due to their indebtedness were to be set free.126

Land at the time could be “sold,” and it was not sale, but rent. The price (rent) of real estate depended on how long there was until a forgiveness year. It was about the awareness that we may work the land, but in the last instance we are merely “aliens and strangers,” who have the land only rented to us for a fixed time. All land and riches came from the Lord.

These provisions express a conviction that freedom and inheritance should not be permanently taken away from any Israelite. Last but not least, this system reminds us that no ownership lasts forever and that the fields we plow are not ours but the Lord’s.

Glean Another social provision was the right to glean, which in Old Testament times ensured at least basic sustenance for the poorest. Anyone who owned a field had the responsibility not to harvest it to the last grain but to leave the remains in the field for the poor.

Tithes and Early Social Net Every Israelite also had the responsibility of levying a tithe from their entire crop. They had to be aware from whom all ownership comes and, by doing so, express their thanks.

“Since the community has an obligation to provide food, shelter, and basic economic goods for the needy, it has a moral right and duty to tax its members for this purpose. In line with this duty, it may have to regulate markets, prices and competition, to protect the interests of its weakest members.”135

In Judaism, charity is not perceived as a sign of goodness; it is more of a responsibility. Such a society then has the right to regulate its economy in such a way that the responsibility of charity is carried out to its satisfaction.

With a number of responsibilities, however, comes the difficulty of getting them into practice. Their fulfillment, then, in cases when it can be done, takes place gradually “in layers.” Charitable activities are classified in the Talmud according to several target groups with various priorities, classified according to, it could be said, rules of subsidiarity.

Do not mistreat an alien or oppress him, for you were aliens in Egypt.140 As one can see, aside from widows and orphans, the Old Testament also includes immigrants in its area of social protection.141 The Israelites had to have the same rules apply for them as for themselves—they could not discriminate on the basis of their origin.

ABSTRACT MONEY, FORBIDDEN INTEREST, AND OUR DEBT AGE If it appears to us that today’s era is based on money and debt, and our time will be written into history as the “Debt age,” then it will certainly be interesting to follow how this development occurred.

Money is a social abstractum. It is a social agreement, an unwritten contract.

The first money came in the form of clay tablets from Mesopotamia, on which debts were written. These debts were transferable, so the debts became currency. In the end, “It is no coincidence that in English the root of ‘credit’ is ‘credo,’ the Latin for ‘I believe.’”

To a certain extent it could be said that credit, or trust, was the first currency. It can materialize, it can be embodied in coins, but what is certain is that “money is not metal,” even the rarest metal, “it is trust inscribed,”

Inseparably, with the original credit (money) goes interest. For the Hebrews, the problem of interest was a social issue: “If you lend money to one of my people among you who is needy, do not be like a moneylender; charge him no interest.”

there were also clearly set rules setting how far one could go in setting guarantees and the nonpayment of debts. No one should become indebted to the extent that they could lose the source of their livelihood:

In the end, the term “bank” comes from the Italian banci, or the benches that Jewish lenders sat on.157

Money is playing not only its classical roles (as a means of exchange, a holder of value, etc.) but also a much greater, stronger role: It can stimulate, drive (or slow down) the whole economy. Money plays a national economic role.

In the course of history, however, the role of loans changed, and the rich borrowed especially for investment purposes,

In such a case a ban on interest did not have great ethical significance. Thomas Aquinas, a medieval scholar (1225-1274), also considers similarly; in his time, the strict ban on lending with usurious interest was loosened, possibly due to him.

As a form of energy, money can travel in three dimensions, vertically (those who have capital lend to those who do not) and horizontally (speed and freedom in horizontal or geographic motion has become the by-product—or driving force?—of globalization). But money (as opposed to people) can also travel through time.

money is something like energy that can travel through time. And it is a very useful energy, but at the same time very dangerous as well. Wherever

Aristotle condemned interest162 not only from a moral standpoint, but also for metaphysical reasons. Thomas Aquinas shared the same fear of interest and he too argued that time does not belong to us, and that is why we must not require interest.

MONEY AS ENERGY: TIME TRAVEL AND GROSS DEBT PRODUCT (GDP)

Due to this characteristic, we can energy-strip the future to the benefit of the present. Debt can transfer energy from the future to the present.163 On the other hand, saving can accumulate energy from the past and send it to the present.

labor was not considered degrading in the Old Testament. On the contrary, the subjugation of nature is even a mission from God that originally belonged to man’s very first blessings.

LABOR AND REST: THE SABBATH ECONOMY

The Jews as well as Aristotle behaved very guardedly toward loans. The issue of interest/usury became one of the first economic debates. Without having an inkling of the future role of economic policy (fiscal and monetary), the ancient Hebrews may have unwittingly felt that they were discovering in interest a very powerful weapon, one that can be a good servant, but (literally) an enslaving master as well.

It’s something like a dam. When we build one, we are preventing periods of drought and flooding in the valley; we are limiting nature’s whims and, to a large extent, avoiding its incalculable cycles. Using dams, we can regulate the flow of water to nearly a constant. With it we tame the river (and we can also gain

But if we do not regulate the water wisely, it may happen that we would overfill the dam and it would break. For the cities lying in the valley, their end would be worse than if a dam were never there.

If man lived in harmony with nature before, now, after the fall, he must fight; nature stands against him and he against it and the animals. From the Garden we have moved unto a (battle)field.

Only after man’s fall does labor turn into a curse.168 It could even be said that this is actually the only curse, the curse of the unpleasantness of labor, that the Lord places on Adam.

Both Plato and Aristotle consider labor to be necessary for survival, but that only the lower classes should devote themselves to it so that the elites would not have to be bothered with it and so that they could devote themselves to “purely spiritual matters—art, philosophy, and politics.”

Work is also not only a source of pleasure but a social standing; It is considered an honor. “Do you see a man skilled in his work? He will serve before kings.”170 None of the surrounding cultures appreciate work as much. The idea of the dignity of labor is unique in the Hebrew tradition.

Hebrew thinking is characterized by a strict separation of the sacred from the profane. In life, there are simply areas that are holy, and in which it is not allowed to economize, rationalize, or maximize efficiency.

the message of the commandment on Saturday communicated that people were not primarily created for labor.

This dimension has disappeared from today’s economics. Economic effort has no goal at which it would be possible to rest. Today we only know growth for growth’s sake, and if our company or country prospers, that does not…

the purpose of creation was not just creating but that it had an end, a goal. The process was just a process, not a purpose. The whole of Being was created so…

ancient Greek economic ethos, we will examine two extreme approaches to laws and rules. While the Stoics considered laws to be absolutely valid, and utility had infinitesimal meaning in their philosophy, the Epicureans, at least in the usual historical explanation, placed utility and pleasure in first place—rules were to be made based on the principle of utility.

CONCLUSION: BETWEEN UTILITY AND PRINCIPLE The influence of Jewish thought on the development of market democracy cannot be overestimated. The key heritage for us was the lack of ascetic perception of the world, respect to law and private…

poets actually went even further, and with their speech they shaped and established reality and truth. Honor, adventure, great deeds, and the acclaim connected with them played an important role in the establishment of the true, the real.

those who are famous will be remembered by people. They become more real, part of the story, and they start to be “realized,” “made real” in the lives of other people. That which is stored in memory is real; that which is forgotten is as if it never existed.

“epic and tragic poets were widely assumed to be the central ethical thinkers and teachers of Greece; nobody thought of their work as less serious, less aimed at truth, than the speculative prose treatises of historians and philosophers.”5 Truth and reality were hidden in speech, stories, and narration.

general? In the end, poetry could be more sensitive to the truth than the philosophical method or, later, the scientific method. “Tragic poems, in virtue of their subject matter and their social function, are likely to confront and explore problems about human beings and luck that a philosophical text might be able to omit or avoid.”8

The quality of mathematics research in the United States today is the envy of the scientific world. This is a direct result of the openness and inclusivity of the profession.

Can Americans maintain this unmatched excellence in the future? There are worrisome signs that suggest not.

The Organization for Economic Cooperation and Development compares mathematical proficiency among 15-year-olds by country worldwide. According to its 2018 report, America ranked 37th while China, America’s main competitor for world leadership, came in first.

This is despite the fact that the United States is the fifth-highest spender per pupil among the 37 developed OECD nations

This massive failure of our K-12 education system trickles through the STEM pipeline.

At the undergraduate level, too few American students are prepared for higher-level mathematics courses. These students are then unprepared for rigorous graduate-level work

According to our own experiences at the universities where we teach, an overwhelming majority of American students with strong math backgrounds are either foreign-born or first-generation students who have additional support from their education-conscious families. At all levels, STEM disciplines are more and more dependent on a constant flow of foreign talent.

There are many reasons for this failure, but the way that we educate and prepare teachers is particularly influential. The vast majority of K-12 math teachers are graduates of teacher-preparation programs that teach very little substantive mathematics

This has led to a constant stream of ill-advised and dumbed-down reforms. One of the latest fads is anti-racist mathematics. Promoted in several states, the bizarre doctrine threatens to further degrade the teaching of mathematics.

Another major concern is the twisted interpretation of diversity, equity, and inclusion (DEI).

Under the banner of DEI, universities are abandoning the use of standardized tests like the SAT and GRE in admissions, and cities are considering scrapping academic tracking and various gifted programs in schools, which they deem “inequitable.”

such programs are particularly effective, when properly implemented, at discovering and encouraging talented children from disadvantaged backgrounds.

The new 2021 Mathematics Framework, currently under consideration by California’s Department of Education, does away “with all tracking, acceleration, gifted programs, or any instruction that involves clustering by individual differences, without expressing any awareness of the impact these drastic alterations would have in preparing STEM-ready candidates.”

These measures will not only hinder the progress of the generations of our future STEM workforce but also contribute to structural inequalities, as they are uniquely detrimental to students whose parents cannot send them to private schools or effective enrichment programs.

These are just a few examples of an unprecedented fervor for revolutionary change in the name of Critical Race Theory (CRT), a doctrine that views the world as a fierce battleground for the narratives of various identity groups.

This will only lead to a further widening of racial disparities in educational outcomes while lowering American children’s rankings in education internationally.

Ill-conceived DEI policies, often informed by CRT, and the declining standards of K-12 math education feed each other in a vicious circle

Regarding minorities, in particular, public K-12 education all too often produces students unprepared to compete, thus leading to large disparities in admissions at universities, graduate programs, and faculty positions. This disparity is then condemned as a manifestation of structural racism, resulting in administrative measures to lower the evaluation criteria. Lowering standards at all levels leads eventually to even worse outcomes and larger disparities, and so on in a downward spiral.

A case in point is the recent report by the American Mathematical Society that accuses the entire mathematics community, with the thinnest of specific evidence, of systemic racial discrimination. A major justification put forward for such a grave accusation is the lack of sufficient representation of Black mathematicians in the professio

the report, while raising awareness of several ugly facts from the long-ago past, makes little effort to address the real reasons for this, mainly the catastrophic failure of the K-12 mathematical educational system.

The National Science Foundation, a federal institution meant to support fundamental research, is now diverting some of its limited funding to various DEI initiatives of questionable benefit.

Meanwhile, other countries, especially China, are doing precisely the opposite, following the model of our past dedication to objective measures of excellence. How long before we will see a reverse exodus, away from the United States?

The present crisis can still be reversed by focusing on a few concrete actions:

Improve schools in urban areas and inner-city neighborhoods by following the most promising education programs. These programs demonstrate that inner-city children benefit if they are challenged by high standards and a nurturing environment.

Follow the lead of other highly successful rigorous programs such as BASIS schools and Math for America, which focus on rigorous STEM curricula, combined with 21st-century teaching methods, and recruit talented teachers to help them build on their STEM knowledge and teaching methods.

Increase, rather than eliminate, tailored instruction, both for accelerated and remedial math courses.

Reject the soft bigotry of low expectations, that Black children cannot do well in competitive mathematics programs and need dumbed-down ethnocentric versions of mathematics.

Uphold the objective selection process based on merit at all levels of education and research.

ways of working are critical in mathematical work and when they are taught and valued, many more students contribute, leading to higher achievement

mathematics education we suffer from the widespread, distinctly American idea that only some people can be “math people.” This idea has been disproved by scientific research showing the incredible potential of the brain to grow and adapt. But the idea that math is hard, uninteresting, and accessible only to “nerds” persists. 

harsh stereotypical thinking—mathematics is for select racial groups and men. This thinking, as well as the teaching practices that go with it, have provided the perfect conditions for the creation of a math underclass.

There is a good reason for this: Justification and reasoning are two of the acts that lie at the heart of mathematics. They are, in many ways, the essence of what mathematics is.  Scientists work to prove or disprove new theories by finding many cases that work or counter-examples that do not. Mathematicians, by contrast prove the validity of their propositions through justification and reasoning.

does not simply test a mathematical definition, as the first does. It requires that students visualize a triangle, use transformational geometry, consider whether different cases satisfy the mathematical definition, and then justify their thinking.

online platform explaining research evidence on ability and the brain and on good mathematics teaching, for teachers and parents. The course had a transformative effect. It was taken by 40,000 people, and 95 percent said they would change their teaching or parenting as a result.

The young people who are successful in today’s workforce are those who can discuss and reason about productive mathematical pathways, and who can be wrong, but can trace back to errors and work to correct them.

American idea that those who are good at math are those who are fast. Speed is revered in math classes across the U.S., and students as young as five years old are given timed tests—even though these have been shown to create math anxiety in young children. Parents use flash cards and other devices to promote speed, not knowing that they are probably damaging their children’s mathematical development

The fact of being quick or slow isn't really relevant

gives more time for depth and exploration than the curricula it has replaced by removing some of the redundant methods students will never need or use.

The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.” A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.

Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math.

California’s two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.

a definitive analysis by the Georgetown Center on Education and the Workforce forecasts that in the decade ahead a mere 5 percent of entry-level workers will need to be proficient in algebra or above.

“mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required.

I fully concur that high-tech knowledge is needed to sustain an advanced industrial economy. But we’re deluding ourselves if we believe the solution is largely academic.

Nor will just passing grades suffice. Many colleges seek to raise their status by setting a high mathematics bar. Hence, they look for 700 on the math section of the SAT, a height attained in 2009 by only 9 percent of men and 4 percent of women. And it’s not just Ivy League colleges that do this: at schools like Vanderbilt, Rice and Washington University in St. Louis, applicants had best be legacies or athletes if they have scored less than 700 on their math SATs.

A January 2012 analysis from the Georgetown center found 7.5 percent unemployment for engineering graduates and 8.2 percent among computer scientists.

“Our civilization would collapse without mathematics.” He’s absolutely right.

Quantitative literacy clearly is useful in weighing all manner of public policies

Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.

Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.

This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry.

I hope that mathematics departments can also create courses in the history and philosophy of their discipline, as well as its applications in early cultures. Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet

Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.

The true work of the mathematician is not experienced until the later parts of graduate school, when the student is challenged to create knowledge in the form of a novel proof. It is common to fill page after page with an attempt, the seasons turning, only to arrive precisely where you began, empty-handed — or to realize that a subtle flaw of logic doomed the whole enterprise from its outset. The steady state of mathematical research is to be completely stuck. It is a process that Charles Fefferman of Princeton, himself a onetime math prodigy turned Fields medalist, likens to ‘‘playing chess with the devil.’’ The rules of the devil’s game are special, though: The devil is vastly superior at chess, but, Fefferman explained, you may take back as many moves as you like, and the devil may not. You play a first game, and, of course, ‘‘he crushes you.’’ So you take back moves and try something different, and he crushes you again, ‘‘in much the same way.’’ If you are sufficiently wily, you will eventually discover a move that forces the devil to shift strategy; you still lose, but — aha! — you have your first clue.

Tao has emerged as one of the field’s great bridge-­builders. At the time of his Fields Medal, he had already made discoveries with more than 30 different collaborators. Since then, he has also become a prolific math blogger with a decidedly non-­Gaussian ebullience: He celebrates the work of others, shares favorite tricks, documents his progress and delights at any corrections that follow in the comments. He has organized cooperative online efforts to work on problems. ‘‘Terry is what a great 21st-­century mathematician looks like,’’ Jordan Ellenberg, a mathematician at the University of Wisconsin, Madison, who has collaborated with Tao, told me. He is ‘‘part of a network, always communicating, always connecting what he is doing with what other people are doing.’’

Most mathematicians tend to specialize, but Tao ranges widely, learning from others and then working with them to make discoveries. Markus Keel, a longtime collaborator and close friend, reaches to science fiction to explain Tao’s ability to rapidly digest and employ mathematical ideas: Seeing Tao in action, Keel told me, reminds him of the scene in ‘‘The Matrix’’ when Neo has martial arts downloaded into his brain and then, opening his eyes, declares, ‘‘I know kung fu.’’ The citation for Tao’s Fields Medal, awarded in 2006, is a litany of boundary hopping and notes particularly ‘‘beautiful work’’ on Horn’s conjecture, which Tao completed with a friend he had played foosball with in graduate school. It was a new area of mathematics for Tao, at a great remove from his known stamping grounds. ‘‘This is akin,’’ the citation read, ‘‘to a leading English-­language novelist suddenly producing the definitive Russian novel.’’

For their work, Tao and Green salvaged a crucial bit from an earlier proof done by others, which had been discarded as incorrect, and aimed at a different goal. Other maneuvers came from masterful proofs by Timothy Gowers of England and Endre Szemeredi of Hungary. Their work, in turn, relied on contributions from Erdos, Klaus Roth and Frank Ramsey, an Englishman who died at age 26 in 1930, and on and on, into history. Ask mathematicians about their experience of the craft, and most will talk about an intense feeling of intellectual camaraderie. ‘‘A very central part of any mathematician’s life is this sense of connection to other minds, alive today and going back to Pythagoras,’’ said Steven Strogatz, a professor of mathematics at Cornell University. ‘‘We are having this conversation with each other going over the millennia.’’

As a group, the people drawn to mathematics tend to value certainty and logic and a neatness of outcome, so this game becomes a special kind of torture. And yet this is what any ­would-be mathematician must summon the courage to face down: weeks, months, years on a problem that may or may not even be possible to unlock. You find yourself sitting in a room without doors or windows, and you can shout and carry on all you want, but no one is listening.

An effort to prove that 1 equals 0 is not likely to yield much fruit, it’s true, but the hacker’s mind-set can be extremely useful when doing math. Long ago, mathematicians invented a number that when multiplied by itself equals negative 1, an idea that seemed to break the basic rules of multiplication. It was so far outside what mathematicians were doing at the time that they called it ‘‘imaginary.’’ Yet imaginary numbers proved a powerful invention, and modern physics and engineering could not function without them.

Early encounters with math can be misleading. The subject seems to be about learning rules — how and when to apply ancient tricks to arrive at an answer. Four cookies remain in the cookie jar; the ball moves at 12.5 feet per second. Really, though, to be a mathematician is to experiment. Mathematical research is a fundamentally creative act. Lore has it that when David Hilbert, arguably the most influential mathematician of fin de siècle Europe, heard that a colleague had left to pursue fiction, he quipped: ‘‘He did not have enough imagination for mathematics.’’

Many people think that substantial progress on Navier-­Stokes may be impossible, and years ago, Tao told me, he wrote a blog post concurring with this view. Now he has some small bit of hope. The twin-prime conjecture had the same feel, a sense of breaking through the wall of intimidation that has scared off many aspirants. Outside the world of mathematics, both Navier-­Stokes and the twin-prime conjecture are described as problems. But for Tao and others in the field, they are more like opponents. Tao’s opponent has been known to taunt him, convincing him that he is overlooking the obvious, or to fight back, making quick escapes when none should be possible. Now the opponent appears to have revealed a weakness. But Tao said he has been here before, thinking he has found a way through the defenses, when in fact he was being led into an ambush. ‘‘You learn to get suspicious,’’ Tao said. ‘‘You learn to be on the lookout.’’

exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory

When something new is encountered, the follow-up steps usually require mathematical and statistical methods to move the analysis forward. If that step proves too technically difficult for the person who made the discovery, a mathematician or statistician can be added as a collaborator

Ideas in science emerge most readily when some part of the world is studied for its own sake. They follow from thorough, well-organized knowledge of all that is known or can be imagined of real entities and processes within that fragment of existence

Ramped up and disciplined, fantasies are the fountainhead of all creative thinking. Newton dreamed, Darwin dreamed, you dream. The images evoked are at first vague. They may shift in form and fade in and out. They grow a bit firmer when sketched as diagrams on pads of paper, and they take on life as real examples are sought and found.

Over the years, I have co-written many papers with mathematicians and statisticians, so I can offer the following principle with confidence. Call it Wilson's Principle No. 1: It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.

If your level of mathematical competence is low, plan to raise it, but meanwhile, know that you can do outstanding scientific work with what you have. Think twice, though, about specializing in fields that require a close alternation of experiment and quantitative analysis. These include most of physics and chemistry, as well as a few specialties in molecular biology.

Newton invented calculus in order to give substance to his imagination

Darwin had little or no mathematical ability, but with the masses of information he had accumulated, he was able to conceive a process to which mathematics was later applied.

For aspiring scientists, a key first step is to find a subject that interests them deeply and focus on it. In doing so, they should keep in mind Wilson's Principle No. 2: For every scientist, there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence.

Beyond the grammars of geometry and algebra lies a domain of not math-like but text-like compositions and meanings (of semantics beyond mathematics).

17. Word and world both have grammars that don’t fit our available mathematical rules.

18. Reality is relational, and not entirely objective. Subject and object aren’t separable, they’re entangled, inescapably. “Objective” is always relative to some other system/observer. 

We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.

the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not. If such simulations are possible in theory, he reasons, then eventually humans will create them — presumably many of them. If this is so, in time there will be many more simulated worlds than nonsimulated ones. Statistically speaking, therefore, we are more likely to be living in a simulated world than the real one.

The jury is still out on the simulation hypothesis. But even if it proves too far-fetched, the possibility of the Platonic nature of mathematical ideas remains — and may hold the key to understanding our own reality.

After dallying with physics at university, Hairer moved into mathematics. The realisation that ideas in theoretical physics can be overturned and swiftly consigned to the dustbin did not appeal. “I wouldn’t really want to put my name to a result that could be superseded by something else three years later,” he said. “In mathematics, if you obtain a result then that is it. It’s the universality of mathematics, you discover absolute truths.”

Hairer’s expertise lies in stochastic partial differential equations, a branch of mathematics that describes how randomness throws disorder into processes such as the movement of wind in a wind tunnel or the creeping boundary of a water droplet landing on a tissue. When the randomness is strong enough, solutions to the equations get out of control. “In some cases, the solutions fluctuate so wildly that it is not even clear what the equation meant in the first place,” he said.

With the invention of regularity structures, Hairer showed how the infinitely jagged noise that threw his equations into chaos could be reframed and tamed.

One common strategy for thinking about this is to suggest that what we used to call the whole universe is just a small part of everything there is, and that we live in a kind of bubble universe, a small region of something much larger

Newton realized there had to be some force holding the moon in its orbit around the earth, to keep it from wandering off, and he knew also there was a force that was pulling the apple down to the earth. And so what suddenly struck him was that those could be one and the same thing, the same force

That was a physical discovery, a physical discovery of momentous importance, as important as anything you could ever imagine because it knit together the terrestrial realm and the celestial realm into one common physical picture. It was also a philosophical discovery in the sense that philosophy is interested in the fundamental natures of things.

There are other ideas, for instance that maybe there might be special sorts of laws, or special sorts of explanatory principles, that would apply uniquely to the initial state of the universe.

The basic philosophical question, going back to Plato, is "What is x?" What is virtue? What is justice? What is matter? What is time? You can ask that about dark energy - what is it? And it's a perfectly good question.

right now there are just way too many freely adjustable parameters in physics. Everybody agrees about that. There seem to be many things we call constants of nature that you could imagine setting at different values, and most physicists think there shouldn't be that many, that many of them are related to one another. Physicists think that at the end of the day there should be one complete equation to describe all physics, because any two physical systems interact and physics has to tell them what to do. And physicists generally like to have only a few constants, or parameters of nature. This is what Einstein meant when he famously said he wanted to understand what kind of choices God had --using his metaphor-- how free his choices were in creating the universe, which is just asking how many freely adjustable parameters there are. Physicists tend to prefer theories that reduce that number