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Since the 1960s, advances in resuscitation had helped to revive thousands of people who might otherwise have died. About 10% or 20% of those people brought with them stories of near-death experiences in which they felt their souls or selves departing from their bodies

According to several international surveys and studies, one in 10 people claims to have had a near-death experience involving cardiac arrest, or a similar experience in circumstances where they may have come close to death. That’s roughly 800 million souls worldwide who may have dipped a toe in the afterlife.

In the 1970s, a small network of cardiologists, psychiatrists, medical sociologists and social psychologists in North America and Europe began investigating whether near-death experiences proved that dying is not the end of being, and that consciousness can exist independently of the brain. The field of near-death studies was born.

in 1975, an American medical student named Raymond Moody published a book called Life After Life.

Meanwhile, new technologies and techniques were helping doctors revive more and more people who, in earlier periods of history, would have almost certainly been permanently deceased.

“We are now at the point where we have both the tools and the means to scientifically answer the age-old question: What happens when we die?” wrote Sam Parnia, an accomplished resuscitation specialist and one of the world’s leading experts on near-death experiences, in 2006. Parnia himself was devising an international study to test whether patients could have conscious awareness even after they were found clinically dead.

Borjigin, together with several colleagues, took the first close look at the record of electrical activity in the brain of Patient One after she was taken off life support. What they discovered – in results reported for the first time last year – was almost entirely unexpected, and has the potential to rewrite our understanding of death.

“I believe what we found is only the tip of a vast iceberg,” Borjigin told me. “What’s still beneath the surface is a full account of how dying actually takes place. Because there’s something happening in there, in the brain, that makes no sense.”

Over the next 30 years, researchers collected thousands of case reports of people who had had near-death experiences

near-death studies was already splitting into several schools of belief, whose tensions continue to this day. One influential camp was made up of spiritualists, some of them evangelical Christians, who were convinced that near-death experiences were genuine sojourns in the land of the dead and divine

Moody was their most important spokesman; he eventually claimed to have had multiple past lives and built a “psychomanteum” in rural Alabama where people could attempt to summon the spirits of the dead by gazing into a dimly lit mirror.

It is no longer unheard of for people to be revived even six hours after being declared clinically dead. In 2011, Japanese doctors reported the case of a young woman who was found in a forest one morning after an overdose stopped her heart the previous night; using advanced technology to circulate blood and oxygen through her body, the doctors were able to revive her more than six hours later, and she was able to walk out of the hospital after three weeks of care

The second, and largest, faction of near-death researchers were the parapsychologists, those interested in phenomena that seemed to undermine the scientific orthodoxy that the mind could not exist independently of the brain. These researchers, who were by and large trained scientists following well established research methods, tended to believe that near-death experiences offered evidence that consciousness could persist after the death of the individua

Their aim was to find ways to test their theories of consciousness empirically, and to turn near-death studies into a legitimate scientific endeavour.

Finally, there emerged the smallest contingent of near-death researchers, who could be labelled the physicalists. These were scientists, many of whom studied the brain, who were committed to a strictly biological account of near-death experiences. Like dreams, the physicalists argued, near-death experiences might reveal psychological truths, but they did so through hallucinatory fictions that emerged from the workings of the body and the brain.

Between 1975, when Moody published Life After Life, and 1984, only 17 articles in the PubMed database of scientific publications mentioned near-death experiences. In the following decade, there were 62. In the most recent 10-year span, there were 221.

Today, there is a widespread sense throughout the community of near-death researchers that we are on the verge of great discoveries

“We really are in a crucial moment where we have to disentangle consciousness from responsiveness, and maybe question every state that we consider unconscious,”

“I think in 50 or 100 years time we will have discovered the entity that is consciousness,” he told me. “It will be taken for granted that it wasn’t produced by the brain, and it doesn’t die when you die.”

it is in large part because of a revolution in our ability to resuscitate people who have suffered cardiac arrest

In a medical setting, “clinical death” is said to occur at the moment the heart stops pumping blood, and the pulse stops. This is widely known as cardiac arrest

Loss of oxygen to the brain and other organs generally follows within seconds or minutes, although the complete cessation of activity in the heart and brain – which is often called “flatlining” or, in the case of the latter, “brain death” – may not occur for many minutes or even hours.

That began to change in 1960, when the combination of mouth-to-mouth ventilation, chest compressions and external defibrillation known as cardiopulmonary resuscitation, or CPR, was formalised. Shortly thereafter, a massive campaign was launched to educate clinicians and the public on CPR’s basic techniques, and soon people were being revived in previously unthinkable, if still modest, numbers.

scientists learned that, even in its acute final stages, death is not a point, but a process. After cardiac arrest, blood and oxygen stop circulating through the body, cells begin to break down, and normal electrical activity in the brain gets disrupted. But the organs don’t fail irreversibly right away, and the brain doesn’t necessarily cease functioning altogether. There is often still the possibility of a return to life. In some cases, cell death can be stopped or significantly slowed, the heart can be restarted, and brain function can be restored. In other words, the process of death can be reversed.

In his book, Moody distilled the reports of 150 people who had had intense, life-altering experiences in the moments surrounding a cardiac arrest. Although the reports varied, he found that they often shared one or more common features or themes. The narrative arc of the most detailed of those reports – departing the body and travelling through a long tunnel, having an out-of-body experience, encountering spirits and a being of light, one’s whole life flashing before one’s eyes, and returning to the body from some outer limit – became so canonical that the art critic Robert Hughes could refer to it years later as “the familiar kitsch of near-death experience”.

In 2019, a British woman named Audrey Schoeman who was caught in a snowstorm spent six hours in cardiac arrest before doctors brought her back to life with no evident brain damage.

That is a key tenet of the parapsychologists’ arguments: if there is consciousness without brain activity, then consciousness must dwell somewhere beyond the brain

Some of the parapsychologists speculate that it is a “non-local” force that pervades the universe, like electromagnetism. This force is received by the brain, but is not generated by it, the way a television receives a broadcast.

In order for this argument to hold, something else has to be true: near-death experiences have to happen during death, after the brain shuts down

To prove this, parapsychologists point to a number of rare but astounding cases known as “veridical” near-death experiences, in which patients seem to report details from the operating room that they might have known only if they had conscious awareness during the time that they were clinically dead.

At the very least, Parnia and his colleagues have written, such phenomena are “inexplicable through current neuroscientific models”. Unfortunately for the parapsychologists, however, none of the reports of post-death awareness holds up to strict scientific scrutiny. “There are many claims of this kind, but in my long decades of research into out-of-body and near-death experiences I never met any convincing evidence that this is true,”

In other cases, there’s not enough evidence to prove that the experiences reported by cardiac arrest survivors happened when their brains were shut down, as opposed to in the period before or after they supposedly “flatlined”. “So far, there is no sufficiently rigorous, convincing empirical evidence that people can observe their surroundings during a near-death experience,”

The parapsychologists tend to push back by arguing that even if each of the cases of veridical near-death experiences leaves room for scientific doubt, surely the accumulation of dozens of these reports must count for something. But that argument can be turned on its head: if there are so many genuine instances of consciousness surviving death, then why should it have so far proven impossible to catch one empirically?

The spiritualists and parapsychologists are right to insist that something deeply weird is happening to people when they die, but they are wrong to assume it is happening in the next life rather than this one. At least, that is the implication of what Jimo Borjigin found when she investigated the case of Patient One.

In the moments after Patient One was taken off oxygen, there was a surge of activity in her dying brain. Areas that had been nearly silent while she was on life support suddenly thrummed with high-frequency electrical signals called gamma waves. In particular, the parts of the brain that scientists consider a “hot zone” for consciousness became dramatically alive. In one section, the signals remained detectable for more than six minutes. In another, they were 11 to 12 times higher than they had been before Patient One’s ventilator was removed.

“As she died, Patient One’s brain was functioning in a kind of hyperdrive,” Borjigin told me. For about two minutes after her oxygen was cut off, there was an intense synchronisation of her brain waves, a state associated with many cognitive functions, including heightened attention and memory. The synchronisation dampened for about 18 seconds, then intensified again for more than four minutes. It faded for a minute, then came back for a third time.

n those same periods of dying, different parts of Patient One’s brain were suddenly in close communication with each other. The most intense connections started immediately after her oxygen stopped, and lasted for nearly four minutes. There was another burst of connectivity more than five minutes and 20 seconds after she was taken off life support. In particular, areas of her brain associated with processing conscious experience – areas that are active when we move through the waking world, and when we have vivid dreams – were communicating with those involved in memory formation. So were parts of the brain associated with empathy. Even as she slipped irre

something that looked astonishingly like life was taking place over several minutes in Patient One’s brain.

Although a few earlier instances of brain waves had been reported in dying human brains, nothing as detailed and complex as what occurred in Patient One had ever been detected.

Given the levels of activity and connectivity in particular regions of her dying brain, Borjigin believes it’s likely that Patient One had a profound near-death experience with many of its major features: out-of-body sensations, visions of light, feelings of joy or serenity, and moral re-evaluations of one’s life. Of course,

“The brain, contrary to everybody’s belief, is actually super active during cardiac arrest,” Borjigin said. Death may be far more alive than we ever thought possible.

“The brain is so resilient, the heart is so resilient, that it takes years of abuse to kill them,” she pointed out. “Why then, without oxygen, can a perfectly healthy person die within 30 minutes, irreversibly?”

Evidence is already emerging that even total brain death may someday be reversible. In 2019, scientists at Yale University harvested the brains of pigs that had been decapitated in a commercial slaughterhouse four hours earlier. Then they perfused the brains for six hours with a special cocktail of drugs and synthetic blood. Astoundingly, some of the cells in the brains began to show metabolic activity again, and some of the synapses even began firing.

The human problem-solvers — 609 high school students from 108 countries — won 58 gold medals, 123 silver and 145 bronze. The A.I. performed at the level of a silver medalist, solving four out of six problems for a total of 28 points. It was the first time that A.I. has achieved a medal-worthy performance on an Olympiad’s problems.

Nonetheless, Dr. Kohli described the result as a “phase transition” — a transformative change — “in the use of A.I. in mathematics and the ability of A.I. systems to do mathematics.”

Dr. Gowers added in an email: “I was definitely impressed.” The lab had discussed its Olympiad ambitions with him a couple of weeks beforehand, so “my expectations were quite high,” he said. “But the program met them, and in one or two instances significantly surpassed them.” The program found the “magic keys” that unlocked the problems, he said.

Haojia Shi, a student from China, ranked No. 1 and was the only competitor to earn a perfect score — 42 points for six problems; each problem is worth seven points for a full solution. The U.S. team won first place with 192 points; China placed second with 190.

The Google system earned its 28 points for fully solving four problems — two in algebra, one in geometry and one in number theory. (It flopped at two combinatorics problems.) The system was allowed unlimited time; for some problems it took up to three days. The students were allotted only 4.5 hours per exam.

“The fact that we’ve reached this threshold, where it’s even possible to tackle these problems at all, is what represents a step-change in the history of mathematics,” he added. “And hopefully it’s not just a step-change in the I.M.O., but also represents the point at which we went from computers only being able to prove very, very simple things toward computers being able to prove things that humans can’t.”

“Mathematics requires this interesting combination of abstract, precise and creative reasoning,” Dr. Davies said. In part, he noted, this repertoire of abilities is what makes math a good litmus test for the ultimate goal: reaching so-called artificial general intelligence, or A.G.I., a system with capabilities ranging from emerging to competent to virtuoso to superhuman

In January, a Google DeepMind system named AlphaGeometry solved a sampling of Olympiad geometry problems at nearly the level of a human gold medalist. “AlphaGeometry 2 has now surpassed the gold medalists in solving I.M.O. problems,” Thang Luong, the principal investigator, said in an email.

Dr. Hubert’s team developed a new model that is comparable but more generalized. Named AlphaProof, it is designed to engage with a broad range of mathematical subjects. All told, AlphaGeometry and AlphaProof made use of a number of different A.I. technologies.

One approach was an informal reasoning system, expressed in natural language. This system leveraged Gemini, Google’s large language model. It used the English corpus of published problems and proofs and the like as training data.

The informal system excels at identifying patterns and suggesting what comes next; it is creative and talks about ideas in an understandable way. Of course, large language models are inclined to make things up — which may (or may not) fly for poetry and definitely not for math. But in this context, the L.L.M. seems to have displayed restraint; it wasn’t immune to hallucination, but the frequency was reduced.

Another approach was a formal reasoning system, based on logic and expressed in code. It used theorem prover and proof-assistant software called Lean, which guarantees that if the system says a proof is correct, then it is indeed correct. “We can exactly check that the proof is correct or not,” Dr. Hubert said. “Every step is guaranteed to be logically sound.”

Another crucial component was a reinforcement learning algorithm in the AlphaGo and AlphaZero lineage. This type of A.I. learns by itself and can scale indefinitely, said Dr. Silver, who is Google DeepMind’s vice-president of reinforcement learning. Since the algorithm doesn’t require a human teacher, it can “learn and keep learning and keep learning until ultimately it can solve the hardest problems that humans can solve,” he said. “And then maybe even one day go beyond those.”

Dr. Hubert added, “The system can rediscover knowledge for itself.” That’s what happened with AlphaZero: It started with zero knowledge, Dr. Hubert said, “and by just playing games, and seeing who wins and who loses, it could rediscover all the knowledge of chess. It took us less than a day to rediscover all the knowledge of chess, and about a week to rediscover all the knowledge of Go. So we thought, Let’s apply this to mathematics.”

Dr. Gowers doesn’t worry — too much — about the long-term consequences. “It is possible to imagine a state of affairs where mathematicians are basically left with nothing to do,” he said. “That would be the case if computers became better, and far faster, at everything that mathematicians currently do.”

“There still seems to be quite a long way to go before computers will be able to do research-level mathematics,” he added. “It’s a fairly safe bet that if Google DeepMind can solve at least some hard I.M.O. problems, then a useful research tool can’t be all that far away.”

A really adept tool might make mathematics accessible to more people, speed up the research process, nudge mathematicians outside the box. Eventually it might even pose novel ideas that resonate.

One of the key themes in "Wise Animals" is the idea that technology is far from neutral. Chatfield argues that the way innovation has progressed was not the only possible path and that we must keep an open mind about the possibilities