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Emilio Ergueta

Hungarian Student Wins International Philosophy Olympiad - Hungary Today - 0 views

hungarytoday.hu/...onal-philosophy-olympiad-72368

hungary international philosophy olympiad education

shared by Emilio Ergueta on 05 Jun 15 - No Cached
  • 17-year-old Hungarian student Iván Merker has won a shared gold medal at the 23rd International Philosophy Olympiad held in the Estonian city of Tartu, Henrik Farkas, leader of the Hungarian team and member of the Hungarian Society of Philosophy has disclosed.
  • Each year, two Hungarian students are invited to the International Philosophy Olympiad who have already proven their knowledge in the subject as finalists of a national competition for secondary school students and at the Hungarian qualifiers for the international event.
  • The jury evaluated the compositions based on five considerations: understanding of the subject, coherence, the ability to argue, originality and proficiency in the area.
Javier E

AlphaProof, a New A.I. from Google DeepMind, Scores Big at the International Math Olymp... - 0 views

www.nytimes.com/...-math-alphaproof-deepmind.html

math AI methods strategy research knowledge language

shared by Javier E on 25 Jul 24 - No Cached
  • Last week the DeepMind researchers got out the gong again to celebrate what Alex Davies, a lead of Google DeepMind’s mathematics initiative, described as a “massive breakthrough” in mathematical reasoning by an A.I. system.
  • A pair of Google DeepMind models tried their luck with the problem set in the 2024 International Mathematical Olympiad, or I.M.O., held from July 11 to July 22 about 100 miles west of London at the University of Bath.
  • The event is said to be the premier math competition for the world’s “brightest mathletes,” according to a promotional post on social media.
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  • 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
  • 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.
  • 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.
  • 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.
  • 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.
Javier E

A Billionaire Mathematician's Life of Ferocious Curiosity - The New York Times - 0 views

www.nytimes.com/...fe-of-ferocious-curiosity.html

math creativity proof role model

shared by Javier E on 26 Jul 15 - No Cached
  • James H. Simons likes to play against type. He is a billionaire star of mathematics and private investment who often wins praise for his financial gifts to scientific research and programs to get children hooked on math.But in his Manhattan office, high atop a Fifth Avenue building in the Flatiron district, he’s quick to tell of his career failings.He was forgetful. He was demoted. He found out the hard way that he was terrible at programming computers. “I’d keep forgetting the notation,” Dr. Simons said. “I couldn’t write programs to save my life.”After that, he was fired.His message is clearly aimed at young people: If I can do it, so can you.
  • Down one floor from his office complex is Math for America, a foundation he set up to promote math teaching in public schools. Nearby, on Madison Square Park, is the National Museum of Mathematics, or MoMath, an educational center he helped finance. It opened in 2012 and has had a quarter million visitors.
  • Dr. Simons received his doctorate at 23; advanced code breaking for the National Security Agency at 26; led a university math department at 30; won geometry’s top prize at 37; founded Renaissance Technologies, one of the world’s most successful hedge funds, at 44; and began setting up charitable foundations at 56.
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  • With a fortune estimated at $12.5 billion, Dr. Simons now runs a tidy universe of science endeavors, financing not only math teachers but hundreds of the world’s best investigators, even as Washington has reduced its support for scientific research. His favorite topics include gene puzzles, the origins of life, the roots of autism, math and computer frontiers, basic physics and the structure of the early cosmos.
  • In time, his novel approach helped change how the investment world looks at financial markets. The man who “couldn’t write programs” hired a lot of programmers, as well as physicists, cryptographers, computational linguists, and, oh yes, mathematicians. Wall Street experience was frowned on. A flair for science was prized. The techies gathered financial data and used complex formulas to make predictions and trade in global markets.
  • Working closely with his wife, Marilyn, the president of the Simons Foundation and an economist credited with philanthropic savvy, Dr. Simons has pumped more than $1 billion into esoteric projects as well as retail offerings like the World Science Festival and a scientific lecture series at his Fifth Avenue building. Characteristically, it is open to the public.
  • On a wall in Dr. Simons’s office is one of his prides: a framed picture of equations known as Chern-Simons, after a paper he wrote with Shiing-Shen Chern, a prominent geometer. Four decades later, the equations define many esoteric aspects of modern physics, including advanced theories of how invisible fields like those of gravity interact with matter to produce everything from superstrings to black holes.
  • “He’s an individual of enormous talent and accomplishment, yet he’s completely unpretentious,” said Marc Tessier-Lavigne, a neuroscientist who is the president of Rockefeller University. “He manages to blend all these admirable qualities.”
  • Forbes magazine ranks him as the world’s 93rd richest person — ahead of Eric Schmidt of Google and Elon Musk of Tesla Motors, among others — and in 2010, he and his wife were among the first billionaires to sign the Giving Pledge, promising to devote “the great majority” of their wealth to philanthropy.
  • For all his self-deprecations, Dr. Simons does credit himself with a contemplative quality that seems to lie behind many of his accomplishments.“I wasn’t the fastest guy in the world,” Dr. Simons said of his youthful math enthusiasms. “I wouldn’t have done well in an Olympiad or a math contest. But I like to ponder. And pondering things, just sort of thinking about it and thinking about it, turns out to be a pretty good approach.”
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