After Google Deepmind defeated people in everything, from Game Go to strategy board games ,
Now claims to be on the verge of beating the world's best students when solving math tasks.

The London-based Machine-Learning company announced on July 25 that his artificial intelligence (KI) systems have solved four of the six tasks that were given to the students at the International Mathematics Olympics (IMO) 2024 in Bath, Great Britain. The AI ​​provided rigorous, gradual evidence, which were evaluated by two top mathematics and achieved a score of 28/42-only one point from the area of ​​gold medals.

"It is obviously a very important progress," says Joseph Myers, a mathematician from Cambridge, Great Britain, who, together with Fields medalist Tim Gowers, checked the solutions and helped select the original problems for this year.

Deepmind and other companies are in the race to ultimately provide evidence of machines, the essential solve research questions in mathematics . The problems with the IMO, the world's leading competition for young mathematicians, have become a yardstick for progress in the direction of this goal and are seen as a "big challenge" for machine learning, according to the company.

"This is the first time that a AI system was able to achieve services at medal level," said Pushmeet Kohli, Vice President for AI in Science at Deepmind, in a press consultation. "This is an important milestone on the way to building up progressive evidence," said Kohli.

extension

only a few months ago, in January, the deepmind system Alphageometry Services at medals level When solving a type of IMO problems, namely those in the Euclidean geometry. The first AI that works at a gold medal level for the overall test-including questions in algebra, combinatorics and number theory, which are generally considered more demanding than geometry-is entitled to obtain a price of $ 5 million, the AI ​​math Olympiad Prize (AIMO). (The price has strict criteria such as the disclosure of the source code and the work with limited computing power, which means that the current efforts of Deepmind would not qualify.)

In their latest attempt, researchers used Alphageometry2 to solve the geometry problem in less than 20 seconds; The AI ​​is an improved and faster version of your record system, says the deepmind computer specialist Thang Luong.

For the other types of questions, the team developed a completely new system called Alphaproof. Alphaproof solved two algebra problems in the competition and one in number theory, for which it took three days. (The participants of the actual IMO have two sessions of 4.5 hours each.) It was unable to solve the two problems in the combination, another area of ​​mathematics.


close-up of a gold medal, won in the 63rd international math Olympiad by a Romanian participant.

researchers have achieved mixed results when they answer mathematical questions with voice models - the type of system that drive chatbots like chatt. Sometimes the models give the correct answer, but cannot explain their reasoning rationally, and sometimes

Only last week, a team of software companies Numina and Huggingface used a voice model to win an intermediate amio 'progress price' based on simplified versions of IMO problems. The companies made their entire systems open source and made it available for downloading other researchers. But the winners said Nature that language models alone would probably not be enough to solve difficult problems.

only class

alphaproof combines a voice model with the technology of reinforcing learning, which the “Alphazero” engine for attack games such as Go as well as some Specific Mathematical Problems . With increasing learning, a neural network learns through experiments and errors. This works well if its answers can be evaluated using an objective scale. For this purpose, Alphaproof was trained to read and write evidence in a formal language called Lean, which is used in the 'proof assistant' software package of the same name that is popular with mathematicians. For this, AlphaProof tested whether his expenses were correct by doing them in the lean package, which helped to fill out some of the steps in the code.

The training of a voice model requires massive amounts of data, but only a few mathematical evidence were available in Lean. In order to overcome this problem, the team developed an additional network that tried to translate an existing recording of one million problems that were written in natural language, but without translating solutions written in Lean, says Thomas Hubert, a deepmind machine learner researcher who conducted the development of Alphaproof with. "We can learn to prove our approach, even if we have not originally trained on human -written evidence?" (The company was similar to the GO, where his AI learned to play the game by playing against herself, instead of the way people do.)

magical key

Many of the lean translations made no sense, but enough were good enough to bring Alphaproof to the point where it could start its increasing learning cycles. The results were much better than expected, said Gowers at the press consultation. "Many problems with the IMO have this property of the magical key. The problem first looks difficult until you find a magical key that opens it," said Gowers, who works at the Collège de France in Paris.

In some cases, Alphaproof seemed to be able to take this additional step of creativity by giving it a correct step from an infinitely large possible solution. But further analysis is required to determine whether the answers were less surprising than they looked, added Gowers. A similar discourse arose after the surprising 'Zug 37' , the Deepminds Alphago-Bot at his Famous victory in 2016 about the world's best human go player -a turning point for the Ki.

It remains to be seen whether the techniques can be perfected to work at a level of research in mathematics, said Myers at the press review. "Can it expand to other types of mathematics where no millions of problems may be trained?"

"We have reached the point where you can not only prove open research problems, but also problems that are very challenging for the very best young mathematicians in the world," said Deepmind computer specialist David Silver, who was the leading researcher in the development of Alphago in the mid-2010.