This year, a series of LRM, which try to solve a problem step by step instead of spitting the first result that comes to them, they have achieved High scores on the Mathematics exam by American Invitational (AIME), a 5% higher test of the Mathematics students of the US High School.
At the same time, a handful of new hybrid models that combine LLM with some type of fact verification system have also made advances. Emily de Oliveira Santos, mathematics of the University of São Paulo, Brazil, points the Alphaproof of Google Deepmind, a system that combines a LLM with the Deepmind Alphazero game model, as a key milestone. Last year, Alphaproof became the first computer program to match the performance of a silver medalist in the Mathematics International Olympiad, one of the most prestigious mathematical competitions in the world.
And in May, a Deepmind Google Model called Alphaevolve discovered better results than anything that humans had still created for more than 50 non -solving mathematics riddles and several computer problems of the real world.
The increase in progress is clear. “GPT-4 could not make mathematics far beyond the undergraduate level,” says De Oliveira Santos. “I remember trying it at the time of its launch with a problem in the topology, and I could not write more than a few lines without being completely lost.” But when he gave the OPENAI O1 the same problem, an LRM launched in January, nailed it.
Does this mean that such models are ready to become the type of co -author that Darpa expects? Not necessarily, he says: “The problems of the mathematics Olympiad often involve being able to carry out smart tricks, while research problems are much more explorative already have many more, many more mobile pieces.” Success in one type of problem solving may not move to another.
Others agree. Martin Bridson, a mathematician of the University of Oxford, believes that the result of the mathematics Olympiad is a great achievement. “On the other hand, it doesn’t seem amazing,” he says. “It is not a paradigm shift in the sense that ‘Wow, I thought the machines could never do that.’ I expected the machines to do that.”
This is because although the problems in the Mathematics Olympiad, and similar secondary or undergraduate tests such as Aime, are difficult, there is a pattern for many of them. “We have training fields to train high school children to do them,” says Bridson. “And if you can train a lot of people to do those problems, why shouldn’t you be able to train a machine to do them?”
Sergei Gukov, a mathematician of the California Institute of Technology that trains the teams of the Mathematical Olympiad, points out that the style of question does not change too much among competitions. New problems are established every year, but they can be solved with the same old tricks.
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