Abstract:
Remember earlier this month, when mathematicians accused OpenAI of trying to seize the lead and compete for the results of an ultra-difficult mathematical problem, which plunged the company into a public outcry? According to people familiar with the progress of the research, the fact is that OpenAI is very close to solving another mathematical problem in the Millennium Prize problem. The Millennium Prize problem includes a total of seven famous mathematical challenges, and the previously controversial issue of the existence and smoothness of the Navier-Stokes equation is one of them.
The source said that employees within the company expect that the next target, the Hodge conjecture, is expected to be proven in a relatively short period of time. The Hodge Conjecture studies whether certain geometric features of a geometry defined by polynomial equations can always be described by simpler algebraic components. However, it may take longer for OpenAI to announce the proof results. The reason is that the company is studying how to cooperate with the mathematics community to publish the results in an appropriate way to avoid another public relations crisis.
Why is OpenAI interested in these difficult and difficult mathematical problems? After all, solving such problems is expensive: previously proving the results related to the Navier-Stokes equation may have cost millions of dollars. The source said that OpenAI used a variant of the next-generation pre-trained model (codenamed "Doug") to complete this proof.
Some OpenAI researchers believe that after software engineering, mathematics is the next logical area to conquer for large models. The two fields have similar characteristics: both require step-by-step logical reasoning, and most of the results can be automatically verified. Some researchers even judge that the automation changes that have occurred in the field of software engineering in the past year will be repeated in the field of mathematics in the next 6 to 9 months.
In addition, overcoming difficult mathematical problems will also help AI developers promote the automation of machine learning research - machine learning itself involves a lot of mathematics. This type of automation is an important part of their goal of recursive self-improvement (AI independently develops new AI).
Testing the ability of cutting-edge models to solve mathematical problems that have never been proven can also help researchers evaluate the progress level and complex reasoning capabilities of models. If the model can solve difficult problems such as the Navier-Stokes equation and the Hodge conjecture, it may mean that it is also capable of solving equally difficult problems in other fields such as biology and chemistry.
In addition, as long as the results are released without causing strong dissatisfaction among mathematicians, such breakthroughs can also create eye-catching new milestones for OpenAI and serve as publicity chips in the race for general super artificial intelligence, which is naturally beneficial to the company.
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