My take on recent news on mathematics and AI

After reading so many tweets regarding the recent OpenAI’s work on proving +300 long-standing mathematical problems, I decided to write something on it. The following text is based on my thoughts and I will not try to predict the future, at least most human predictions happen to be false. Well, I hope someone reads this and we can share some ideas, that’s what we humans seems to be good at, otherwise good for the tech companies for scraping some freshly human written text to train their models on.

Overall, what do I think about this news?

I think this is great. It is great in the sense that humans have been able to invent a machine that can outperform them in intellectual tasks such as math and/or science.

However, feeling great is not the only feeling I’ve got. As it seems, the tech companies such as OpenAI and Anthropic are racing to also automate research as well. In this case, then me as a part of the research community have a feeling of a lost value. After all, the things like solving mathematical problems and conducting research have been human expertise for a long time. However, it seems it is not anymore or if we take a mild approach, it is not only for humans anymore.

On the other hand, automated research has encouraged many researchers from different institutions to publish numerous papers, some of which are most probably less valuable to read, but we shouldn’t ignore the fact that LLMs have become capable enough to help in development of good scientific papers.

Finally, my “lost value feeling” might root from the uncertainty. The humans are usually scared of something they don’t know or their previous assumptions are turned out to be false. In this case we don’t know what the future will look like but we should acknowledge the change that’s currently happening.

What I don’t like about these news?

Initially, I said it’s great to have such machines. But, the way it is being practiced is not what I really appreciate. First, OpenAI announces that they have succeeded in solving over 100 mathematical open questions. However, they didn’t publish them initially since they wanted to first consult with a group of mathematicians about how to publish them responsibly. It seems their final decision for publishing responsibly was to dump all of the proofs for over 300 problems on GitHub.

If I speak precisely, this threatens open science. For years, we have explored the ideas, reached out to the community and shared not only the results but also the intuitions, implications or insights of the path we took to reach that point.

What about now? Thousands of agents swarmed to solve the problems. The papers they produce are hard enough to read let alone to read the thought process of the thousands of agents that have been running for over 80 hours.

The other issue is the mass production of proofs. We are supposed to learn from these solutions to get new methods, ideas or even questions. If not only companies like OpenAI but also the people in the research community themselves mass produce papers that nobody has got the time to read, then what’s the point of all of this research?

I understand that research in the classic term is greatly being shifted, and I can see the effects, but without defining new values with an updated agenda we risk the beautiful structure of scientific practice we have developed so far.

What type of problems do these models (can) solve?

What I am about to say is clearly obvious, but I’m saying it anyway! They’re clearly focused on solving problems from fields like mathematics, theoretical physics and computer science. The similarity of all of these fields is that you can get them done inside a computer. Other scientific fields that require special laboratory setups seem to be out of reach for these models (maybe for now!). It is unclear that if these LLMs are incorporated into these fields they would produce good results.

However, I’m really supportive of those who can integrate the knowledge of LLMs to solve problems such as cancer that actually threaten human lives.

It is also interesting for me to hear mathematicians’ opinions on how these models actually approach proving the theorems. Are they brute-forcing their way out or do they develop really novel insights or methods to solve them? I think it should be very different than humans.

I have also experienced in many cases that I use LLMs for my course material to prove a theorem, they clearly know the final answer and construct the proof steps in a way to reach to the final answer. The steps followed are clearly logical, but the approach is not the way a human mathematician might attempt to solve.

Conclusion

Well among wonders and despair, I think we need serious adjustments to scientific practices. The era of LLMs is not much different from other great technological advances we have had throughout human history. There were always people who thought this technology would have very deep implications (deeper than what actually happened) or some went against it and tried to stop it. But at last it turned out that the future human usually experiences is much smoother than the future he predicts.

Stopping progress is not the way to go. We should definitely find good ways how we can interact with the artificially intelligent systems to find solutions for our long standing problems, and at last, the most important thing in my opinion is the re-definition of the values.

The current values we have are seriously incompatible with the recent advancements. This does not necessarily mean AI is replacing humans, rather we are experiencing a shift of paradigm where we need to find a new set of values and find proper practices for that.