Recently, there has been a lot of discussion about AI solving open problems in mathematics. With the recent advances in mathematical reasoning by AI systems, some mathematicians have raised concerns about the future of mathematical research and the changing role of human mathematicians.

I understand these concerns, but I think we should look at the situation differently. The purpose of mathematical research is not simply to keep mathematicians occupied with unsolved problems, but to advance our mathematical knowledge and understanding. If AI can help us achieve this, why should we consider it a problem?

Solving problems versus understanding mathematics

There is an important distinction between solving a mathematical problem and understanding the mathematics behind its solution.

Suppose an AI system produces a correct proof of a conjecture that has remained open for decades. The problem is now solved, but this does not necessarily mean that we understand the proof or the mathematical ideas involved.

We can still investigate why the proof works, whether it can be simplified, whether the methods can be generalized, and what other mathematical results follow from it. We could also try to find another proof.

In fact, I think understanding AI-generated mathematical results could become an interesting research direction in itself.

Of course, we must first verify that the proofs are correct. AI systems are still capable of making mistakes, and mathematical rigor should not be compromised.

Are we going to run out of problems?

Mathematics is infinite in scope. There is no reason to believe that we will eventually exhaust all interesting mathematical questions.

Throughout history, new mathematical theories have introduced new concepts and consequently new questions.

Even if AI is capable of solving problems much faster than humans, we might find ourselves exploring mathematical structures that were previously beyond our reach.

Perhaps AI will also help us formulate new questions that we would otherwise never have considered.

An opportunity for independent research

As someone who conducts mathematical research independently alongside my regular job, I find these developments particularly exciting.

AI provides an opportunity to explore unfamiliar mathematical subjects, examine possible approaches to problems, and learn concepts that might otherwise require considerable time and effort.

This does not eliminate the need for independent mathematical thinking. On the contrary, being able to critically examine the results is essential.

I don't see AI as something I need to compete against. I see it as a tool that could help me become a better mathematician.

Ultimately, I think we should focus less on whether AI will outperform or replace mathematicians, and more on what we can learn and discover with its help.

I would be particularly interested in discussing these questions with other mathematicians, especially those who are exploring the use of AI in mathematical research. How can we extract new mathematical insights from AI-generated proofs? Can understanding these proofs lead to new methods, theories, or even entirely new research problems?

After all, humans developed AI in the first place, and that turned out to be a remarkable achievement. Who knows what we might develop next by standing on the shoulders of AI?