AI may be able to do math one day, BUT NOT YET

During the OpenAI boardroom fracas that saw the company’s CEO Sam Altman briefly leave the company, a curious set of media reports reached people’s news feeds. Apparently, engineers at OpenAI were terrified by the mathematical capabilities of the Artificial General Intelligence (AGI) system that OpenAI was working on. It was reported that their AGI could solve math problems that it had never been taught. While there is no way to tell if these are just rumors or even carefully planted stories to change the media narrative of the internal company feud, it does bring up the question of why anyone should be worried or excited about the mathematical abilities of AI.

Maths is crucial
Maths is crucial to tech. In fact, Bhargav Bhatt, Fernholz Joint Professor, Institute for Advanced Study and Princeton University Gehring Professor, University of Michigan, and winner of the 2023 Infosys prize for mathematical sciences, says that every time there is a new scientific or tech breakthrough, the sex appeal of math subjects shoots up. “15 or 20 years ago it was cryptography, and everyone was excited about learning number theory, which forms the basis of cryptography, which in turn forms the basis of any kind of secret communication you want to do online.”

Bhatt says at the moment AI is all the rage, and so linear algebra and some complicated forms of it (like calculus) are gaining popularity.

If AI systems really do end up being proficient in maths, then according to Bhatt it should also be capable of doing anything else that requires thought. “Math teaches you logical thinking and problem solving. And so, if AI can do hard math problems, there’s no reason they should not be able to do other problems in our world that require thought.”

Eng Lim Goh, senior VP of data & AI at Hewlett Packard Enterprise, says it’s useful to think about how large language models (LLM), like the one that powers ChatGPT, actually work to understand AI’s mathematical capabilities. “If you think of what an LLM is, it is essentially trying to predict the next best symbol from all the given symbols before. So, given a sequence of symbols, what’s the next best symbol?”

The problem with this, says Goh, is that in maths getting the ‘next best’ symbol might not be good enough since in maths you are either right or wrong, there is no in-between. “That’s why math is tough for AI. It might have seen enough to solve math at a high school level, or maybe even at the lower undergraduate level, but not beyond that.”

That being said, Goh says AI has been historically very poor when it comes to solving math problems, but it’s gotten a lot better now. “So, this is yet another breakthrough. There are a bunch of breakthroughs needed though.”

Goh says that the excitement generated by the awesome potential capabilities of AI is to be expected but that we should temper it lest we disappoint ourselves. “That’s very typical of excitement. You tend to get excited about its potential. There is usually a gap between potential and delivered capability today.
So, I hope the industry and the community catches up fast enough to meet the expectations of the excitement around AI, or else you may get a disappointing drop.”
What to study

Considering that AI hasn’t cracked the field of mathematics yet, students looking to contribute to tech fields should still master the subject.

To be proficient in the field, Bhatt says the most important thing is to have a solid foundation. “There are some core topics in math that haven’t changed that much, and my advice would be to understand the basics very well. After that, specialisation will be quite easy. But if your foundations are weak, then problems will keep coming up later in life.”

Cultivating a curiosity about how things work is also crucial, says Bhatt. “Having some healthy curiosity about how things work and how things fit together is crucial, and for that it’s important to not specialise too much. If you know only something about one field, it will be hard to know what you actually know. So I would say that as a student it’s more important to have a broad education and be curious about how things work.”

And while respect for authority is usually a good thing, Bhatt says he doesn’t think it’s such a great thing when it comes to learning science. “You really want to understand something and not just take it on faith. If someone senior, like a prize winner, tells you that something is correct, then that’s not so useful. You actually want to know why it is correct and so some healthy scepticism of authority is important.”