What Do People Misunderstand About Being A Mathematician?

If you're not trained as a pure mathematician, some of the questions we consider might seem kind of out there. We aim to find the truth – questions we can answer with no possibility of exceptions.

In some cases, we work very hard to prove theorems where the evidence towards one side is already overwhelming. Some ask, “Why bother trying to prove something when the first thousand examples fit the bill?” “Why explore into the realms that may never coincide with human experience?”

A few years ago, I would have said the answer is to search for beauty and truth. Make no mistake, with that alone, we've come to discoveries as influential as the internet. But now we're in a post-ChatGPT world, and my justification has changed.

As everyone knows, large language models, ChatGPT, DeepSeek, Perplexity AI, Google Gemini, these entities make mistakes.

The way pure mathematicians value attention to detail and the incessant need to prove the claims they make, is exactly what we need when teaching these models how to check their work.

It’s not just about improving the models, it’s developing new kinds of computer science, new kinds of AI.

Let's say you ask a model a question in a very niche field. There may only be 5 or 6 papers on the subject, so the model can very quickly find them and provide an answer.

We used to view these niche problems as the hardest, but now with AI they are seeming more simple to solve.

Yet, for AI, some of the hardest problems are where the literature is crazy saturated, so the models don’t know where to go.

They’re stuck in a maze because there’s so much information out there about general topics, so knowing where to find the truth is much more difficult.

When you understand that, hallucination for seemingly obvious truths makes more sense.