Following curiosity into hard math

The last post in this series is the least practical one.

I have a strong interest in advanced mathematics and no credentials in it. The Riemann Hypothesis is one of the most famous unsolved problems there is. It concerns a pattern in how the prime numbers are spread out. People have been working on it for more than 160 years.

What I did

Over a long series of conversations, I explored one way of approaching the problem with Claude. The approach comes from the branch of mathematics that studies operators, which is the same toolkit that quantum physics is built on.

Let me be plain about the result: I did not solve it. Nobody should read this and think otherwise.

So why do it

Because I could finally ask.

Before this, if I got stuck on page three of a mathematics paper, I stayed stuck. There was nobody to ask what a symbol meant, or why a step followed from the one before it, or whether my idea was new or a well-known dead end.

Now there is. I can ask the basic question, and then the next one, and then the next. I can propose something and be told where it breaks. That is what a patient teacher does, and most adults do not have one.

What I take from this

Learning for its own sake is a good enough reason to use these tools.

River wrote a comic about getting the physics of the very big and the very small to agree, so hard questions run in the family. I wrote about that in A father-son comic book about physics.

Where it falls short

This is where I would be most careful. An AI can make a mathematical argument sound better than it is. It can be agreeable when it should be skeptical. An idea that feels like a breakthrough after midnight should be treated as a guess until someone qualified has checked it.

So ask it to find the flaw, not to confirm the idea. And enjoy the learning for what it is.

Try it

Pick the subject you always wished you understood. Ask the first question you were too embarrassed to ask in school.

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Part of the series 27 ways I actually use AI. Claude drafted this post from the record of our work together.