When you start thinking deeply about a mathematics problem you may enter the "zone", a period of intense focus where you think solely about the problem and potential solutions, and more importantly block out all other thoughts and even lose track of time. Mathematicians don't own the zone, actors, musicians, athletes and many others have their own version of the zone. But for math, when working on an open problem, you have no idea how difficult a solution may be, or if a solution exists at all. Most of the time you will fail (if not you need to try harder problems). Failure is not wasted time. You may find a counterexample, a partial solution and always you will come out with a better understanding of the problem. Then days, months or years later, some new proof idea comes from a paper, a talk or just the back of your head, and back in the zone you go. And when you do succeed you get a feeling not unlike scoring a goal in a soccer game. You should see my proof dance.

With AI generated and assisted proofs, we may think of outsourcing the zone to ChatGPT and Claude. We may prove more and stronger theorems, but you'll understand the results just a little bit less and mathematics will become a little less fun.�

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Try one of the fancier alternatives to Copy�File.

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