Thinking like a Mathematician: The Beauty of Stuckness

The Math with Bad Drawings blog is excellent overall, but I encourage my students to read this article in particular.

Andrew Wiles proved Fermat’s Last Theorem. This theorem said that if \(a, b, c, d\) are all positive integers and \(a^d + b^d = c^d\), then \(d \le 3\). That is, there are solutions for \(a^1 + b^1 = c^1\) and \(a^2 + b^2 = c^2\), but no solutions for any higher power.

This theorem went unproven for a long time. Mathematicians suspected it was true, and Fermat (who created the conjecture) claimed to have a proof. But Wiles’s proof went thousands of pages, and it’s now considered impossible that Fermat had a valid proof.

Wiles’s point in this article is that what makes a mathematician different is that they see frustrations and walls as challenges, not as reasons to give up. I hope all of my students can come to understand that.


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