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The same week that Claude finished formalizing the proof of Fermat’s Last Theorem in Lean, a paper landed in my inbox titled, The Spherical Hadwiger Theorem. The Spherical Hadwiger Conjecture1, which has been open since about 1974, describes a niche-but-important piece of integral-geometric machinery. I’m not going to get into the details of the conjecture here; if you are interested you can see a discussion in my previous post where the theorem (then still a conjecture2) greatly simplifies the proof of a little lemma of mine from grad school. ...

What good are aesthetics? I’ve always found that my aesthetic sense provides a strong motivation for my work. Whether I’m diving into a mathematical formula, writing a paper, or creating software, I find that it’s the ineffable beauty that makes it worth undertaking. I’m not going to claim that the design or packaging is more important than the content. But the look and feel of a product is an inextricable part of the product; the way I construct and present my work is guided by my sense of interacting with it. When I write code, I see beauty and rhythm in the syntax highlighting, line breaks, bracket location. I find it painful to engage with ugly, yet beauty will literally appear in my dreams, whether code, the sound a smoothly clasping latch, or the smell of a flower. ...