Tag: mathematics
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The Habit Nobody Wants
What a self-taught miller can tell us about what actually separates successful researchers from everyone else. Nottingham, sometime around 1823. A miller named George Green climbs the stairs of his father’s windmill after a full day’s work, hauling sacks, tending the grindstones, breathing flour dust, and sits down under a candle with a borrowed mathematics…
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Embrace the Suck
“Embrace the suck” is military slang for accepting that some situations are going to be difficult, uncomfortable, and uncertain, and learning to operate effectively anyway. It’s about finding ways to function when conditions are far from ideal, when you don’t have complete information, and when there’s no clear path forward. Mathematical research is full of…
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The Mathematical Sherlock Holmes
“I consider that a man’s brain originally is like a little empty attic, and you have to stock it with such furniture as you choose… It is a mistake to think that that little room has elastic walls and can distend to any extent. Depend upon it there comes a time when for every addition…
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The Mathematical Polyglot
For the second post in the series look here. The most profound mathematical insights often come from connecting ideas across different fields. But here’s the challenge: mathematical communities speak different languages. An algebraist and an analyst might as well be from different countries, despite often studying closely related structures. Think of mathematical fields as linguistic…
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The Art of the Mathematical Cover Song
For the first post in the series look here. In music, we all recognize the difference between Johnny Cash’s haunting cover of “Hurt” and William Shatner’s infamous interpretation of “Lucy in the Sky with Diamonds” (search for it on YouTube if you want the experience). Both are covers of existing songs, but Cash’s version reveals…
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Everything is a Mathematical Remix
You’ve may have heard of Kirby Ferguson’s documentary series “Everything is a Remix,” which argues that all creative work follows a simple pattern: copy, transform, combine. Ferguson shows how this applies to music, film, and technology, but I want to argue that mathematics provides perhaps the purest example of this principle in action. Consider the…
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What a Chess Engine Knows About Taste
A graduate student wrote to me recently, after reading something I’d posted about how the value in our work is migrating from execution toward judgment. He’d been circling the same thought: that the future of pure mathematics may be governed less by the practical pressures that shaped the profession for the last century and more…
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The Disclosure Tax: Why Mathematicians Are Quietly Avoiding “We Used AI”
Journals and professional societies are converging on a norm: disclose your use of AI. In writing, in editing, in computation, in research itself. You can already see it on arXiv, a growing number of papers, often from well-established authors, include a line acknowledging AI assistance somewhere in the acknowledgments or methods. But in practice, the…
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The Formula That Unlocked the Drawer
A few years ago, a graduate student and I got stuck. We were chasing a conjecture we were both convinced was true; the numerical evidence was overwhelming, the kind that doesn’t leave much room for doubt. We’d handled the low-dimensional case cleanly and knocked out a good many of the sub-cases one dimension up. And…
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Where the Difficulty Went
A few weeks ago I had what I thought was a good idea. There’s a problem in harmonic analysis I’d been turning over for a while; the technical details don’t matter much for the story, but the shape of it does. An existing proof in the literature worked but didn’t feel optimal to me, and…