Tag: mathematics

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…

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…

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…

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…

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…

If you’re deciding whether to apply to a math PhD program, figuring out how to position a research agenda, or sitting in a department wondering which way the wind is blowing, the next few years will matter more than you probably think. The field is in the early stages of a bifurcation, and the ladder…

Editorial Note Recently entrepreneur Matt Shumer published “Something Big Is Happening,” a 5,000-word essay comparing the current AI moment to February 2020, right before COVID changed everything. It reached over 80 million people on X and was covered widely. Shumer wrote it for the people in his life who aren’t paying attention to AI, his…