Of Particular Significance

Tag: Math

[No AI was used in composing this blog post.]

I’ve been trying to get back to the blog recently. But every time I plan to write a blog post, something happens that requires my attention and adds to the list of items I should be writing about.

I’ve decided that the best I can do, for now, is to summarize some of the key stories that have been on my radar. The overarching news, aside from the 2026 physics Nobel Prize, is what you’ve heard: artificial intelligence (AI) is transforming mathematics and high-energy theoretical physics, no question. That said, what is reported in the media about this is usually wrong in key details, and almost always wildly overstates what’s been accomplished. Nevertheless, the advances in AI models in the last couple of months are historic and transformative, and there is every reason to expect this to accelerate. For people like me, 2027 will surely be very different from autumn 2026, which in turn barely resembles spring 2026.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON October 30, 2026

Kepler’s third law is so simple to state that (as shown last time) it is something that any grade school kid, armed with Copernicus’s data and a calculator, can verify. Yet it was 75 years from Copernicus’s publication til Kepler discovered this formula! Why did it take Kepler until 1618, nearly 50 years of age, to recognize such a simple relationship? Were people just dumber than high-school students back then?

Here’s a clue. We take all sorts of math for granted that didn’t exist four hundred years ago, and calculations which take an instant now could easily take an hour or even all day. (Imagine computing the cube root of 4972.64 to part-per-million accuracy by hand.) In particular, one thing that did not exist in Copernicus’ time, and not even through much of Kepler’s, was the modern notion of a logarithm.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON April 7, 2022

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