Azimuth

As part of their big theorem dump, an AI company recently emitted a proof of the ‘quasi-Riemann hypothesis’.

I spend a fair amount of time thinking about the climate crisis and how it’s part of a larger collapse of ecosystems, like how insect biomass in Germany has declined by 75% in the last quarter century, how large predatory fish biomass declined by 90% in t…

These seven equations between binomial coefficients are ‘coincidences’: they aren’t among the four known infinite families.

I’ve been thinking about the exceptional Lie algebra E6, as a spinoff of my project on E7, so I want to get a good mental picture of the E6 root polytope.

As we descend from the base of Earth’s crust through the mantle, the rock does not remain unchanged.

It’s long been a mystery why there are 3 generations of quarks and leptons: three sets of particles, apparently identical except for how they interact with the Higgs boson.

I don’t usually talk about particle physics here.

Maxwell’s equations are invariant under Lorentz transformations.

Paul Schwahn and I have come out with a new paper about octonions and the Standard Model: • The Standard Model gauge group from the exceptional Jordan algebra It builds on things I’ve discussed here, but it goes further.

I’m not completely happy with this interview with Micah Zarin.

The sum of the reciprocals of the primes diverges, but very slowly.

I recently showed you that if you take the regular icosahedron: considered in a coordinate system based on the golden ratio, and then replace √5 by -√5 in all your formulas, you get the great icosahedron: But this fact isn’t an isolated one-off!

I never knew what was so great about the ‘great icosahedron’.

This post starts with the the slides of an elementary talk I gave at Sloans Bar and Grill, in Glasgow, as part of a wonderful series called A Pint of Science.

In 2025, researchers studied a quasicrystal forged in a hypervelocity asteroid collision 600 million years ago—and found that it contains ‘phasons’!

I love quasicrystals—like crystals, but with patterns that never repeat, like Penrose tiles.

I recently asked people on Mastodon “What’s the most surprising fact you’ve learned in the last couple of weeks?”

In the last episode of my column in Notices of the American Mathematical Society, we looked at a particle moving in an attractive central force whose strength is proportional to the inverse cube of the distance from the origin.

We have left the Holocene and entered a new epoch, the Anthropocene, in which the biosphere is rapidly changing due to human activities.

Returning from a trip to New Mexico to explore some Puebloan ruins, I picked up this beautiful chunk of labradorite in the town of Quartzsite.

I’m only now learning about ‘vector meson dominance’—a big idea put forth by Sakurai and others around 1960.

I’m giving a talk online tomorrow at the 2026 Spring Southeastern Sectional Meeting of the American Mathematical Society, in the Special Session on Non-Associative Rings and Algebras.

This time I’m talking about pions: Pions were a revolutionary discovery in the 1930s—part of the first wave of the ‘particle zoo’—but I’m explaining them as a way to work toward the math and physics concepts needed for the Standard Model.