Dec 18, 2012 Expository paper on set theory done categorically. The Modularity Theorem as a Bijection of Sets Apr 19, 2024 Bruce Bartlett floats a version of the Modularity Theorem for elliptic curves ...

Back to modal HoTT. If what was considered last time were all, one would wonder what the fuss was about. Now, there’s much that needs to be said about type dependency, types as propositions, sets, ...

I’ve been blogging a bit about medieval math, physics and astronomy over on Azimuth. I’ve been writing about medieval attempts to improve Aristotle’s theory that velocity is proportional to force, ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

Example: suppose we have a data structure representing an abstract address. An address is, alternatively, an email address or a postal address like in the previous example. We can try to extract a ...

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...

Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively. If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him ...

Whether we grow up to become category theorists or applied mathematicians, one thing that I suspect unites us all is that we were once enchanted by prime numbers. It comes as no surprise then that a ...

It’s an underappreciated fact that the interior of every simplex Δ n \Delta^n is a real vector space in a natural way. For instance, here’s the 2-simplex with twelve of its 1-dimensional linear ...

A note to those arriving from the article in the Chronicle of Higher Education: my opinion may not have been accurately represented in that article. Please read my whole post and judge for yourself.

The second fact is perhaps not very well known. It may even be hard to understand what it means. Though the octonions are nonassociative, for any nonzero octonion g g the map ...

Faster-than-light neutrinos? Boring… let’s see something really revolutionary. Edward Nelson, a math professor at Princeton, is writing a book called Elements in which he claims to prove the ...