John Baez's Stuff

John Baez’s Stuff

I'm the Maxwell Fellow in Public Engagement at the University of Edinburgh and an emeritus professor in the mathematics department at U. C. Riverside. I'm a mathematical physicist. I use category theory to study networks and help researchers use them in scientific software, such as quickly adaptable models of infectious disease. I explain math and physics on my blog, Mastodon, and my column in the Notices of the American Mathematical Society.

What’s New?

I'm giving a talk called Hidden Patterns in the Standard Model at the Higgs Colloquium on Friday October 22nd.

One famous physics popularizer has claimed that while the Standard Model is "the most successful physical theory ever proposed, it is also one of the ugliest". Another possibility is that the Standard Model is more beautiful than we realize, and holds clues we do not yet understand. Here we review some attempts to find hidden patterns in the Standard Model, going back to the work of Georgi, Glashow, Pati and Salam but leading up to recent ideas connected to the octonions.

What's on This Site

This Week's Finds in Mathematical Physics (my column)

Fun Stuff (expository writings and other diversions)

Seminar (tons of course notes)

Serious Stuff (my actual research)

Talks (transparencies of my talks, info on forthcoming talks)

Diary (random thoughts)

Also try my blogging here:

Azimuth The n-Category Café Mathstodon Visual Insight

For common questions about physics, you can't beat this:

Frequently Asked Questions in Physics

I don't maintain this Physics FAQ - Don Koks does, so please send any comments about it to him, not me!

If reading my stuff makes you want to ask questions, take a look at this.

Highlights

Try my free book, What is Entropy?

I've started a book on the mathematics of tuning systems, and you can see a draft. If that's too intense, try my talk on this subject.

I'm also turning my old columns into free books. You can get 3 here:

This Week's Finds in Mathematical Physics: Weeks 1-50, Weeks 51-100, and Weeks 101-151.

If you think fundamental physics is stuck, read my article on the joy of condensed matter physics.

Can we actually remove carbon dioxide from the air? Yes! Can we remove enough to make a difference? Yes! But what are the best ways, and how much can they accomplish? I explained that in my article in Nautilus, an online science magazine.

Read my pop article on algebraic geometry and geometric quantization: The math that takes Newton into the quantum world. And for more of the technical details, read this.

Check out this interview: A quest for beauty and clear thinking. Also check out my talk on Unsolved mysteries of fundamental physics, which is now available on video.

And while you're at it: take a copy of my diary from 2003 to July 2020!

Together with three students at Applied Category Theory 2018, I wrote a paper on biochemical coupling through emergent conservation laws. Try our blog posts about this!

Learn about quantum mechanics and the dodecahedron:

Then read about the glories of the 600-cell (Part 1, Part 2, Part 3), which is a 4-dimensional analogue of the icosahedron:

These posts lead up to a grand conclusion: the Kepler problem and the 600-cell!

And while you're at it, check out my new paper on the icosahedron and E8, and learn about excitonium, Wigner crystals, the universal snake-like continuum, and the connection between braids, entropy and the golden ratio!

Check out my introduction to Kolmogorov complexity and related ideas:

Try my articles on 'struggles with the continuum' — that is, problems with infinities in physics arising from our assumption that spacetime is a continuum:

Part 1 - Problems with infinity. Point particles interacting gravitationally.

Part 2 - The quantum mechanics of nonrelativistic charged point particles.

Part 3 - The relativistic electrodynamics of point particles.

Part 4 - The ultraviolet catastrophe, and quantum field theory.

Part 5 - Quantum field theory: renormalization.

Part 6 - Quantum field theory: summing over Feynman diagrams.

Part 7 - General relativity: the singularity theorems.

Part 8 - General relativity: the cosmic censorship hypothesis. Conclusion.

Read about 'topological crystals':

Part 1 - the basic idea.

Part 2 - the maximal abelian cover of a graph.

Part 3 - embedding topological crystals.

Part 4 - examples of topological crystals.

Take a road trip to infinity:

Part 1: up to εo.

Part 2: up to the Feferman–Schütte ordinal.

Part 3: up to the small Veblen ordinal.

There's a mysterious relation between the discriminant of the icosahedral group:

and the involutes of the cubic parabola:

Learn a bit about quantum gravity, n-categories, crackpots and climate change in my interview on Physics Forums.

Anita Chowdry and I gave a joint lecture on The Harmonograph at the University of Waterloo. You can watch a video of it!

Read the tale of a doomed galaxy:

or if you prefer, read about the mysteries of the inverse cube force law: