John C. Baez's Blog

Neutrinos and Gold

I have a new job here in Scotland: I’m the Maxwell Fellow for Public Engagement. As part of that job I’m starting up a series of videos where I explain math and physics and also interview people here at the University.

Right now I’m calling it Edinburgh Explorations, and here is the first one:

I start by pretending that I’ll embrace controversy, parodying some things I’ve seen on physics YouTube. But in fact that’s the opposite of what I want!

There’s a lot of great math and science out there...

Negative Mass

I’ve been trying to lose weight, so I’ve been studying the physics of negative mass.

Basically it doesn’t exist. But physicists are have run into a serious problem. They think they can use astronomical measurements to put upper bounds on the total mass of all 3 kinds of neutrinos. But when they do this, the upper bound tends to come out negative!

This doesn’t really make sense. In fact, if you look at the details, you’ll see it’s the result of extrapolating an approximate formula beyond it...

Categories for Public Health Modeling

How, exactly, can category theory help modeling in public health? I wrote a paper about this with two people who helped run Canada’s COVID modeling, together with a software engineer and a mathematician at the Topos Institute:

• John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel D. Osgood and Eric Redekopp, A categorical framework for modeling with stock and flow diagrams, in Mathematics of Public Health: Mathematical Modelling from the Next Generation, eds. Jummy David and Jianhong Wu, Spring...

Is Category Theory Being Co-opted?

Is category theory being co-opted? These authors think so:

• Esteban Montero and Brandon Baylor, Category theory is being co-opted, Holon Substack, 7 September 2025.

Category theory offers a powerful new way of viewing the world… if we embrace its lessons and are willing to think in brand new ways. But what are the chances of that? It could easily become just another way for the rich and powerful to get more rich and powerful while the world burns. Applied category theory is already heavi...

Polycyclic Aromatic Hydrocarbons

In 2004, a team of scientists discovered hydrocarbons called anthracene and pyrene in an amazing structure called the Red Rectangle!

Here two stars 2300 light years from us are spinning around each other while pumping out a huge torus of icy dust grains and hydrocarbon molecules. It’s not really shaped like a rectangle or X—it just looks that way from here. The whole scene is about one third of a light year across.

This was first time such complex molecules had been found in space:

• Uma P. Vi...

Mariam Abu Dagga

Today I gave $10,000 to Doctors Without Borders, since they’re doing a lot of good work in Gaza. I made this gift in memory of Mariam Abu Dagga, a freelance photographer who was killed in the Nasser Hospital in the Gaza Strip on August 25th this year.

After the Israeli air force bombed this hospital, Mariam abu Dagga and other journalists rushed in to check on the well-being of their colleague, Reuters journalist Hussam al-Masri. He had fact been killed. In a ‘double tap’ attack, the Israe...

Rupert’s Property

You can cut a hole in a cube that’s big enough to slide an identical cube through that hole! Think about that for a minute—it’s kind of weird.

Amazingly, nobody could prove any convex polyhedron doesn’t have this property! It’s called ‘Rupert’s property’.

Until this week.

This week Steininger and Yurkevich proved there is a convex polyhedron that you can’t cut a hole in big enough to slide the entire polyhedron through the hole. It has 90 vertices, and apparently 240 edges and 152 faces...

Giant Molecular Clouds

This image shows a filament of cosmic dust over ten light years long! It’s part of a giant cloud of cold gas and dust that’s starting to collapse under its own gravity to form stars. Newborn stars are hidden inside. The cosmic dust grains here are so cold that observations at millimeter wavelengths were needed to detect their faint glow, shown as orange in this false-color image.

Giant molecular clouds like this range from 15 to 600 light-years across. And they’re very dense… for outer spac...

The Hayashi Track

When a star first forms, it is powered not by nuclear fusion but simply by gravity. It shrinks, which causes a release of gravitational energy. This tends to heat it, which slows its shrinking. But it releases energy in the form of light, which tends to cool it down. Then it can keep shrinking. So you need math to figure out exactly what happens.

In 1961, Chushiro Hayashi figured it out. Stars between one tenth and twice the mass of the Sun begin life by shrinking while staying at the s...

4-Dimensional Cross-Polytope

When bad news gets me down, I often get insomnia. I wake up in the middle of the night, start thinking about how we’re all doomed, and can’t easily stop. To break out of these doom loops, I do elaborate visualization exercises. They don’t really put me to sleep, they just calm me down. Then later I can fall asleep.

Here’s what I’ve been doing this week. I visualize this shape made of two interpenetrating tetrahedra, called the ‘stella octangula’ or ‘stellated octahedron’. Then I imagi...