214 million years ago an asteroid hit what is now Canada. Now the crater is a ring-shaped reservoir 70 kilometers in diameter: Manicouagan Reservoir. Did this impact cause a mass extinction? The asteroid was 5 kilometers across, while the one that killed the dinosaurs much later … | Continue reading
Can you roll a ball with exactly enough energy to reach the top of a dome, and have it reach the top in a finite amount of time? I’m going to idealize the hell out of this problem so we can easily study it using math. So: no friction, no air resistance… in fact, none […] | Continue reading
guest post by Phillip Helbig Monthly Notices of the Royal Astronomical Society is one of the oldest and most prestigious journals in the fields of astronomy, astrophysics, and cosmology. My latest … | Continue reading
In his book Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, G. H. Hardy tells this famous story: He could remember the idiosyncracies of numbers in an almost uncanny way. It … | Continue reading
The Kepler problem is the study of a particle moving in an attractive inverse square force. In classical mechanics, this problem shows up when you study the motion of a planet around the Sun in the… | Continue reading
This is the color of something infinitely hot. Of course you’d instantly be fried by gamma rays of arbitrarily high frequency, but this would be its spectrum in the visible range. This… | Continue reading
Björn Brembs recently explained how “massive over-payment of academic publishers has enabled them to buy surveillance technology covering the entire workflow that can be used not only to be c… | Continue reading
The structure of benzene is fascinating. Look at all these different attempts to depict it! Let me tell you a tiny bit of the history. In 1865, August Kekulé argued that benzene is a ring of… | Continue reading
As the chlorophyll wanes, now is the heyday of the xanthophylls, carotenoids and anthocyanins. These contain carbon rings and chains whose electrons become delocalized… their wavefunct… | Continue reading
The Topos Institute is trying to hire a postdoc to work on polynomial functors! Here is the ad, written by David Spivak. Dear all, I’m happy to announce that Topos Institute is hiring a postd… | Continue reading
I love this movie showing a solution of the Kuramoto–Sivashinsky equation, made by Thien An. If you haven’t seen her great math images on Twitter, check them out! I hadn’t known about K… | Continue reading
Infinity is a very strange concept. Like alien spores floating down from the sky, large infinities can come down and contaminate the study of questions about ordinary finite numbers! Here’s … | Continue reading
I’d like to explain a conjecture about Wigner crystals, which we came up with in a discussion on Google+. It’s a purely mathematical conjecture that’s pretty simple to state, moti… | Continue reading
The Babylonians knew an amazingly good approximation to the square root of 2 back around 1700 BC. But did they know it was just an approximation? | Continue reading
Whoa! Today a Dutch court ordered Shell to reduce its carbon emissions by 45% by 2030 from 2019 levels! “The court orders Royal Dutch Shell, by means of its corporate policy, to reduce its CO… | Continue reading
“Black dwarf supernovae”. They sound quite dramatic! And indeed, they may be the last really exciting events in the Universe. It’s too early to be sure. There could be plenty of t… | Continue reading
I published a slightly different version of this article in Nautilus on February 24, 2021. Everyone seems to be talking about the problems with physics: Woit’s book Not Even Wrong, SmolinR… | Continue reading
I’m giving a talk in Latham Boyle and Kirill Krasnov’s Perimeter Institute workshop Octonions and the Standard Model on Monday April 5th at noon Eastern Time. This talk will be a review… | Continue reading
Massachusetts law requires that the state get 3,200 megawatts of offshore wind power by 2035. This would be about 20% of the electricity they consume. But so far they get only about 120 megawatts f… | Continue reading
One problem with the Anthropocene is that our economic systems undervalue forms of “natural capital” for which there are no markets, or poorly developed markets. I’m talkin… | Continue reading
Nuclear physics is complicated compared to atomic physics, because the strong force is complicated compared to the electromagnetic force, and nucleons—protons and neutrons—are bag-like … | Continue reading
I’ve been thinking about Petri nets a lot. Around 2010, I got excited about using them to describe chemical reactions, population dynamics and more, using ideas taken from quantum physics. Th… | Continue reading
Do you want to get involved in applied category theory? Are you willing to do a lot of work and learn a lot? Then this is for you: • Applied Category Theory 2021 — Adjoint School. Application… | Continue reading
This August a fire swept through the Mojave National Preserve in southern California and killed about a million Joshua trees. Let us take a moment to mourn them, along with the ancient coastal redw… | Continue reading
The Japanese take pride in ‘shinise’: businesses that have lasted for hundreds or even thousands of years. This points out an interesting alternative to the goal of profit maximi… | Continue reading
I now have a semiannual column in the Notices of the American Mathematical Society! I’m excited: it gives me a chance to write short explanations of cool math topics and get them read by up t… | Continue reading
A while ago I wanted to figure out how to prove one of Ramanujan’s formulas. I figure this is the sort of thing every mathematician should think about at least once. I picked the easiest one … | Continue reading
This blog does not allow discussion of partisan politics. But I can still list some ways in which US environmental policy will change if Biden becomes president. First and foremost, the US will rej… | Continue reading
According to the United States Fish and Wildlife Service, about 300,000 birds were killed by wind turbines in the US in 2015. Another study estimated that wind turbines killed about 500,000 birds a… | Continue reading
This is a wonderful development! Micah Halter and Evan Patterson have taken my work on structured cospans with Kenny Courser and open Petri nets with Jade Master, turned it into a practical softwar… | Continue reading
Roger Penrose just won Nobel Prize in Physics “for the discovery that black hole formation is a robust prediction of the general theory of relativity.” He shared it with Reinhard Genzel… | Continue reading
The physics of water is endlessly fascinating. The phase diagram of water at positive temperature and pressure is already remarkably complex, as shown in this diagram by Martin Chaplin: Click for a… | Continue reading
An European Union commission has voted to ban the use of lead ammunition near wetlands and waterways! The proposal now needs to be approved by the European Parliament and Council. They are expected… | Continue reading
Why is biodiversity ‘good’? To what extent is this sort of goodness even relevant to ecosystems—as opposed to us humans? I’d like to study this mathematically. To do this, w… | Continue reading
I think we need a ‘compositional’ approach to classical mechanics. A classical system is typically built from parts, and we describe the whole system by describing its parts and then sa… | Continue reading
Wow! Elena Di Lavore and Xiaoyan Li explained how to make a category of Petri nets that’s a model of linear logic! I consider myself a sort of expert on Petri nets, but I didn’t know th… | Continue reading
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Most of us have been staying holed up at home lately. I spent the last month holed up writing a paper that expands on my talk at a conference honoring | Continue reading
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If you’re wanting to learn some applied category theory, register for the tutorials that are taking place on July 5, 2020 as part of ACT2020! Applied category theory offers a rigorous mathema… | Continue reading
Due to the coronavirus outbreak, many universities are moving activities online. This is a great opportunity to open up ACT2020 to a broader audience, with speakers from around the world. The confe… | Continue reading
Here’s a fun challenge for people confined due to coronavirus. The E8 lattice is a thing of beauty, taking full advantage of the magic properties of the number 8. The octahedron has 8 sides. … | Continue reading
If you click on this picture, you’ll see a zoomable image of the Milky Way with 84 million stars: But stars contribute only a tiny fraction of the total entropy in the observable Universe. If… | Continue reading
A slightly different version of this article I wrote first appeared in Nautilus on November 28, 2019. Water rushes into Venice’s city council chamber just minutes after the local government rejects… | Continue reading
Schrödinger and Einstein helped invent quantum mechanics. But they didn’t really believe in its implications for the structure of reality, so in their later years they couldn’t … | Continue reading
You probably that planets go around the sun in elliptical orbits. But do you know why? In fact, they’re moving in circles in 4 dimensions. But when these circles are projected down to 3-dimen… | Continue reading
Here’s the first of a series of blog articles on how technology can help address climate change: • Adam Marblestone, Climate technology primer (1/3): basics. Adam Marblestone is a research sc… | Continue reading
I wrote something for the Spanish newspaper El País, which has a column on mathematics called “Café y Teoremas”. Ágata Timón helped me a lot with writing this, and she also translated i… | Continue reading