In Our Time podcast has episode on Pierre-Simon Laplace

I have another mathematics-themed podcast to share. It’s again from the BBC’s In Our Time, a 50-minute program in which three experts discuss a topic. Here they came back around to mathematics and physics. And along the way chemistry and mensuration. The topic here was Pierre-Simon Laplace, who’s one of those people whose name you learn well as a mathematics or physics major. He doesn’t quite reach the levels of Euler — who does? — but he’s up there.

Laplace might be best known for his work in celestial mechanics. He (independently of Immanuel Kant) developed the nebular hypothesis, that the solar system formed from the contraction of a great cloud of dust. We today accept a modified version of this. And for studying the question of whether the solar system is stable. That is, whether the perturbations every planet has on one another average out to nothing, or to something catastrophic. And studying probability, which has more to do with these questions than one might imagine. And then there’s general mechanics, and differential equations, and if that weren’t enough, his role in establishing the Metric system. This and more gets discussion.

In Our Time podcast has episode on Émile du Châtelet

I have another in my occasional series of podcasts mentioning something of mathematical interest. This is another one from the BBC’s In Our Time, a 50-minute program of three experts discussing a topic. Here the topic is Émile du Châtelet, an 18th century French noblewoman noted for translating Newton’s Principia Mathematica into French. It’s by accounts an outstanding translation, still regarded as one of the best translations the book has had.

This is not the whole of her work, though my understanding is she’d be worth noticing even if it were. Part of the greatness of the translation was putting Newton’s mathematics — which he had done as geometric demonstrations — into the calculus of the day. The experts on In Our Time’s podcast argue that she did a good bit of work advancing the state of calculus in doing this. She’d also done a good bit of work on the problem of colliding bodies.

A major controversy was, in modern terms, whether momentum and kinetic energy are different things and, if they are different, which one collisions preserve. Châtelet worked on experiments — inspired by ideas of Gottfried Wilhelm Liebniz — to show kinetic energy was its own thing and was the important part of collisions. We today understand both momentum and energy are conserved, but we have the advantage of her work and the people influenced by her work to draw on.

She’s also renowned for a paper about the nature and propagation of fire, submitted anonymously for the Académie des Sciences’s 1737 Grand Prix. It didn’t win — Leonhard Euler’s did — but her paper and her lover Voltaire’s papers were published.

Châtelet was also surprisingly connected to the nascent mathematics and physics scene of the time. She had ongoing mathematical discussions with Pierre-Louis Maupertuis, of the principle of least action; Alexis Clairaut, who calculated the return of Halley’s Comet; Samuel König, author of a theorem relating systems of particles to their center of mass; and Bernard de Fontenelle, perpetual secretary of the Acadeémie des Sciences.

So for those interested in the history of mathematics and physics, and of women who are able to break through social restrictions to do good work, the podcast is worth a listen.

I spent much of the time waiting for a mention of Chatelier’s principle which never came. This because Chatelier’s principle’s — about the tendency of a system in equilibrium to resist changes — is named for Henry Louis Le Chatelier, a late 19th/early 20th century chemist with, so far as I know, no relation to Émile du Châtelet. I hope this spares you the confusion I felt.

Paul Dirac discussed on the In Our Time podcast

It’s a touch off my professed mathematics focus. Also off my comic strips focus. But Paul Dirac was one of the 20th century’s greatest physicists, this in a century rich in great physicists. Part of his genius was in innovative mathematics, and in trusting strange implications of his mathematics.

This week the BBC podcast In Our Time, a not-quite-hourlong panel show discussing varied topics, came to Paul Dirac. It can be heard here, or from other podcast sources. I get it off iTunes myself. The discussion is partly about his career and about the magnitude of his work. It’s not going to make anyone suddenly understand how to do any of his groundbreaking work in quantum mechanics. But it is, after all, an hourlong podcast for the general audience about, in this case, a physicist. It couldn’t explain spinors.

And even if you know a fair bit about Dirac and his work you might pick up something new. This might be slight: one of the panelists mentioned Dirac, in retirement, getting to know Sting. This is not something impossible, but it’s also not a meeting I would have ever imagined happening. So my week has been broadened a bit.

The web site for In Our Time doesn’t have a useful archive category for mathematics, at least that I could find. But many mathematical topics are included in the archive of science subjects, including important topics like the kinetic theory of gases and the work of Emmy Noether.