146 | Emily Riehl on Topology, Categories, and the Future of Mathematics

146 | Emily Riehl on Topology, Categories, and the Future of Mathematics

"A way that math can make the world a better place is by making it a more interesting place to be a conscious being." So says mathematician Emily Riehl near the start of this episode, and it's a good summary of what's to come. Emily works in realms of topology and category theory that are far away from practical applications, or even to some non-practical areas of theoretical physics. But they help us think about what is possible and how everything fits together, and what's more interesting than that? We talk about what topology is, the specific example of homotopy — how things deform into other things — and how thinking about that leads us into groups, rings, groupoids, and ultimately to category theory, the most abstract of them all.

Support Mindscape on Patreon.

Emily Riehl received a Ph.D in mathematics from the University of Chicago. She is currently an associate professor of mathematics at Johns Hopkins University. Among her honors are the JHU President's Frontier Award and the Joan & Joseph Birman Research Prize. She is author of Categorical Homotopy Theory, and co-author of the upcoming Elements of ∞-Category Theory. She competed on the United States women's national Australian rules football team, where she served as vice-captain.


Episoder(416)

339 | Ned Block on Whether Consciousness Requires Biology

339 | Ned Block on Whether Consciousness Requires Biology

It's become increasingly clear that the Turing Test -- determining whether human interlocutors can tell whether a conversation is being carried out by a human or a machine -- is not a good way to thin...

5 Jan 1h 11min

Holiday Message 2025 | The Romance of the University

Holiday Message 2025 | The Romance of the University

Time for the holiday message! Rounding off the year with a brief and casual reflection on some issue that doesn't quite rise to the level of a full solo podcast. And hopefully something uplifting. Thi...

22 Des 202542min

AMA | December 2025

AMA | December 2025

Welcome to the December 2025 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Pa...

15 Des 20253h 36min

338 | Ryan Patterson on the Physics of Neutrinos

338 | Ryan Patterson on the Physics of Neutrinos

The story goes that Wolfgang Pauli, who first proposed the existence of neutrinos, was embarrassed to have done so, as it was considered uncouth to hypothesize new particles that could not be detected...

8 Des 20251h 26min

337 | Kevin Zollman on Game Theory, Signals, and Meaning

337 | Kevin Zollman on Game Theory, Signals, and Meaning

Game theory is a way of quantitatively describing what happens any time one thing interacts with another thing, when both things have goals and potential rewards. That's a pretty broad class of intere...

1 Des 20251h 17min

336 | Anil Ananthaswamy on the Mathematics of Neural Nets and AI

336 | Anil Ananthaswamy on the Mathematics of Neural Nets and AI

Machine learning using neural networks has led to a remarkable leap forward in artificial intelligence, and the technological and social ramifications have been discussed at great length. To understan...

24 Nov 20251h 14min

AMA | November 2025

AMA | November 2025

Welcome to the November 2025 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Pa...

17 Nov 20253h 34min

335 | Andrew Jaffe on Models, Probability, and the Universe

335 | Andrew Jaffe on Models, Probability, and the Universe

Science has an incredibly impressive track record of uncovering nonintuitive ideas about the universe that turn out to be surprisingly accurate. It can be tempting to think of scientific discoveries a...

10 Nov 20251h 17min

Populært innen Vitenskap

fastlegen
rekommandert
tingenes-tilstand
rss-rekommandert
jss
liberal-halvtime
villmarksliv
rss-paradigmepodden
forskningno
sinnsyn
fjellsportpodden
pod-britannia
nevropodden
rss-nysgjerrige-norge
tidlose-historier
hva-er-greia-med
diagnose
rss-overskuddsliv
smart-forklart
rss-lundqvist-podden