174 | Tai-Danae Bradley on Algebra, Topology, Language, and Entropy

174 | Tai-Danae Bradley on Algebra, Topology, Language, and Entropy

Mathematics is often thought of as the pinnacle of crisp precision: the square of the hypotenuse of a right triangle isn't "roughly" the sum of the squares of the other two sides, it's exactly that. But we live in a world of messy imprecision, and increasingly we need sophisticated techniques to quantify and deal with approximate statistical relations rather than perfect ones. Modern mathematicians have noticed, and are taking up the challenge. Tai-Danae Bradley is a mathematician who employs very high-level ideas — category theory, topology, quantum probability theory — to analyze real-world phenomena like the structure of natural-language speech. We explore a number of cool ideas and what kinds of places they are leading us to.

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Tai-Danae Bradley received her Ph.D. in mathematics from the CUNY Graduate Center. She is currently a research mathematician at Alphabet, visiting research professor of mathematics at The Master's University, and executive director of the Math3ma Institute. She hosts an explanatory mathematics blog, Math3ma. She is the co-author of the graduate-level textbook Topology: A Categorical Approach.


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334 | Daniel Whiteson on the Physics of and by Aliens

334 | Daniel Whiteson on the Physics of and by Aliens

The universe as revealed by physics is objective: it's out there, existing and behaving in ways that are completely independent of human thought. But the process by which we learn about the universe, ...

3 Nov 20251h 14min

333 | Gordon Pennycook on Unthinkingness, Conspiracies, and What to Do About Them

333 | Gordon Pennycook on Unthinkingness, Conspiracies, and What to Do About Them

Why are people wrong all the time, anyway? Is it because we human beings are too good at being irrational, using our biases and motivated reasoning to convince ourselves of something that isn't quite ...

27 Okt 20251h 10min

332 | Dmitri Tymoczko on the Mathematics Behind Music

332 | Dmitri Tymoczko on the Mathematics Behind Music

Music is math that you can dance to. The fact that certain notes sound good when played together, or in succession, is related to the mathematical properties of the frequencies to which they correspon...

20 Okt 20251h 21min

AMA | October 2025

AMA | October 2025

Welcome to the October 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 Pat...

13 Okt 20253h 37min

331 | Solo: Fine-Tuning, God, and the Multiverse

331 | Solo: Fine-Tuning, God, and the Multiverse

Certain features of our universe seem unnatural to us. These include "constants of nature" such as the cosmological constant and the mass of the Higgs boson, as well as features of the initial conditi...

6 Okt 20251h 54min

330 | Petter Törnberg on the Dynamics of (Mis)Information

330 | Petter Törnberg on the Dynamics of (Mis)Information

A characteristic of complex systems is that individual components combine to exhibit large-scale emergent behavior even when the components were not specifically designed for any particular purpose wi...

29 Sep 20251h 12min

329 | Steven Pinker on Rationality and Common Knowledge

329 | Steven Pinker on Rationality and Common Knowledge

Getting along in society requires that we mostly adhere to certainly shared norms and customs. Often it's not enough that we all know what the rules are, but also that everyone else knows the rules, a...

22 Sep 20251h 16min

328 | Mary Roach on Replacing Parts of Our Bodies

328 | Mary Roach on Replacing Parts of Our Bodies

Like any machine, bodies occasionally break down, and it's natural to go in search of a replacement part. Ancient societies featured simple prosthetics for teeth, noses, and limbs, while modern medici...

15 Sep 20251h 7min

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