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.


Episoder(416)

321 | David Tong on Open Questions in Quantum Field Theory

321 | David Tong on Open Questions in Quantum Field Theory

Quantum field theory is the basis for our most successful theories of fundamental physics. And yet, there are things we don't understand about it. Some of these puzzles are relatively well-known, whil...

14 Jul 20251h 19min

AMA | July 2025

AMA | July 2025

Welcome to the July 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 Patreo...

7 Jul 20254h 3min

320 | Solo: Complexity and the Universe

320 | Solo: Complexity and the Universe

Our universe started out looking very simple: hot, dense, smooth, rapidly expanding. According to our best current model, it will end up looking simple once again: cold, dark, empty. It's in between -...

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319 | Bryan Van Norden on Philosophy From the Rest of the World

319 | Bryan Van Norden on Philosophy From the Rest of the World

It is common to refer to philosophy as "a series of footnotes to Plato." But in the original quote, Alfred North Whitehead was more careful: he limited his characterization to "the European philosophi...

23 Jun 20251h 12min

318 | Edward Miguel on the Developing Practice of Development Economics

318 | Edward Miguel on the Developing Practice of Development Economics

Economics is seeing an upsurge in the importance of controlled, reproducible empirical studies. One area where this has had a great impact is on development economics, which studies the economies of l...

16 Jun 20251h 20min

317 | Nicole Rust on Why Neuroscience Hasn't Solved Brain Disorders

317 | Nicole Rust on Why Neuroscience Hasn't Solved Brain Disorders

The human brain is extremely complicated, but decades of careful neuroscientific research have revealed quite a bit about how it works, including how certain genes affect particular brain behaviors. N...

9 Jun 20251h 14min

AMA | June 2025

AMA | June 2025

Welcome to the June 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 Patreo...

2 Jun 20253h 23min

316 | Niayesh Afshordi and Phil Halper

316 | Niayesh Afshordi and Phil Halper

Einstein's general theory of relativity, plus some reasonable assumptions about the universe and what it's made of, has a remarkable implication: that as we trace cosmic evolution into the far past, w...

26 Mai 20251h 28min

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