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.

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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.


Jaksot(416)

224 | Edward Tufte on Data, Design, and Truth

224 | Edward Tufte on Data, Design, and Truth

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223 | Tania Lombrozo on What Explanations Are

223 | Tania Lombrozo on What Explanations Are

There are few human impulses more primal than the desire for explanations. We have expectations concerning what happens, and when what we experience differs from those expectations, we want to know th...

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222 | Andrew Strominger on Quantum Gravity and the Real World

222 | Andrew Strominger on Quantum Gravity and the Real World

Quantum gravity research is inspired by experiment — all of the experimental data that supports quantum mechanics, and supports general relativity — but it's only inspiration, not detailed guidance. S...

9 Tammi 20231h 24min

221 | Adam Bulley on How Mental Time Travel Makes Us Human

221 | Adam Bulley on How Mental Time Travel Makes Us Human

One of the most powerful of all human capacities is the ability to imagine ourselves in hypothetical situations at different times. We can remember the past, but also conjure up possible futures that ...

2 Tammi 20231h 20min

Holiday Message 2022: Thinking Really Slowly

Holiday Message 2022: Thinking Really Slowly

Welcome to that beloved Mindscape annual tradition, the Holiday Message. An opportunity for a quicker and less-well-thought-out solo episode to round off another year. Ironically, this year the theme ...

19 Joulu 202247min

220 | Lara Buchak on Risk and Rationality

220 | Lara Buchak on Risk and Rationality

Life is rich with moments of uncertainty, where we're not exactly sure what's going to happen next. We often find ourselves in situations where we have to choose between different kinds of uncertainty...

12 Joulu 20221h 16min

AMA | December 2022

AMA | December 2022

Welcome to the December 2022 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...

5 Joulu 20223h 15min

219 | Dani Bassett and Perry Zurn on the Neuroscience and Philosophy of Curiosity

219 | Dani Bassett and Perry Zurn on the Neuroscience and Philosophy of Curiosity

It's easy enough to proclaim that we are curious creatures, but what does that really mean? What kinds of curiosity are there? And how does curiosity arise in our brains? Perry Zurn and Dani Bassett a...

28 Marras 20221h 2min

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