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)

200 | Solo: The Philosophy of the Multiverse

200 | Solo: The Philosophy of the Multiverse

The 200th episode of Mindscape! Thanks to everyone for sticking around for this long. To celebrate, a solo episode discussing a set of issues naturally arising at the intersection of philosophy and ph...

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199 | Elizabeth Cohen on Time and Other Political Values

199 | Elizabeth Cohen on Time and Other Political Values

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198 | Nick Lane on Powering Biology

198 | Nick Lane on Powering Biology

The origin of life here on Earth was an important and fascinating event, but it was also a long time ago and hasn't left many pieces of direct evidence concerning what actually happened. One set of cl...

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197 | Catherine Brinkley on the Science of Cities

197 | Catherine Brinkley on the Science of Cities

The concept of the city is a crucial one for human civilization: people living in proximity, bringing in resources from outside, separated from the labors of subsistence so they can engage in the trad...

16 Touko 20221h 8min

AMA | May 2022

AMA | May 2022

Welcome to the May 2022 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). I take the large number of questio...

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196 | Judea Pearl on Cause and Effect

196 | Judea Pearl on Cause and Effect

To say that event A causes event B is to not only make a claim about our actual world, but about other possible worlds — in worlds where A didn't happen but everything else was the same, B would not h...

9 Touko 20221h 16min

195 | Richard Dawkins on Flight and Other Evolutionary Achievements

195 | Richard Dawkins on Flight and Other Evolutionary Achievements

Evolution has equipped species with a variety of ways to travel through the air — flapping, gliding, floating, not to mention jumping really high. But it hasn't invented jet engines. What are the diff...

2 Touko 20221h 18min

194 | Frans de Waal on Culture and Gender in Primates

194 | Frans de Waal on Culture and Gender in Primates

Humans are related to all other species here on Earth, but some are closer relatives than others. Primates, a group that includes apes, monkeys, lemurs, and others besides ourselves, are our closest r...

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