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)

230 | Raphaël Millière on How Artificial Intelligence Thinks

230 | Raphaël Millière on How Artificial Intelligence Thinks

Welcome to another episode of Sean Carroll's Mindscape. Today, we're joined by Raphaël Millière, a philosopher and cognitive scientist at Columbia University. We'll be exploring the fascinating topic ...

20 Maalis 20231h 57min

229 | Nita Farahany on Ethics, Law, and Neurotechnology

229 | Nita Farahany on Ethics, Law, and Neurotechnology

Every time our brain does some thinking, there are associated physical processes. In particular, electric currents and charged particles jump between neurons, creating associated electromagnetic field...

13 Maalis 20231h 12min

AMA | March 2023

AMA | March 2023

Welcome to the March 2023 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 Patre...

6 Maalis 20233h 1min

228 | Skye Cleary on Existentialism and Authenticity

228 | Skye Cleary on Existentialism and Authenticity

God is dead, as Nietzsche's madman memorably reminded us. So what are we going to do about it? If there is no powerful force out there to guide us and give meaning to our lives, how are we supposed to...

27 Helmi 20231h 16min

227 | Molly Crockett on the Psychology of Morality

227 | Molly Crockett on the Psychology of Morality

Most of us strive to be good, moral people. When we are doing that striving, what is happening in our brains? Some of our moral inclinations seem pretty automatic and subconscious. Other times we have...

20 Helmi 20231h 11min

226 | Johanna Hoffman on Speculative Futures of Cities

226 | Johanna Hoffman on Speculative Futures of Cities

Cities are incredibly important to modern life, and their importance is only growing. As Geoffrey West points out, the world is adding urban areas equivalent to the population of San Francisco once ev...

13 Helmi 20231h 12min

AMA | February 2023

AMA | February 2023

Welcome to the February 2023 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...

6 Helmi 20233h 7min

225 | Michael Tomasello on The Social Origins of Cognition and Agency

225 | Michael Tomasello on The Social Origins of Cognition and Agency

Human beings have developed wondrous capacities to take in information about the world, mull it over, think about a suite of future implications, and decide on a course of action based on those delibe...

30 Tammi 20231h 22min

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