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

<p>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&nbsp;<em>exactly</em>&nbsp;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.</p><p><em>Support Mindscape on&nbsp;</em><a href="https://www.patreon.com/seanmcarroll" rel="noopener noreferrer" target="_blank"><em>Patreon</em></a><em>.</em></p><p>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&nbsp;<a href="https://math3ma.institute/" rel="noopener noreferrer" target="_blank">Math3ma Institute</a>. She hosts an explanatory mathematics blog,&nbsp;<a href="https://www.math3ma.com/" rel="noopener noreferrer" target="_blank">Math3ma</a>. She is the co-author of the graduate-level textbook&nbsp;<a href="https://mitpress.mit.edu/books/topology" rel="noopener noreferrer" target="_blank"><em>Topology: A Categorical Approach</em></a>.</p><ul><li><a href="https://www.math3ma.com/" rel="noopener noreferrer" target="_blank">Web site</a></li><li><a href="https://scholar.google.com/citations?user=UotbaiIAAAAJ&amp;hl=en" rel="noopener noreferrer" target="_blank">Google Scholar publications</a></li><li><a href="https://twitter.com/math3ma" rel="noopener noreferrer" target="_blank">Twitter</a></li><li><a href="https://www.youtube.com/watch?v=wiadG3ywJIs&amp;ab_chan