Conducting the Mathematical Orchestra From the Middle | Mathematics - Quanta Magazine

Rachel Crowell, math and science writer based in Iowa Emily explains, Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

 Some of Emily Riehl's books on a table.
Riehl takes pride in her expository writing, which includes a forthcoming textbook that rewrites infinity category theory.

Emily Riehl sees similarities between the viola, which she grew up playing, and the mathematical field of higher category theory, in which she is currently a leading participant. She thinks of the two as the “glue” of their respective domains; just as the viola creates a richer orchestral sound, “there’s a sense in which category theory makes mathematics deeper,” she said.

The categorical perspective emerged in mathematics in 1945 when Samuel Eilenberg and Saunders Mac Lane published their radical paper, “General Theory of Natural Equivalences.” It proposed a deeply unconventional idea, arguing that mathematics needed to do away with the equal sign, and the whole simplistic notion of equality, and replace it with the deeper, more sophisticated idea of “equivalence.”

Instead of calling two things exactly equal, Eilenberg and Mac Lane urged mathematicians to embrace sophisticated new mathematical structures that captured the many ways in which two things might be the same, or equivalent...

Quanta Magazine recently spoke with Riehl about her forthcoming book as well as her years playing high-level Australian rules football, how her identity as a queer woman has been “protective” in mathematics, and the obligation mathematicians have to address the social justice issues of the moment. This interview is based on phone and email interviews and has been condensed and edited for clarity.
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Source: Quanta Magazine