Mike Shulman

San Diego, CA

http://www.sandiego.edu/~shulman

I am an associate professor of mathematics at the University of San Diego. My research is in homotopy type theory and higher category theory.

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Has incorrect notation ever led to a mistaken proof?

ct.category-theory soft-question ho.history-overview notation asked Aug 9, 2018 at 17:16

mathoverflow.net

55 votes

Should we say that fractions "are" or "represent" numbers?

primary-education fractions asked Apr 1, 2014 at 21:59

matheducators.stackexchange.com

48 votes

How to correct an error in a submitted paper?

publishing asked Apr 21, 2010 at 15:50

mathoverflow.net

47 votes

Brown representability for non-connected spaces

at.algebraic-topology brown-representability asked Aug 16, 2012 at 19:33

mathoverflow.net

45 votes

The formal p-adic numbers

ct.category-theory topos-theory constructive-mathematics p-adic-numbers asked Aug 12, 2015 at 23:22

mathoverflow.net

38 votes

Why are profinite topologies important?

ct.category-theory gn.general-topology profinite-groups asked Dec 15, 2010 at 4:14

mathoverflow.net

37 votes

A calculus book that uses differentials?

calculus textbooks infinitesimals asked Mar 13, 2014 at 21:40

matheducators.stackexchange.com

35 votes

Internal logic of the topos of simplicial sets

ct.category-theory lo.logic topos-theory categorical-logic asked Mar 11, 2014 at 0:43

mathoverflow.net

32 votes

Can ZFC → NBG be iterated?

set-theory ct.category-theory lo.logic asked Jan 5, 2011 at 22:44

mathoverflow.net

29 votes

Teaching logic with a proof assistant

proofs logic technology-in-education asked Mar 15, 2014 at 21:04

matheducators.stackexchange.com

Top Answers

219

Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?

mathoverflow.net

106

What properties make $[0,1]$ a good candidate for defining fundamental groups?

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The "derived drift" is pretty unsatisfying and dangerous to category theory (or at least, to me)

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Can skeleta simplify category theory?

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What packages do people load by default in LaTeX?

tex.stackexchange.com

How to rewrite mathematics constructively?

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Why is Set, and not Rel, so ubiquitous in mathematics?

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Has anyone ever accidentally "proven" a false theorem with type-in-type?

proofassistants.stackexchange.com

Is pure mathematics useful outside of mathematics itself?

mathoverflow.net

Why did Voevodsky consider categories "posets in the next dimension", and groupoids the correct generalisation of sets?

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Nonequivalent definitions in Mathematics

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Nonequivalent definitions in Mathematics

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A better way to explain forcing?

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Reasons to believe Vopenka's principle/huge cardinals are consistent

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Nonequivalent definitions in Mathematics

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Equality vs. isomorphism vs. specific isomorphism

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How do you define (infinity,1) categories in Homotopy Type Theory?

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Homotopy Type Theory: What is it?

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What is the correct definition of localisation of a category?

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Why is the definition of the higher homotopy groups the "right one"?

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How can category theory help my research in set theory?

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Set theory for category theory beginners

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Defining $SU(n)$ in HoTT

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Formalizations of the idea that something is a function of something else?

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Sheaf-theoretic approach to forcing

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Where are some interesting places where the axiom of choice crops up in category theory?

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Category of categories as a foundation of mathematics

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What is wrong with ZFC?

math.stackexchange.com

What is homology anyway?

mathoverflow.net

When size matters in category theory for the working mathematician

mathoverflow.net