Resources

Welcome!

I have gathered the materials on this page in the spirit of sharing what I've learned, admired, or found useful as a student and researcher in mathematics — from practical resources to things that simply made me smile.

Mathematical Writing

I have come to appreicate the importance of mathematical exposition, both in my own writing and in papers I read. Clear, well-crafted writing makes mathematics more accessible and enjoyable. I have been especially inspired by the writing styles of Paul Halmos, John Stillwell, and my mentor Andreas Blass, among others.

For all mathematical writers:

Keith Conrad's Advice on Mathematical Writing.
N. Steenrod, P. Halmos, M. Schiffer, J. Dieudonné – How to Write Mathematics. American Mathematical Society, 1973.

For first-time proof-writers:

Demonstration. Proof Beyond the Possibility of Doubt. U(M) Mathematics. August 16, 2023 version.

Quotes

These have been included because of the story they tell.

"There is no math without courage."

– Bar Roytman [As quoted in S. DeBacker – Math Missive. U(M) Mathematics, 2023.]

"The Axiom of Choice is obviously true; the Well-Ordering Principle is obviously false; and who can tell about Zorn's Lemma?"

– Jerry Bona, 1977 [E. Schechter – Handbook of Analysis and Its Foundations. Academic Press, 1997.]

"Have you ever chopped up a watermelon? Cause this one is making me believe in the axiom of choice: it definitely feels like it could be reassembled into twice the watermelon I bought."

– Clara Huggins, 2025 [Personal communication.]

"Mathematics in Göttingen? There is really none anymore."

– David Hilbert, ~1934, in response to the Nazi Minister of Education's question on the state of mathematics in Göttingen after being 'freed from Jewish influence' [As quoted in C. Reid – Hilbert. Springer, 1972.]

"God exists since mathematics is consistent, and the devil exists since we cannot prove it."

– André Weil [As quoted in H. Eves – Mathematical Circles Adieu. Prindle, Weber, and Schmidt, 1977.]

"[Model theory is] the geography of tame mathematics."

– Ehud Hrushovski [As quoted in S. Buss, A. Kechris, A. Pillay, and R. Schore – The Prospects for Mathematical Logic in the Twenty-First Century. The Bulletin of Symbolic Logic, 7(2):169-196, 2001.]