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.
These have been included because of the story they tell.
"There is no math without courage."
– Bar Roytman [As quoted in a 2023 U(M) Math Missive written by Stephen DeBacker.]
"Mathematics is a function of who does mathematics."
– Federico Ardila-Mantilla, 2025 [University of Michigan Marjorie Lee Brown Colloquium.]
"Mathematics is the study of things that come out a certain way because there is no other way they could possibly be."
– Jordan Ellenberg [As quoted in his book How Not to Be Wrong. Penguin Press, 2014.]
"Sometimes the most beautiful facts about familiar objects can only be seen by broadening your view far beyond the familiar."
– Grant Sanderson (3Blue1Brown), 2026 [UW-Madison Math Colloquium.]
"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.]
"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.]
"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.]
"If you see one tautology, then you have seen one tautology."
– Kevin Schwartz, 2026 [Pi Day Comedy, Madison, WI.]
"[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.]
"Being a physicist is hard, but it's better than having to work for a living."
– Aurelio Grillo [As quoted in G. Parisi – In a Flight of Starlings: The Wonder of Complex Systems. Penguin Press, 2023.]
See also:
Some notes written by me can be found under Teaching
Ronnie Chen's Notes on Set Theory written for a first graduate course in set theory
Keith Conrad's Expository Papers on various topics
Especially for UW-Madison graduate students preparing for quals:
Chiara Travesset's A Careless Introduction to Computability Theory
Ivan Aidun's Notes on Algebra prepared for the Summer Enhancement Program
Especially for students in Calculus courses:
Steve Butler's sites for Calc 1, Calc 2, Calc 3, Differential Equations
Here are some resources for logicians.
Recent preprints: arxiv.org/list/math.LO/recent.
The Association for Symbolic Logic is an international organization supporting research and critical studies in logic.
The Graduate Student Conference in Logic meets every April at one of Notre Dame, UW-Madison, UIC, or UChicago. Recent website links: 2026, 2025, 2024, 2023.
A list of logic groups around the world: settheory.net/world.
computability.org is a resource for the computability theory community.
The computability zoos are an online database of classes of Turing degrees, enumeration degrees, and reverse math priciples.
The Reverse Mathematics Zoo is a program to help organize relations (known implications/non-implications) among various mathematical principles (studied from a reverse-mathematical perspective).
The Model Theory Network (Modnet) lists meetings and events relevant to model theory.
Open Logic Project: openlogicproject.org
See also:
Hongyu Zhu's conferences page for more conferences
Steffen Lempp's home page and Mariya Soskova's home page for more relevant links
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:
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.
Reading mathematics can be a daunting experience, even for more experienced mathematicians. Below are some resources and texts at a more introductory level that I have found helpful.
"What is ..."
The "What is ... " column of the Notices of the American Mathematical Society provides short, non-technical articles offering orientation to varied subjects. Armin Straub maintained a list of the articles in this column before there was an official such list.
Other Expository Articles
MAA's American Mathematical Monthly publishes original expository research.
The Mathematical Intelligencer publishes articles about mathematics, about mathematicians, and about the history and culture of mathematics.
See also
I compiled this information when I was an undergraduate at the University of Michigan. Some of these links may be outdated.
Summer Research Opportunities:
Math REU Programs site maintained by Steve Butler
National Science Foundation (NSF) funded REU Sites
American Mathematical Society (AMS) REU listings
Undergraduate Math Conferences:
JMM usually has an AMS-SIAM Special Session for undergraduates
For UMich Math Students:
Consider taking an independent study course
Lab of Geometry at Michigan (Math 440) is a semester-long mathematics research and computing experience, offered in the Fall and Winter semesters.
Explorations in Mathematical Research (Math 389) is also a semester-long course meant to introduce undergraduates to math research, offered in the Winter semester.
Jokes:
Math jokes collected by Andrej and Elena Cherkaev
Math jokes collected by Tanya Khovanova
Poetry:
YouTube videos:
Any of 3Blue1Brown's videos, especially Taylor Series, Inscribed Squares, Group Theory, Colliding Blocks
Quanta Magazine's Biggest Breakthroughs series
Ravi Vakil's The Mathematics of Doodling
Misc:
This section is currently under construction. If you would like the template for any of my writing, slides, posters, etc., please send me an email.