Dealing with infinity *without* the axiom of choice

How to construct larger and larger "infinities"

Fighting ABC Conjecture misinformation with information

Confidently WRONG (about how NSF funding works)

From ill-posed to well-posed, from sloppy solution to (mostly) rigorous solution

An ill-posed integro-differential equation

Meta thoughts about discussing infinity online

Values of pi_e, the constant that generalizes pi to ellipses

A "closed-form" formula for the circumference of an ellipse

The "fake math news" about Pythagoras, Hippasus, and square root of 2

Is 2*Infinity larger than Infinity?

An elementary proof of Euler's identity (and Euler's formula)

Is the infinite of numbers in [0,2] larger than the infinity of numbers in [0,1]?

Round up of terrible reporting of math in the media

An open problem in number theory

Bryan Birch at PCMI 2009, speaking on "Heegner's Friends, the Modular Functions"

What is zero to the zero to the zero (0^0^0)?

Professors afraid of AI and ChatGPT? Not me

What's e^e^e^e^(ln(ln(ln(ln(7)))))?

On Immigration and Funding

Why do we need a proof of the infinitude of the primes?

Reading the first 3 pages of Mochizuki's papers on IUTT

The diss book reviews by Mordell and Lang

What is 0^0 (zero to the zero)?

Higher math is "insanely difficult"

The latest two chapters of ABC Conjecture drama

Is Math "unreasonably effective" at describing the universe?

On unethical scientific behavior (of Newton in particular)

Why do children learn to do subtractions like this?

An example of a 3-adic number

Why aren't kids learning the subtraction algorithm that we learned!?

The proof of "1+1=2"

Who was the "greatest scientific mind" of all time? ... NOT Newton.

Local rings and localization of Z

On gratuitous math phobia

The end of the Universe is coming "sooner" than expected!

Using the Sylow Theorems - 44 - A First Course in Abstract Algebra

How to fight imposter syndrome back

My Favorite Proof in Abstract Algebra

The Area of a Dodecagon is 3R^2

The Third Sylow Theorem - 43 - A First Course in Abstract Algebra

What if pi = 3? What could go wrong!? EVERYTHING!

The Second Sylow Theorem - 42 - A First Course in Abstract Algebra

Dr. Panchanathan (previous NSF director) received an honorary PhD from UConn

The Premier League, Fibonacci, and Probability

The First Sylow Theorem - 39 - A First Course in Abstract Algebra

Cauchy's Theorem - 38 - A First Course in Abstract Algebra

What does math research look like?

Introduction to the Sylow Theorems - 37 - A First Course in Abstract Algebra

Consequences of the Class Equation - 36 - A First Course in Abstract Algebra

The Class Equation - 35 - A First Course in Abstract Algebra

The Orbit-Stabilizer Theorem - 34 - A First Course in Abstract Algebra

Properties of Group Actions - 33 - A First Course in Abstract Algebra

Group Actions - 32 - A First Course in Abstract Algebra

Why doesn't the math department determine the advisor for each grad student?

Normalizers - 41 - A First Course in Abstract Algebra

The Sylow Theorems (Examples) - 40 - A First Course in Abstract Algebra

Complex Multiplication -- by Jared Weinstein (Boston University)

Breaking News in Number Theory (April, 2025)

"Feynman's" integration trick (differentiation under the integration sign)