On June 30, 2025, Mark Brittenham and Susan Hermiller uploaded a preprint to the arXiv called “Unknotting number is not additive under connected sum” (and an updated version on September 15, 2025). In it, they surprised the mathematical community by giving a counterexample to a long-standing conjecture in knot theory. The story was picked up…
Tag: mathematics
Mathematics Departments at Liberal Arts Colleges
I was looking for information about mathematics programs at other liberal arts colleges, so I put together this collection of links. I thought others might find it helpful, so I’m posting it here. (I actually asked ChatGPT to assemble this list. It did an OK, but not great, job. About 70% of the links were…
Making the Mandelbrot Set with Excel
The Mandelbrot set is one of the most stunning geometric objects in all of mathematics. In this blog post, I will show how to generate the Mandelbrot set below using Excel. It is also an example of how you can use AI (I used ChatGPT) to help with a task like this. (Here is the…
Math class technology policy: Fall 2023 edition
I decided to address the use of technology—especially generative AI and large language models like ChatGPT and Bard—in the syllabi for my classes this fall. Here’s the current draft of my technology policy for my upcoming calculus classes. If you have thoughts or observations, leave them in the comments below. Also, feel free to copy,…
Mathematicians’ Phone Passcodes
A character in a novel I was reading used the passcode 1729 for his house’s security system. He did so because of the famous Hardy-Ramanujan anecdote about the number. That got me to thinking. What would mathematicians of the past have used for their passcodes? I tweeted some ideas and got some great responses with…
How to Present a Mathematical Proof or Problem
There are many useful websites containing advice on how to give a good mathematics presentation (such as those listed here). But these are written for scholars who are giving lectures on their research. They focus on organizing the talk, putting the research in context, deciding what to include or not include, designing slides, pacing and…
Tales of Impossibility: Now Published!
I’m very excited to announce that my new book, Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (Princeton University Press, 2019), is now available! (OK. It was published about a month ago, but I am just now getting around to blogging about it.) Like my previous book, Euler’s Gem (Princeton University…
Make Your Own Pythagorean Cup
My parents recently went to Greece. They brought me back a souvenir—a practical joke cup called a “Pythagorean cup.” The legend behind the cup is that Pythagoras or one of the Pythagoreans invented this cup to prevent gluttony. The vessel looks like a cup with an odd pillar in the center. When you fill it…
Card Table Proof of the Pythagorean Theorem
We own a standard card table that we leave tucked away in the basement until the kids want to have a lemonade stand on the front sidewalk or we need the extra table space for a large Thanksgiving dinner. It is the standard kind with legs that fold underneath it so it is easy to store….
Editing mathematical writing
As I mentioned in a previous post, I’ve been assigning large-scale collaborative writing projects in my mathematics classes. I’ve had my topology students write a textbook for their class, and this semester I’ve been doing the same in my discrete mathematics class. As I mentioned in that post, the approach has been very successful, but…
David Richeson: Division by Zero 