I was excited to contribute this piece to the New York Times Learning Network about A.I.-assisted mathematics. The way we do math is changing, and the change brings with it many compelling and challenging questions. The New York Times has some great resources to utilize, and I hope this piece for the NYT Learning Network can help establish context for teachers and students.
The article is freely available without subscription here.
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In just a few years artificial intelligence tools have progressed from solving formulaic math contest problems to generating novel proofs of long-standing open conjectures. The way math is done is changing, and more change is coming. Anyone interested in math should be paying attention to the unfolding story of AI-assisted mathematics, and this is especially true for math teachers, whose current students will enter a world where “doing math” is likely to mean something dramatically different than it does today.
Kevin Hartnett’s “The Proof in the Code” is an excellent entry point into that world. Hartnett tells the origin story of Lean, a mathematical formalization tool playing part in the AI-assisted mathematics revolution. Originally developed by researchers at Microsoft to debug code, Lean is now being used in synthesis with generative AI tools like large language models to debug mathematical proofs. The results have been astonishing.
“The Proof in the Code” is the story of the people and the ideas behind Lean, but it’s also the story about how we’ve arrived at a place where one of the world’s leading mathematicians recently felt obligated to say “It’s not necessarily the end of mathematics”. Hartnett’s book is a satisfying read for anyone interested in science and technology, but for teachers and learners of math, “The Proof in the Code” isn’t just a compelling tale of recent theoretical advances. It’s part of the backstory of the next chapter of human mathematics.
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I’m excited to be presenting Connecting Classroom Math to AI at the upcoming NCTM meeting in New Orleans. I think math teachers are uniquely positioned to help students develop healthy, productive, and realistic attitudes toward artificial intelligence tools by making sure that these tools are understood as applications of mathematics.
Here’s the session description:
Artificial Intelligence tools are everywhere and are likely to affect our lives in profound and lasting ways. To help prepare our students for an AI-driven future, let’s make sure they recognize that these tools are fundamentally applications of mathematics. In this session, we’ll see how topics from the MS/HS curriculum lead directly to the math that underlies technologies like LLMs, chatbots, and more, and we’ll discuss how to make these connections clear and compelling for our students.
You can find all the session details here.
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A snow day snow array! I thought of punching out that one stubborn entry, but let it be in the spirit of wabi-sabi. It’s like the Great British Baking Show’s missing raspberry.
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I’ve always found it cool that if you double the smaller acute angle in a 3-4-5 triangle you get the larger acute angle in a 7-24-25 right triangle. You can see this as a consequence of the double angle formula for sine. If 
In fact, if the sine and cosine of an angle are both rational, then so will be the sine and cosine of twice that angle. This gives a way to turn Pythagorean triples into new Pythagorean triples!
For example, suppose 
By the Pythagorean identity
And so
which of course also follows directly from algebra.
For example, using this process
Originally posted on Mastodon.
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