Calculus is not for Mathematicians

Monday, February 23rd, 2026

I’m going to respond to Michael Xue here because, as is all too common, the comment form simply isn’t working.

Spoken like a true mathematician. Harvard Reform might indeed have left a generation of students less prepared for advanced mathematics than ever before, but it’s not as if there’s any shortage of advanced mathematicians today, and more importantly it’s not like future mathematicians were then or now the primary audience for calculus classes. I’d estimate that well more than 90% of students who actually use calculus do so in physics, engineering, economics, and other scientific fields. Mathematics for mathematics’s sake was always a small minority. I learned calculus the old way, but I never understood it until I taught it the new way.

Newton, Leibniz, Euler, and Gauss didn’t need epsilon delta proofs. Neither do students of calculus, with the sole exception of the small minority who are trying to become pure mathematicians, and they can pick it up in their first real analysis course.

What kind of show is Severance?

Saturday, February 21st, 2026

Yes, I know I’m a little late to the party, but I’m about through the end of Season 1 of Severance, and there’s one meta question I’m asking myself. No, it’s not what is actually going on, how does severance work, or what the purpose of the Lumon Corporation is, though these are all reasonable questions. My question is more what kind of show am I watching? In particular, am I watching a show like Lost and Dollhouse or am I watching a show like The Prisoner or The X-Files? Because if it’s the latter, I’m going to hate myself for getting sucked into this.
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Perplexity beats Gemini Pro

Friday, February 20th, 2026

Over the last couple of days I was working on a relatively complex software integration project for image generation with stable diffusion. I had dozens of different pieces from multiple websites to download, configure, integrate, and debug. None of it was particularly well documented. In the past, I would have read what documentation existed, most of which was out of date, experimented a lot, and asked a number of questions on Reddit or other forums. This time, instead of bothering a lot of people online, I decided to use LLMs and chatbots to assist me and explain to me in detail what I needed to do when and how to accomplish my task. The results weren’t pretty.
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