# Maybe-Mathematical Musings

## A Fictional History of Numbers, Part 1: Counting, Fractions, and Algebra

Mathematicians deal with lots of different kinds of "numbers". But where do they come from? In this series we'll see where different types of exotic numbers came from, and what reasonable questions we need them to answer. In Part 1, we're starting off with the simplest types of numbers: the algebraic numbers. We'll see how we could have invented square roots and weirder things on our own, just by asking one reasonable question after another.

## Motivating the Integral with Euler's Method

I realized you can "prove" the Fundamental Theorem of Calculus by using Euler's method for solving differential equations. It's a fun way to motivate the integral, but not one that I'm actually going to use in class.

## Writing Calculus Tests with ChatGPT

ChatGPT is cool, but doesn't seem useful yet for doing serious intellectual work. But is it useful for more routine stuff? I wanted to see if I could use ChatGPT to write test questions for my calculus courses. I'm experimenting with using ChatGPT to write test questions. My verdict: not completely useless!

## Why I'm Not Scared of the New Chatbots

Modern AI chatbots like ChatGPT are impressive, but they work in very specific and limited ways. They produce surprisingly human-like text—as long as the human isn't paying attention. And that tells us a lot about what we can expect this technology to do for us.