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The Hardest Math I've Ever Really Used

How to Talk Mathematics Seminar, Toronto February 23 2026

Abstract. We'll talk about How to Talk Mathematics, at least partially, by talking mathematics.

What's the hardest math I've ever used in real life? Me, myself, directly - not by using a cellphone or a GPS device that somebody else designed? And in "real life" - not while studying or teaching mathematics?

I use addition and subtraction daily, adding up bills or calculating change. I use percentages often, though mostly it is just "add 15 percents". I seldom use multiplication and division: when I buy in bulk, or when I need to know how many tiles I need to replace my kitchen floor. I've used powers twice in my life, doing calculations related to mortgages. I've used a tiny bit of geometry and algebra for a tiny bit of non-math-related computer graphics I've played with. And for a long time, that was all. In my talk I will tell you how recently a math topic discovered only in the 1800s made a brief and modest appearance in my non-mathematical life. There are many books devoted to that topic and a lot of active research. Yet for all I know, nobody ever needed the actual formulas for such a simple reason before.

URL. https://drorbn.net/to26.

Handout. hardest.pdf, hardest.html, (source files: pensieve).

The program used with the presentation is available (and very lightly documented) at HandoutBrowser.js.