It’s back to school season, and at my house that’s already meant a lot of math. Both of my kids are taking quantitative science courses along with math courses, so every few nights I’m getting to help with math-related homework of one sort or another. It’s an interesting opportunity to see what I remember and don’t remember from when I took those classes, and what comes easier with more experience and what doesn’t. Fundamental principles seem to stick better than specific techniques. For example, I helped my son with a physics problem by setting up a system of five equations with five unknown quantities. Was that the simplest way to solve it, or was there some shortcut I was forgetting? I don’t know, I just knew my way would work.

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# number theory

## Science Corner: Math Goes Sci-Fi & A Blog Film Festival

In the ten-day window when the dates are all palindromes (9 10 19, 9 11 19, etc.), let’s have some math news. Fans of Douglas Adams’ *The Hitchhiker’s Guide to the Galaxy* can rarely pass up an opportunity for a *42* reference. The number is famously the answer given in the book to the ultimate question of life, the universe and everything. And now, it is also the answer to which number was most recently proven to be representable as the sum of three cubes. As with many math puzzles, the statement is simple but the solution is challenging. Given an integer like 42, find three other integers that, when cubed, add up to 42. As it happens, the numbers in question turn out to be -80538738812075974, 80435758145817515, and 12602123297335631. They are on the order of tens of quadrillions; those numbers are so big I had to install special software on my computer just to verify the solution. So you can imagine it would take a while to try all the smaller possibilities and combinations.

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