Tobias Dantzig, a relatively unknown American mathematician — a footnote in the annals of mathematicianery, is an absolute GIANT in my head. You’ve never heard of this guy, have you? I didn’t think so. If you have, it’s only because I’ve just told you about him.
Tobias Dantzig, I’m learning as I peruse his Wikipedia page, was born in Imperial Russia (the Karenina kind), studied under freaking-Henri Poincaré (“The Last Universalist”), suffered the loss of his brother at the hands of the Nazis (er, nothing clever to say here), emigrated to America to obtain a Ph.D., and taught at Johns Hopkins, Columbia, and the University of Maryland. Man, this guy was even cooler than I thought he was.
I don’t know why memory works like it does, but in my internal pensieve I have a vivid memory of walking through the library in my junior year of high school. You see, I had no friends because I was a loser (who, me???) so yah, I spent a lot of lunch periods ambling around in the library, acting like I wasn’t a loser (Editor’s note: consider being less honest about being a loser). I only realized years later that walking around the library wasn’t exactly helping my social status.
I happened by serendipity to notice a book entitled Number, by Tobias Dantzig. Or, more completely (and Dantzig is my hero for this title):
Number: The Language of Science (A critical survey written for the cultured non-mathematician)
Now if that isn’t a great title, I don’t know what is. That’s the kind of spine you want to see in a library — one that makes your own spine tingle with envy (Editor’s note: now THAT is good writing). Number is apparently the only book he ever wrote, probably because the title of his first was just Too Good.
To further set the scene, I would like to point out that I had just finished my sophomore year Algebra 2 class with a D. Yes, a D, though I ended up turning it around the second semester to a B. I don’t care what you say, Algebra 2 was hard — my D-B was not for lack of trying. I tried my dat’gum giblets off and came out of that class without a ton of enthusiasm for the sport of mathematics.
Cut to that day of my junior year (the previous paragraph was a flashback within a flashback): for some reason, I picked Number up and started in. I was absolutely gobsmacked. It almost smacked my gobs clean out of me!
You see, Number helped junior-year “bad-at-math” me discover that math was actually not about logarithmic polynomials. Math was astonishing. Number taught me that math was far more than plain old “interesting” — anything can be interesting, you Philistines!— no no, Dantzig taught me that math provided a deep mystery that we humans, including scores of talented mathematicians with brains like overgrown melons bursting with thought-juice, over the course of millennia, standing astern with lead lines in hand, sounding the depths, could not properly fathom.
Dantzig also taught me that math is beautiful because it scales in difficulty with the learner. It is, in point of fact, not opinion, an untenable challenge. Did you know (FACT TIME) that there’s not a single mathematician that figured it all out? Euler read Virgil’s Aeneid one time through and could quote it from beginning to end. Gauss, at 19 years old, solved a geometry problem that eluded all of humanity for the prior 2,000 years. John Wallis (who is not in the same league as Gauss or Euler) was once asked for “the integral part of the square root of 3×10^40”, which he worked on in his head for several hours then recited the answer from memory.
Their stories don’t stop there, though. Euler, given years to work on it, could not crack Fermat’s Last Theorem. Gauss, before he did the mortal coil shuffle, left us with the Gauss Conjecture — which is a fancy way of saying “a thing he couldn’t quite figure out.”
The beautiful thing about math is that it stymied each of these people just like Algebra 2 stymied me my sophomore year.
Do you have any idea how this knowledge affects a young, impressionable idiot?
Dantzig taught me that math is hard for everybody (everybody!), and the real fun of it— the real fun of anything difficult is that it’s difficult. Up until that point, high-school-me thought the fun part of problem-solving was after you solved it and you’ve gone on to playing hacky sack instead of solving problems. Dantzig threw a glass of cold water in my face — that’s just ridiculous! The real fun of problem-solving is all the thinking you get to do in the middle of it. The agitated sleep you get while wrestling a solution. The thinking-showers you need to keep your brain from overheating.
The rest of my story (while there remains quite a bit left to go) is that I went to college to get a degree in math. It was the hardest thing I could think to do, and the thing that I was apparently worst at. Now I spend my days working on other stuff I’m bad at, like programming things I don’t quite know how to program and the real fun of all of it is staring off into the distance as a result I don’t really know how to get to. I get to close my eyes and imagine the steps I might take. The experiments I might do to get there. The mistakes I’ll make and need to unmake.
Do something worth doing. Do something hard.