I is for...

Imaginary!

You know, like that friend you had who was always causing trouble when you were... what? Numbers? Oh, you mean the ones that mathematicians spent centuries ignoring!

It's true! I mean, for a long time mathematicians didn't want to admit that zero or negative numbers were useful either, but that's another topic entirely. So, back in ancient Greece, this guy, Heron of Alexandria, taught at the Musaeum (you may heard of their library, it was kind of a big deal). This guy was cool. As in, he was researching cybernetics back around 50 AD and invented the first vending machine. And he quite possibly discovered imaginary numbers.

G is for...

Galois!

Folks, let me tell you a little story, a story about a man of the mathematical cloth who lived way back in ancient France...

Okay, I'm not just going to rip off Stefanie, the Ballad of Galois, by the Klein Four Group... by the way, if you haven't heard their mathematics acapella, you're living 1 nth of your life, where n is inversely proportional to your love of math (for some n between 1 and positive infinity, obviously).

Evariste Galois was a radical mathematician, in the teenage mutant ninja turtles vernacular. At nineteen, the man had practically invented a new branch of mathematics (group theory, it's cool stuff), or at least laid the groundwork for future mathematicians to explore. We're still finding ways of applying his theories today, in everything from image processing to music theory to molecular orbits to the solution of a Rubik's Cube.

He was also a political activist, a Republican who spoke out against the reign of Louis Philippe in the early 1800s. He was imprisoned for his political views, denied admission to the most prestigious college for mathematics in France because his instructors couldn't follow his reasoning, and was expelled from the only academy that would take him after publicly criticizing the school's director.

And after all that, he was killed in duel over the honor of the woman he loved. So here's to Galois, the thinker, the lover, the fighter. We salute the memory of what you were, and lament the dream of what you might have been.

F is for...

Fermat's Last Theorem!

Even if you're not into math, you've probably heard of this one. Back in 1637, Pierre de Fermat conjectured that no three positive integers a, b, and c could satisfy the equation a^n + b^n = c^n for any integer value of n greater than two. He scribbled this conjecture in the margin of a copy of Arithmetica. Fermat went on to claim he had a proof for this, but it was too long to fit in the margin. By the time of his death, he had not produced this proof.

A few mathematicians tackled this problem over the years. Okay, more than a few. More like nearly every mathematician for the next 358 years. Finally, in 1995, Andrew John Wiles managed to prove it... his proof was over 100 pages long, took seven years of research, and made use of techniques that did not exist in Fermat's time. Wiles was knighted for his contribution to mathematics.

I remember my first encounter with the Last Theorem. Back in high school, in the first linear algebra class I'd ever taken, on the first day of class, we were asked disprove the theorem as homework, the equation scrawled on the whiteboard in the last few moments of class as if it was no big deal. Now, back in those days my Google-fu was weak and my work ethic was strong, so I went at it with a gusto. And I arrived at class the next day feeling utterly despondent, having found exactly zero solutions and having no idea why. Oh math... I think that's the day I fell in love with you.

I feel like I should talk about Fourier analysis and how it can do anything if you're clever enough, or Fibonacci numbers and how they're already doing everything whether you're clever or not... but instead, I'll just ask this: do you think Fermat had a solution? Or was he just another mathematical rebel without a cause (more on that tomorrow)?