Tag Archives: greene’s theorem

Goin’ Green


Today we learned about Green’s Theorem. So who is this Green fellow?

[Edit: Okay, originally I was just going to talk about Green ‘cause while Green’s Theorem is just a special case of Stokes’ Theorem, we haven’t learned the latter yet. But turns out both Green and Stokes are named George and that’s hilarious, so we must press on and speak of both.]

So who are these two fellows?

George Green lived from 1793 – 1841. Like what seems to be a large proportion of mathematicians at the time, he was British. He lived in Nottingham. There are two reasons why these are interesting facts:

1. Nottingham, at the time, wasn’t really burning it up intellectually. Only about 25-50% of children received any sort of education, and Greene himself attended an academy for only one year when he was 8. It took him until age 36 to gather enough money (and free time) to afford a higher education (and he died when he was 47, so unfortunately he didn’t have too much time to enjoy it).

2. Despite the setbacks as far as formal education goes, Green was a very smart dude. He was largely self-taught (obviously) and once he finally got to Cambridge he pretty much kicked ass. What’s most interesting, though, are his studies in math. Historians aren’t exactly sure how Green reached the understanding of calculus that was necessary for developing his theorem. He likely used the “Mathematical Analysis,” which was a form of calculus Leibniz developed, but this was during the post Newton-Leibniz controversy over calculus and England pretty much forbade the use of everything calculus-related that originated from Leibniz. ‘Cause they had Newton’s calculus. Never mind that Newton’s notation was inferior and didn’t lend itself to the applications/developments that Leibniz’ notation did and that forbidding the better notation/methods from the England set the country back in mathematical advancements for like a century.* But somehow Green got a hold of it and made his improvements and came up with his theorem and was generally awesome. (LEIBNIZ POWER! Okay, I’m done).

And what about George Stokes? Who was he? Stokes’ life overlapped the end of Green’s life (1819 – 1903). Stokes was Irish and rocked the fields of fluid dynamics, optics, and mathematical physics. He actually did quite a variety of things, so I’m just going to list a few.

  • He came up with a way to calculate the terminal velocity of a sphere falling in a viscous fluid (Stokes’ Law!)
  • He expressed a mathematical description of rainbows using a divergent series, something that wasn’t really understood just yet by most.
  • He was secretary and then president of the Royal Society.
  • He wrote a paper in which he tried to describe the variation in gravity across the earth’s surface.
  • And, of course, Stokes’ Theorem in math.


Sorry, I’m going to keep doing these little mathematician snippets until…well, until I feel like stopping. So ha.

*I’m not bitter.