“The product of mathematics is clarity and understanding. … The real satisfaction from mathematics is in learning from others and sharing with others. “
To put it lightly, this guy was pretty freaking smart. At one point in the 70’s, professors advised students not to go into Thurston’s line of mathematics after college, because he was solving too many theorems for there to be any work left for them to do by the time they graduated. First off, he worked with geometric things called foliations, which basically have to do with these things called manifolds, which have to do with these other things called tangent bundles (see what I mean? his EARLY work can’t even be understand by someone without a PhD). Thurston’s shining moment was probably his geometrization conjecture, which led to many other conjectures in math. The conjecture revolved around 3-manifolds, which are topological figures where each point is 3 dimensional, and the fact that they can be broken down into pieces, which each follow one of the eight geometric structures.
Whatever that means. (Shout out to this article for breaking the conjecture down to at least a little bit of common english!)
“We are servants rather than masters in mathematics.”
He was also a brainiac, a French one at that. He solved the quintic equation, which, according to Wikipedia, looks like this:
I’m going to have to agree with Charles here, and admit that this equation pretty much has the upper hand to me in a math fight.
“To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession.”
Blaise was actually a genius. He dabbled in philosophy, religion, science, and mathematics. By the age of 16, he had already published a paper on conics. He created and manufactured his own calculation machine, is said by his sister to have “taught himself geometry”, and worked with probability theory.
“God exists since mathematics is consistent, and the devil exists since its consistency cannot be proved.”
Besides being a pretty clever guy, Hermann casually connected mathematics with theoretical physics. He basically took someone else’s equations on electromagnetic fields, and connected it with geometry by way of describing it’s geometric properties in space-time. This opened up a lot more dialogue in the field of differential geometry. Hermann also worked a lot with group theory, specifically talking about atoms through the view of groups in matrices. This breakthrough formed quantum theory.
You go mathematicians, paving the way for math-lovers everywhere!