In physics and engineering there are some pretty strange equations, but for the most part they result from a logical build up of more elementary functions. On the other hand this……
1 / [sym]p[/sym] = ([sym]Ö[/sym]8 / 9801) [sym]S[/sym]{(4n)![1103 + 23369n] / (n!)(396)[sup]411[/sup] } n = 0 to infinity
……is beyond me.
Where could a formula like this have come from?
I know, I know, from someone’s brain, but HOW? Is there some kind of logical flow of thought that could produce this monstrosity? Or did it just pop out whole?
If that is one of Ramanujan’s formulas, it just popped out whole. His inventiveness and imagination awed, and continue to awe, other mathematicians, so it’s no wonder we mere laymen are overwhelmed.
Yeah, Ramanujan was a pretty smart dude. He just invented stuff like that, without knowing how. He was self-taught, and people are still trying to decipher his notebooks.
I have some experince dealing with math gurus(#1). From what I have seen I came to a conclusion that is probably un-supportable(SP?). IMHO, people who excel at math have a brain-wired talent for the field. Wheather that comes from genes or the environment, I don’t know. For whatever reason complex math to us mortals is easy to them. At the same time they do work really hard at what they do. So, maybe, talent + drive == genuis.
But I could be wrong.
Eric
#1. I grew up around PHD’s in Math and Physics. All recieved 4.0’s.(#2) #2. While doing tech support for Intuit I spoke to a guy who I thought was the dumbest MF I had ever encountered. He couldn’t even drag and drop on a Mac. We had to restart and while waiting I asked him what he did. He responded “Oh, I am a nerosurgeon(SP?) at John Hopkins”. D’oh, guess he wasn’t that stupid, just focused else where.
> Plus, Ramanujan was entirely self taught wasn’t he?
Well, no, actually. Here’s the way the life of Ramanujan is usually told:
He came from a poor Indian family (around the end of the nineteenth century). He taught himself math with no help from anyone else. He worked as a clerk. When he was in his mid-twenties, he wrote the English mathematician G. H. Hardy with a list of theorems he had proved. Hardy was so impressed by them that he arranged for Ramanujan to come to England to work with him.
Here’s the truth:
Ramanujan came from a Brahmin family, middle-class by Indian turn-of-the-century standards. He was already recognized in childhood as a genius. At 16 he entered university on a scholarship. He was so concentrated on math, however, that he neglected his other subjects and lost his scholarship. He was already working with other Indian mathematicians, and it was arranged that he would work as a clerk during the day while working on his math at night. Before he wrote Hardy, he had already published one mathematical paper. Another Indian mathematician told him that Hardy was probably the one person who was closest to the mathematical research he was doing, so he wrote him about his research, and Hardy was indeed impressed by his work.
Ramanujan was probably the best example of a mathematician having an intuitive sense of what kind of theorem was correct. He was thus able to produce hundreds of possible theorems, many of which he or someone else eventually proved to be correct. Many of his proposed theorems weren’t correct though. Non-mathematicians may not realize this, but there are two different sorts of skills needed for proving original theorems. One is a sort of intuition by which one can sense approximately what kind of theorem ought to be true and approximately how one goes about doing the proof. The other is a grasp of the details of actually doing the proof. It’s possible to be good at one skill and not so good at the other. Ramanujan is an example of a mathematician who had a good intuitive sense but who was poor at working through the details of a proof.
Maybe it’s divine inspiration. IIRC Ramanujan credited much of his skill to the goddess Shiva who, he says, visited him in his dreams.
Of course, if you don’t buy gods visiting people in their dreams and providing mathematical insight, then one might suppose the person’s brain was just wired right and their subconcious manifested its inspirations as visions of deities handing out mathematical wisdom.
I had heard that originally Hardy thought Ramanujan’s work was a joke as much of what he sent were previously proven theorems. Initially dismissing Ramanujan something nagged at Hardy and he had a second look and saw two things: A) The already proven theorems were proved by Ramanujan in a distinct and unique way (mostly a lack of training in the western formalism of math) and B) A few unique theorems no one had seen before. Hardy then realized he had a unique talent facing him and proceeded to send for Ramanujan to continue his studies in Europe.