The Man Who Knew InfinityDVD - 2015
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Ramanujan to Hardy: "An equation for me has no meaning unless it expresses a thought of God"
Hardy: P(4) = 5. Now, all that means is there are five ways to add up the number 4. 1 + 1 + 1 + 1, 3 + 1, 2 + 1 + 1, 2 + 2, and 4.
Littlewood: Seems simple enough.
Hardy: Yeah. So it does. But when you raise the number of P(100), there are 204,226 different combinations. Major MacMahon did it by hand. Took him weeks. And now he thinks he can figure out a formula. Plug in the number, any number, and out comes the number of partitions. Like magic.
Littlewood: I take it you have tried to crack this one before?
Hardy: It's considered impossible. Unsolvable. A bloody rabbit hole mystery of the universe.
Littlewood: Until now?
Hardy: You see, I'm what you call an atheist.
Ramanujan: No, sir. You believe in God. You just don't think He likes you.
Hardy: Let me ask you something. Why do you do it, any of this?
Ramanujan: Because I have to. I see it.
Hardy: Like Euler. Form for its own sake. An art unto itself. And, like all art, it reflects truth. It's the only truth I know. It's my church. And you, just as Mozart could hear an entire symphony in his head you dance with numbers to infinity. But this dance, this art, does little to endear us to certain factions who see us as mere conjurors. So if we are going to challenge areas of mathematics that are so well trod, we cannot afford to be wrong.
Hardy: Life for me is... It's always been mathematics.
Ramanujan: You wanted to know how I get my ideas.
Ramanujan: My God. Namagiri. She speaks to me. Puts formulas on my tongue when I sleep, sometimes when I pray. Do you believe me?
Hardy: But I don't believe in God. I don't believe in anything I can't prove.
Ramanujan: Then you can't believe in me. Don't you see? An equation has no meaning to me unless it expresses a thought of God. Maybe it is better that we just remain what we were.
Hardy: When I was at school, I remember one of my chaplains saying,"You know God exists
because He's like a kite, "and you can feel the tug on the string and know that He's up there." I said, "What if there's no wind and the kite can't fly?" No, I... I can't believe in God. I don't believe
in the immemorial wisdom of the East, but I do believe in you.
Hardy's speech in nominating Ramanujan as a Cambridge Fellow, first ever Indian (part 2 of 2:)
Well, despite everything in my being set to the contrary, perhaps he is right. For is this not exactly our justification for pure mathematics? We are merely explorers of infinity in the pursuit of absolute perfection. We do not invent these formulae, they already exist and lie in wait for only the very brightest of minds, like Ramanujan, ever to divine and prove. So, in the end, I have been forced to consider, who are we to question Ramanujan, let alone God? Thank You.
Hardy's speech in nominating Ramanujan as a Cambridge Fellow, first ever Indian (part 1 of 2:)
So, now we see the work on partitions and the enormous breakthrough that has been achieved. All this, mind you, by a man whose limitations of knowledge when I met him were as startling as was its profundity. Opinions may differ as to the importance of Ramanujan's work and the influence it may or may not have on the mathematics of the future, but one gift it does show
is its profound and invincible originality. Mr. Littlewood once told me that "every positive integer is one of Ramanujan's personal friends." I believe this to be true. He told me that an equation for him had no meaning unless it expressed a thought of God.
1729. No, Hardy. It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways. (Known as the Hardy–Ramanujan number: 1729 = 1^3 + 12^3 = 9^3 + 10^3, from wikipedia.)
Hardy remembering Ramanujan:
It is difficult to put into words... What I owe Ramanujan. His originality has been a constant source of suggestion to me ever since I first met him. And his death is one of the worst blows I have ever felt. But now I say to myself when I'm depressed, and I find myself forced to listen to tiresome and pompous people, "Well, I've done something you could never have done. "I have collaborated
with both Littlewood and Ramanujan "on something like equal terms."
SummaryAdd a Summary
The tale of a relationship between a young Indian mathematics genius, Ramanujan, and his tutor at Cambridge University, G.H. Hardy, in the years before World War I. Through their eyes the reader is taken on a journey through numbers theory.
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