eiθ = cos θ + i sin θ? Ha ha ha...

In which Ludwig tries to find jokes rooted in serious mathematics

It's been a while since we did a post on mathematics. A young hedonist in New York posted a delightful piece about mathematical encounters on Broadway and 102^nd, and this has inspired us to dust off a few items.

Serious things first. Most Indians have heard of G. H. Hardy of course, as Srinivasa Ramanujan's correspondent, mentor, teacher, student, and friend. Robert Kanigel's biography of Ramanujan necessarily contains pages and pages of engrossing information about Hardy. The great man was an atheist, his politics was left of centre and he was a sort of maniacal cricket buff. One year his New Year resolutions were

1. Prove the Riemann hypothesis
2. Make 211 not out in the fourth innings of the last test match at the Oval [which was something like hitting a grand slam home run while behind by three runs in the ninth inning of the World Series' final game]
3. Find an argument for the nonexistence of God that will convince the general public
4. Be the first man at the top of Mt. Everest
5. Be proclaimed the first president of the U.S.S.R, of Great Britain, and Germany.
6. Murder Mussolini

Kanigel's book has another anecdote which is equally entertaining.

Another story neatly combined his love of cricket, his pleasure in the sun, his warfare with God, and his madcap bent. One of his collaborators, Marcel Reisz, was staying at the place Hardy shared with his sister in London. Hardy ordered him to step outside, open umbrella clearly in view, and yell up to God, "I am Hardy, and I am going to the British Museum." This, of course, would draw a lovely day from God, who had nothing better to do than thwart Hardy. Hardy would then scurry off for an afternoon's cricket, fine weather presumably assured.

What can you say about a man whose cricket teams include "God(F), God(S), God(HG)" (F = Father, S = Son, HG = Holy Ghost!)? His mantelpiece sported photographs of Einstein, Jack Hobbs and Lenin. Later in life, when he found his mathematical powers on the decline, he wrote A Mathematician's Apology. This "book of haunting sadness" [C. P. Snow] is actually a long essay about the uses of mathematics, the motivations of mathematicians (and indeed anyone engaged in creative work), the aesthetics of mathematics, and a reflection of his own decades long engagement with the field.

(i)

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. ... The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

(ii)

The best mathematics is serious as well as beautiful--'important' if you like, but the word is very ambiguous, and 'serious' expresses what I mean much better.

(iii)

I still say to myself when I am depressed, and find myself forced to listen to pompus and tiresome people, "Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms."

The entire essay is available here for free download. Makes for a very thought provoking afternoon's reading.

Anyway, this was supposed to be a post about jokes rooted in serious mathematics. Here's one that we posted once already, but doesn't lose anything in a retelling. It is paraphrased from Simon Singh's Fermat's Last Enigma.

Grafitti on New York City subway wall:

xⁿ + yⁿ = zⁿ

There is no value of n>2 for which the above is true. I have found a truly remarkable proof of this, but my train is coming and I have to go...

Zeno of Elea came up with variations of his paradox, and these have given rise to possibly multiple funnies. We present a couple.

The dichotomy paradox leads to the following mathematical joke. A mathematician, a physicist and an engineer were asked to answer the following question. A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them every ten seconds (i.e., if they are distance d apart at time 0, they are d/2 at t = 10, d/4 at t = 20, d/8 at t = 30, and so on.) When do they meet at the center of the dance hall? The mathematician said they would never actually meet because the series is infinite. The physicist said they would meet when time equals infinity. The engineer said that within one minute they would be close enough for all practical purposes.

Another one is actually a cartoon, which we've been unable to unearth. So we'll just tell the joke.

[Scene: City street, ancient Greece. Two philosophers (bearded), run into each other.]
Phil I: Hey, it seems Zeno didn't come to work today...
Phil II [chuckles]: Yeah, wait till you hear his excuse!

That one is truly brilliant, we thought.

Any others?