The Man Who Loved Only Numbers

Paul Erdos was an amazing and prolific mathematician whose life as a world-wandering numerical nomad was legendary. He published almost 1500 scholarly papers before his death in 1996, and he probably thought more about math problems than anyone in history. Like a traveling salesman offering his thoughts as wares, Erdos would show up on the doorstep of one mathematician or another and announce, "My brain is open." After working through a problem, he'd move on to the next place, the next solution.

Hoffman's book, like Sylvia Nasar's biography of John Nash, A Beautiful Mind, reveals a genius's life that transcended the merely quirky. But Erdos's brand of madness was joyful, unlike Nash's despairing schizophrenia. Erdos never tried to dilute his obsessive passion for numbers with ordinary emotional interactions, thus avoiding hurting the people around him, as Nash did. Oliver Sacks writes of Erdos: "A mathematical genius of the first order, Paul Erdos was totally obsessed with his subject--he thought and wrote mathematics for nineteen hours a day until the day he died. He traveled constantly, living out of a plastic bag, and had no interest in food, sex, companionship, art--all that is usually indispensable to a human life."

The Man Who Loved Only Numbers is easy to love, despite his strangeness. It's hard not to have affection for someone who referred to children as "epsilons," from the Greek letter used to represent small quantities in mathematics; a man whose epitaph for himself read, "Finally I am becoming stupider no more"; and whose only really necessary tool to do his work was a quiet and open mind.

Hoffman, who followed and spoke with Erdos over the last 10 years of his life, introduces us to an undeniably odd, yet pure and joyful, man who loved numbers more than he loved God--whom he referred to as SF, for Supreme Fascist. He was often misunderstood, and he certainly annoyed people sometimes, but Paul Erdos is no doubt missed. --Therese Littleton

Thoughts and Quotes while reading:

"Erdos's motto was not "Other cities, other maidens" but "Another roof, another proof" (p 6)

"A mathematician," Erdos was fond of saying, "is a machine for turning coffee into theorems" (p 7) Which just reminds me so much of Jeff Haag.

"His language had a special vocabulary -- not just "the SF" and "epsilon" (children) but also "bosses" (women), "slaves" (men), "captured" (married), "liberated" (divorced), "recaptured" (remarried), "noise" (music), "poison" (alcohol), "preaching (giving a mathematics lecture), "Sam" (the United States), "Joe" (the Soviet Union). When he said someone had "died," Erdos meant that the person has stopped doing mathematics. When he said someone has "left," the person had died. (p 8)

"In mathematics, Erdos's style was one of intense curiosity, a style he brought to everything else he confronted. Part of his mathematical success stemmed from his willingness to ask fundamental questions, to ponder critically things that other had taken for granted." (p 21) This reminds me so much of Larry Schlussler, to ask the questions that everyone else takes for granted, and for which most people don't have a good answer. And when they do come up with an answer, it gives everyone the chance and reason to grow.

I found it fascinating that you can create perfect numbers from Mersenne primes with this formula: (2ⁿ-1)(2ⁿ⁺-1), for any number n such that (2ⁿ-1) is a Mersenne prime.
(p 47)
"Ramsey theory takes its name from Frank Plumpton Ramsey, a brilliant student of Bertrand Russell, G. E. Moore, Ludwig Wittgenstein, and John Maynard Keynes..." (p 51) My goodness, can you imagine being a student of those greats? Keynes, who we get Keynesian economics, Russell, the mathematician and philosopher, and while I don't know much of Moore and Wittgenstein, now I want to!

I need to look more into how Godel proved "that any formal mathematical system robust enough to include the laws of arithmetic would be unable to prove its own consistency" (p 111). And I love how it changed the Principia Mathematica from a consistent mathematical truth, into a historical curiosity.

On p 114 it is discussed how triangles, in the real world, don't really have angle sums of 180^º, the angle sums are a bit less, maybe 179.999. In physics, I think cosmos, and modern physics, we discussed how certain mathematical truths seem to fall apart at the very small, and the very large, and how, on non-flat spaces (spheres or cylinders) triangle angle sums change as well! So take that Euclid, your mathematics aren't consistent in all spaces or places.

So the topic of Unit Fractions came up, and I just wanted to copy down the formula here, so I can play with it later:

Which it says you can applied ad infinitum. Interesting, right?!

There is a theory on p 182 about pseudo-primes which is based off the idea that a number n is prime if the expression 2ⁿ - 2 is a multiple of n. So 5 is prime because 2⁵ - 2 is 30, which is divisible by 5. Interesting again. Maybe I'll play with some more numbers. The test fails, at the number 341. Maybe I'll write a quick program, that could test them side by side, and determine if true.

You can find the sum of all the numbers from 1 to n using this formula: (n²+n)/2

The question of e came up the other day and I didn't remember where it came from. Formula here for posterity:

So Duncan's father and I got into a discussion about game shows, and whether when faced with 3 doors to choose from, if once you make you choice, the host gets rid of one of the doors, and lets you choose again, should you change your choice? I feel solace in the fact that it threw off Erdos, as much as it seems to have thrown off me. See the table below, which exhausts the options and choices: