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Cushing your luck: properties of randomly chosen numbers

Long-time Aperiodical muse David Cushing has made a bet with us that he can give us an interesting post every Friday for the next ten weeks. Every week that he sends a post, we buy him a bar of chocolate. Every week that he doesn’t send us a post, he buys us a bar of chocolate. For his first trick, David is going to do some unnatural things with the natural numbers.

The greatest common divisor (gcd) of two or more integers is the greatest integer that evenly divides those integers. For example, the gcd of $8$ and $12$ is $4$ (usually written as $\gcd(8,12)=4$). Two integers are called coprime (or “relatively prime”) if their gcd is equal to $1$.

A reasonable question to ask is,

Given two randomly chosen integers $a$ and $b$, what is the probability that $\gcd(a,b)=1$?

Erdős Centennial conference

The Hungarian Academy of Sciences, the Alfréd Rényi Institute of Mathematics, the Eötvös Loránd University and the János Bolyai Mathematical Society  have announced a conference dedicated to the 100th anniversary of Paul Erdős from 1st-5th July 2013 in Budapest, Hungary.

Porl Air-dursh: a public service announcement

Since we’re all talking and writing about Paul Erdős today, I just thought I’d make a little post clearing up how to write, and how to say, his name.

f(Erdős) = 100

Today is the 100th anniversary of the birth of Paul Erdős, or as most people would call it, Erdős’ 100th birthday. So, Happy Birthday Paul. And if you’ve never heard of him, let’s see what people at his birthday party are saying about the Man Who Loved Only Numbers. Please note: all birthday parties are strictly fictional.

Probably the greatest mathematician of the twentieth century, Paul Erdős … was so eccentric that he made Einstein look normal. He was 11 before he ever tied his shoes, 21 before he ever buttered toast, and died without ever boiling an egg. Erdős lived on the road, traveling from conference to conference, owning nothing but math notebooks and a suitcase or two. His life consisted of math, nothing else.

– Clifford Goldstein, in The Mules That Angels Ride (2005), p. 125

Saharon Shelah has written more than 1000 papers

From David Roberts on Google+:

Saharon Shelah, the well-known Israeli set-theorist and logician, has passed 1000 papers!

The page was updated with a rush of almost twenty papers, taking him over the line. Notably, paper #1000 is not listed. +Richard Elwes and I were wondering what the topic of this (rather artificial) milestone paper would be.

Every now and then, when finding a citation for a paper, you come across one of these giants of prolificacy and their unreasonably long lists of publications. It makes me wonder why I don’t just give up and let them discover all the maths.

Shelah was the first recipient of the Erdős Prize and he is certainly following in the great man’s footsteps – though he’s still got a way to go before he can think about beating Erdős’s approximately (can’t blame him for losing count) 1525 publications.