Who wants to be a millionaire

In Italy, as in the rest of the world, no one cares about numbers, unless they are followed by the symbol of the local currency. In our case €.

Punctually, any simple questions about numbers not dealing with money, soon becames a hard number’s problems:

Italy:

Row: you are the 13th (counting from the head) and 13th (counting from the tail) on a row.

Multiplication: The results of the multiplication of all the digits you can find on a mobile-phone.

Triangle: How many heigth has a triangle?

Rest of the world:

How much daylight…

What is 11 multiplied by 12? local currency

Erdos vs. Selberg

We are going to tell a strange yarn revolving around Erdos numbers  and an introverted Scandinavian mathematician: Atle Selberg.

When Nazi Germany occupied Norway, he remained isolated from the rest of the scientific community . In those years, he gained a demonstration of the Dirichlet’s Theorem  (without the RH) and he approached a demonstration of the theorem of prime numbers of Gauss.

In his solitude Selberg had never published with anyone, nor ever discussed his ideas with other mathematicians. But ones upon a time… he  became a friend of Paul Turan, and Atle revealed him some of their results. Turan, for misfortune of Selberg, was a great friend of Erdos, and inevitably the ideas of Atle reached the ears of the hungarian mathematician.

Once, Erdos’ friendship  saved the Turan’s lives. Indeed, in 1945, the mathematician was caught by Russian troops in Budapest, recently released, in possession of many sheets containing strange formulas and codes, that seemed Nazi coded instructions! Turan managed to survive only because the good Erdos testified for him.

Came back to us. Erdos,  barely aware of Atle’s results, used them to prove a generalized version of Bertrand’s postulate. Selberg was happy: it was the missing card to prove the theorem of prime numbers!

Selberg confided his result to Erdos, who immediately began to spread the notice in the world, pressing Atle for a four hands article. In a short time, thanks to an extensive network of correspondence and conferences, the news of the demonstration came in every faculties of mathematics in the world. Unfortunately, however, someone began to say that the theorem was proved by Erdos. Once, indeed, a mathematician  said to Selberg, ignoring who it was: “Have you heard? Erdos and a scandinavian mathematician prooved the theorem of prime numbers! ”

It was the spark that made the vase overflow … Selberg locked himself again in the solitude, hating Erdos for the rest of the life.

Throughout Selberg has collaborated once with another mathematician, signing with him an article. He was Saradavam Chowla, who had Erdos number of 1.

Thus Selberg obtained EN 2.

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Erdos numbers – part 1

This is the first of a series of articles about Erdos’ numbers (EN).  We will understand what they are, then we’ll deal with not-mathematics versions, the concept of scale-free network, and some amusing anecdotes.

Paul Erdos was a Hungarian mathematician. A strange person, but a genius. He worked in many different fields: combinatorics, graph theory, number theory, analysis, numerical, …

Thanks to his way of doing and his eccentricity, Paul is certainly one of the most popular mathematics of the twentieth century (he died in the nineties). I talked with italian mathematicians who met him during some conferences in Italy and they have reported that it was a wonderful person. An applicant’s sentence has now become, in our environment, a real say, and even the summary of the mathematician lifestyle:

“A mathematician is a device for turning coffee into theorems.”

After Euler, Erdos is the mathematician who has produced more publications: it is estimated that 511 different mathematicians have had the honor to sign an article with him.

We are not going to explore his main results, concentrating ourselfes on the Erdos’ numbers. The sequence counts the publication distance from the great mathematician. Naturally Erdos is awarded of EN 0, while the 511 mathematicians who have published with him has EN 1. In the same way, mathematicians who have published with at least one of these 511 have EN 2, and so forth. Currently we know that more than 8000 people may have Erdos number of 2.

Of course there are mathematicians in the past (prior to Erdos) owning an EN, eg Frobenius (the morphisms one) EN is 3, Dedekind (the sections one) EN is 7, and it seems that Gauss and Euler (we don’t need to introduce them) have an EN too.

The baseball player Hank Aaron was one of the 511, having been the subject of a mathematical study and having signed with Erdos a baseball ball.

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