The four-year-old who discovered negative numbers

If the Martians had contact with Earth during Pál Erdős’ lifetime, Erdős would have had every chance of being appointed ambassador representing our planet. Extraterrestrials would certainly appreciate his earthly intelligence. Pál Erdős spoke the language of the universe, number theory, fluently and intelligently.

Pál Erdos on the closing day of the commemorative conference organized to celebrate the centenary of the mathematician’s birth in the building of the Hungarian Academy of Sciences on July 5, 2013 Photo: MTI / Tibor Illyés

It is also no coincidence that Erdos did not lose sight of the imperfections of life. He had no wife, no children, no home, no credit cards, no job, not even a spare pair of shoes, in fact he had nothing in the world except a handbag with a few clothes in it and a notebook. He wasn’t picky about food either, if it wasn’t for the lack of black coffee.

A mathematician is a machine that turns coffee into theorems

He said. Erdős devoted his life to the service of mathematics.

Mathematics is the most frightening science for many. Most people with some education can trace the explanation of the Big Bang or some genetic problem, but their arithmetic interests are limited to navigating their bank statements. On the other hand, mathematicians consider mathematics to be the purest creation of the human soul, and many of them respected Pal Erdos as the best practitioner of this science in our century.

When Erdös arrived in a city where he usually lectured, he called one of his fellow mathematicians and declared:

My mind is here in the city.

One would think he was considered an uninvited guest when he stumbled across a place like that, but there is no doubt about it, the hosts considered his brain a public treasure and felt it was their collective duty to look after it. They housed him, took care of his meals, and even washed his clothes. In Pál Erdős, the cosmopolitan Jew is reincarnated. His country, Hungary, moaned under tyrants for the most part during his lifetime. Many family members of Germans were murdered during Hitler’s time. Erdos himself returned the favor of his friends who took care of his daily needs with brilliant intellectual creations built from numbers, charts and logic.

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Capture the spy.
Pal Erdos (left) as a suspected spy arrested in the US, 1941. Photo: Getty Images/New York Daily News Archive/NY Daily News
[…] Pál Erdős’ parents were also mathematicians, so they were probably happy when, at the age of four, their son announced that he had discovered negative numbers. As his twentieth birthday approaches, he makes discoveries about prime numbers. Prime numbers are only divisible by themselves and by 1. The raw number, for example, is 1913, the year of Erdos’s birth, and he was 83 years old – that’s how old he was when he died of a heart attack in Warsaw, where he was attending a sports conference. Using a more elegant approach, Erdős helped give new shape to a theory of prime numbers that had previously been developed by a mathematician. At the time, this fact of arms belied the importance of the construction of the Panama Canal, which made bypassing South America unnecessary.

This sort of thing is neat, but do the thousand or more studies associated with Pál Erdős’ name represent any practical value? He himself did not strive for practical use. He stated that it was sufficient for the evidence to be “extremely beautiful”. No matter how abstract scientific mathematics may be, it still appears in one way or another wherever it can be used. For example, combinatorics, a branch of mathematics discovered by Erdős, can be used to calculate the number of squares needed to cover irregular areas. His work on graph theory is used in the design of communication networks.

Erdös did not hesitate to put his unusual left hemisphere at the service of the many young mathematicians just beginning their careers. The promising mathematician marked the location of the seedlings with epsilon, the Greek letter used to describe small quantities in mathematics, but the epsilon could be called Uncle Paley. Erdos made trouble for them and rewarded them with a few hundred dollars if they worked it out. In this way, he distributed his modest income from lectures and scholarly prizes (among other things, he received the Israel-established Wolf Prize, an honor in mathematics with the same status as the Nobel Prize in other scientific fields). One of his colleagues compared Pál Erds to a bee, which tirelessly traveled around the world and fertilized various fields of mathematics.

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