I once made friends with a couple of graduate math students. They were accompanying visiting professors, at a year-long symposium at the Trumann Research Institute. I was still a naïve first year student and they began to initiate me in some of the lore of the world of mathematics. They taught me to appreciate the mathematical mind by acknowledging its rigorous preoccupation with the link between proof and knowledge. I heard about Georg Cantor, who founded modern set theory, and Kurt Godel, who proved the incompleteness theorems. Both of them were known for being at times out of touch with reality. Recently many people have also become familiar with John Forbes Nash Junior, Nobel Prize Laureate and subject of the book and synonymous film “A Beautiful Mind”.
At the same time the circle of mad mathematicians was getting bigger, due to the young Professor Saharon Shelah. He was making a name for himself at the symposium, for driving colleagues insane by solving dilemmas they had been working on for years. Sometimes the inspiration would take minutes and often solutions occurred to him while in or on the toilet.
My new friends introduced me to other prolific mathematicians. Among them Paul Erdos who was also renowned for his ability to overhear a discussion of a problem in an unknown field of mathematics and to come back with the solution in minutes.
In his infancy his father already started teaching him about prime numbers and infinite sets. His mother on the other hand spoiled him excessively to compensate for two children previously lost to scarlet fever. Consequently Erdos independently discovered the notion of negative numbers at the age of three, but was unable to butter his own toast until he was twenty.
He later coined small children as "epsilons", wives as "bosses" and God as the "Supreme Fascist". He also remarked that a mathematician was a “machine for turning coffee into theorems”.
Many of the problems he considered were easy to state but hard to prove. He simplified and extended Chebyschev’s proof that between any two whole positive numbers N and 2N (N’s multiple by 2), a prime number can always be found. He also showed that provided N is at least 7, then between N and 2N there are always at least two primes numbers.
Without a permanent academic appointment or home, Erdos travelled the world with two small suitcases, rarely staying anywhere for longer than a couple of weeks. So immense were his discoveries, that Mathematicians all over the world classified themselves by their "Erdos number". This has a value of “1”, if they collaborated directly with Erdos. It has a value of “2”, if they collaborated with someone who collaborated with him directly (and whose own Erdos number was therefore “1”), a value of “3” if they collaborated with someone whose own Erdos number was “2”, and so on.
My new friends introduced me to other prolific mathematicians. Among them Paul Erdos who was also renowned for his ability to overhear a discussion of a problem in an unknown field of mathematics and to come back with the solution in minutes.In his infancy his father already started teaching him about prime numbers and infinite sets. His mother on the other hand spoiled him excessively to compensate for two children previously lost to scarlet fever. Consequently Erdos independently discovered the notion of negative numbers at the age of three, but was unable to butter his own toast until he was twenty.
He later coined small children as "epsilons", wives as "bosses" and God as the "Supreme Fascist". He also remarked that a mathematician was a “machine for turning coffee into theorems”.
Many of the problems he considered were easy to state but hard to prove. He simplified and extended Chebyschev’s proof that between any two whole positive numbers N and 2N (N’s multiple by 2), a prime number can always be found. He also showed that provided N is at least 7, then between N and 2N there are always at least two primes numbers.
Once upon a time three professors went on holiday together to a faraway island, in the middle of the ocean. The first one was a Statistician, the second an Engineer, and the third a Mathematician. After their plane had landed they took a taxi from the airport to their hotel. On the way they observed the passing scenery, distant hills and wild vegetation, and generally enjoyed the overall beauty of nature. Suddenly they noticed something in a field not very far away. There were three animals that looked exactly like cows, except that curiously they were pink and had bright green spots. The Statistician immediately said, "In this country all the cows are pink with bright green spots”. "No," the Engineer responded, "in this country, we have just seen three cows that are pink with bright green spots". ”No, no," said the Mathematician, "in this country, we have just seen three cows, each of which has at least one side that is pink with bright green spots".