My Brain is Open

“My Brain is Open,” he announced through the phone as it was picked up by his colleague on the other side.

The colleague knew the voice, for he probably had a number 1, already — or soon it would be number 1.

Erdős number of 1, of course.

You see, Paul Erdős was interested in searching for proofs from THE BOOK.

No, not the bible.

THE BOOK.

Paul Erdős, Architect Rational,  (pronounced Err-dish; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory.

He had his own idiosyncratic vocabulary: he spoke of “The Book“, an imaginary book in which God had written down the best and most elegant proofs for mathematical theorems. Lecturing in 1985 he said, “You don’t have to believe in God, but you should believe in The Book.” He himself doubted the existence of God, whom he called the “Supreme Fascist” (SF). He accused the SF of hiding his socks and Hungarian passports, and of keeping the most elegant mathematical proofs to himself. When he saw a particularly beautiful mathematical proof he would exclaim, “This one’s from The Book!“. This later inspired a book entitled Proofs from THE BOOK. [Wikipedia, revised]

Paul was a Unique Eccentric in an eccentric field: mathematics.  He had no interests outside mathematics. His world possessions could fit in one suitcase, since he had no home.  He gave away everything else, including money. He had no wife or children.  In 1938, he began his peripatetic life style, he had accepted his first American position as a scholarship holder at Princeton University. At this time, he began to develop the habit of traveling from campus to campus. He would not stay long in one place and traveled back and forth among mathematical institutions until his death.

Rationals are wont to attribute to themselves the understanding, comprehension, or insight into the dimensions of whatever problems they are currently working on. Not just partial insight will do.  The Rationals task themselves to achieve a complete grasp of dimensions, for without it their course of action is fraught with error. And error, in their view, leads inevitably and inexorably to failure, which of course Rationals avoid as best they can. Surely those of other temperament would, if they could, achieve insight, but it’s no big deal for them.  After all, they have more important things to be concerned about, so if their insight is less than total, they will settle for less. Not the Rationals. Too much is at stake to settle for less. Especially, without insight they cannot acquire the competence, the knowledge, and the discernment that are necessary for advancement in their chosen field of science, technology, research, or development.

They [Designers, Architects] regard most discussions as a search for understanding, and so try to eliminate inconsistencies, no matter who is guilty of them. It is burdensome for them to listen to nonsense, even in casual conversation, without pointing out the speaker’s error, and this makes communication with them an uncomfortable experience for those who come in contact with these rare individuals. [Personology page 261]

Paul was naturally inclined to mathematics from a very early age.

Paul Erdős was born in Budapest, Hungary on March 26, 1913. His parents were both Jewish mathematicians from a vibrant intellectual community. His fascination with mathematics developed early—at the age of three, he could calculate how many seconds a person had lived. Both of Erdős’s parents were high school mathematics teachers, and Erdős received much of his early education from them. Erdős always remembered his parents with great affection. At 16, his father introduced him to two of his lifetime favorite subjects—infinite series and set theory. During high school, Erdős became an ardent solver of the problems proposed each month in KöMaL, the Mathematical and Physical Monthly for Secondary Schools. Erdős later published several articles in it about problems in elementary plane geometry. In 1934, at the age of 21, he was awarded a doctorate in mathematics. [Wikipedia]

Because of his prolific output, friends created the Erdős number as a humorous tribute. An Erdős number describes a person’s degree of separation from Erdős himself, based on their collaboration with him, or with another who has their own Erdős number. Erdős alone was assigned the Erdős number of 0 (for being himself), while his immediate collaborators could claim an Erdős number of 1, their collaborators have Erdős number at most 2, and so on. Approximately 200,000 mathematicians have an assigned Erdős number, and some have estimated that 90 percent of the world’s active mathematicians have an Erdős number smaller than 8 (not surprising in light of the small world phenomenon). Due to collaborations with mathematicians, many scientists in fields such as physics, engineering, biology, and economics have Erdős numbers as well.

Oh yes, I have an Erdős number of 3 — Not, that I notice or care 😉 !?

“God may not play dice with the universe, but something strange is going on with the prime numbers.” — Paul Erdős

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