Erdös numbers have been a part of the myth of
mathematicians for many years. Due to the very high frequency of
interdisciplinary collaboration in science today and due to the fact that mathematics
is basic to science disciplines, very large numbers of non-mathematicians also
have finite Erdös numbers. Not only that; many linguists, political scientists,
and Nobel laureates have finite (less than 8) Erdös numbers.
The Erdös number is the "collaborative
distance" 0, or 1, or 2, or 3, or 4, or … between a person and
mathematician Paul Erdös, as measured by authorship of mathematical papers. It
was created by friends as a comical accolade to the massive contribution of Erdös
to mathematics. Erdös is considered as was one of the terrific modern writers
of mathematical papers, and has become well-known in scientific circles as a
tongue-in-cheek measurement of mathematical celebrity. Paul Erdös is the one
person having an Erdös number of zero. For any authors other than Erdös, if the
author has coauthored with Erdös or an author of Erdös number n a number, then
that author's Erdös number is one more than n. Lower the value of n, the author
is more closure to Paul Erdös’s mathematical ability.
Paul Erdös was a dominant and nomadic Hungarian
mathematician. He spent a portion of his life living out of a suitcase and
writing papers with those scholars willing to give him room and board. He
published more papers during his life (at least 1,400) than any other
mathematicians in history including the Swiss mathematician and physicist
Leonhard Euler who is considered the father of Calculus. Paul Erdös was born in
In 2004, Bill Tozier, a researcher with an Erdös number
of 4, offered the chance for collaboration to attain an Erdös number of 5 in an
auction on eBay. The final bid was $1,031, though apparently the winning bidder
had no intention to pay. The winner who already had an Erdös number of 3
considered it a "mockery", and said "papers have to be worked
and earned, not sold, auctioned or bought". It is teasingly said that
American baseball player Hank Aaron has an Erdös number of 1 because he
autographed a baseball with Erdös when
Krishnaswami Alladi, Sarvadaman Chowla, Hansraj Gupta,
Renu Laskar, M. Ram Murty, V Kumar Murty, SB Rao, Navin Singhi and Mathukumalli
V Subbarao earned Erdös number 1. There are many (25 to 50) mathematicians of
Indian origin who have Erdös number 2. There will be no more mathematicians
with Erdös number 1 while Professor Paul Erdös died "in action" of a
heart attack on 20 September 1996, at the age of 83, while attending a
conference in Warsaw, Poland.
There are other funny numbers similar to Erdös number.
The “Bacon number” is an application of the same idea to the movie
industry, connecting actors that appeared in a film together to the actor Kevin
Bacon. Although this is the most well-known "number", it was
conceived of in 1994, 25 years after the Erdös number spin off. The lowest
known Erdös-Bacon is 3 for Daniel Kleitman a mathematics professor at
Massachusetts Institute of Technology (MIT) who acted in 1997 Oscar awarded
movie “Good will Hunting”; Kleitman’s Erdös number is 1 and his Bacon number is
2.
Reference may also be made to: http://www.oakland.edu/enp/
From the
Internet
http://en.wikipedia.org/wiki/Erd%C5%91s_number
If
Erdös wrote around 1,400 mathematical articles in his
lifetime, mostly co-written. He had 511 direct collaborators; these are the
people with Erdös number 1. The people who have collaborated with them (but not
with Erdös himself) have an Erdös number of 2 (8,162 people as of 2007), those
who have collaborated with people who have an Erdös number of 2 (but not with
Erdös or anyone with an Erdös number of 1) have an Erdös number of 3, and so
forth. A person with no such coauthorship chain connecting to Erdös has an Erdös
number of infinity (or an undefined one).
Erdös's vocabulary include:
·
Children were
referred to as "epsilons" (in mathematics, particularly calculus, an
arbitrarily small positive quantity is commonly denoted by that Greek letter
(ε));
·
Women were
"bosses";
·
Men were
"slaves";
·
People who stopped
doing math had "died";
·
People who
physically died had "left";
·
Alcoholic drinks
were "poison";
·
Music was
"noise";
·
People who had
married were "captured";
·
People who had
divorced were "liberated";
·
To give a
mathematical lecture was "to preach" and
·
To give an oral
exam to a student was "to torture" him/her.
Erdös
problems
Throughout his career, Erdös would offer prizes for
solutions to unresolved problems. These ranged from $25 for problems that he
felt were just out of the reach of current mathematical thinking, to several
thousand dollars for problems that were both difficult to attack and
mathematically significant. There are thought to be at least a thousand such
outstanding prizes, though there is no official or comprehensive list. The
prizes remain active despite Erdös's death; Ronald Graham is the (informal)
administrator of solutions. Winners can get either a check signed by Erdös (for
framing only) or a cashable check from Graham.
Perhaps the most notable of these problems is the Erdös
conjecture on arithmetic progressions:
If the sum of the reciprocals of a sequence of integers
diverges, then the sequence contains arithmetic progressions of arbitrary
length.
If true, it would solve several other open problems in
number theory (although one main implication of the conjecture, that the prime
numbers contain arbitrarily long arithmetic progressions, has since been proved
independently as the Green-Tao theorem.) The problem is currently worth
US$5000.