The Erdös Number Explained

One's Erdös Number is a measure of how close one is to the main thrust of the evolution of man, as especially measured by one's productivity in realms that require mathematics, and in one's possession of the inherent mathematical capability of Kutzpah. It is a thoughful extension of the concept of the Erdös Number, which especially showed how far professional mathematicians in their publications are from the main stream of contemporary mathematics. Both the narrowly defined Erdös Number and the more progressive Erdös Number requires a chain of joint publications linking the person being assessed with the extraordinary mathematician Paul Erdös. However, for the narrowly defined concept, one needs a chain of papers published in the mathematical literature, whereas the broader concept has a more encompassing definition of a joint publication.

An Erdös Number of 1 is awarded to a researcher who has joined in one publication with the outstanding mathematician Paul Erdös(1913-1996). There are 507 such researchers, in fact 201 of them wrote two (or more) publications with Erdös. Likewise, joint publication with someone with an Erdös Number of 1, yields an Erdös Number of 2. Currently, there are 6419 reported Erdös Number 2 individuals. And so on.

The official Erdös Number Project computes Erdös Numbers only via a path through papers eligible for citation in a professional journal. The compilers of The Erdös Number Project Extended take a more generous perspective, and extend the concept of the Erdös Number to become the Erdös Number embodying a wider and deeper range of collaboration.

These web pages constitute our FAQ on the Erdös Number, just who or what is eligible, the youngest, oldest, and most fabjous awardees. In fact, fiction, animal, mineral, vegetable, or in the spiritual realm.

Which Movie Star has the best ( = the lowest ) Erdös Number?
Pix of actor Matt Damon co-writer and
star of Good Will Hunting Good Will Hunting, was conceived and scripted in part by Matt Damon. The technical consulant for that movie -- Dan Kleitman -- was a mathematician with the notably low Erdös Number of 2 -- so that Matt Damon, by this collaboration, gained the low Erdös Number of 3. Note that the award is not on the basis that Matt Damon played the role of a mathematical prody in Good Will Hunting -- it is the joint publication that counts.
Who is The Youngest to Gain an Erdös Number?

Dr Harvey Cohen supervises two-year old
 Alexander Zeno Cohen operating +- keyboard
 1975 microcomputer. Monitor is adapted TV Alexander Zeno Cohen.
Alexander was only two years and four months old when a joint publication appeared which via the extended principles of mathematical genealogy gained him an an Erdös Number of 4. (He was NOT three-years old as per the caption below.) Alexander's precocity might be attributed to his exposure, from the age of twelve months, to the educational programs of the OZNAKI Project, which was the first educational robotics project that was microcomputer based.
He is shown, aged twenty months, with his father, using the 2-key (+ -) keypad for use with the PLUSMINUS program, a Tiny Tots Calculator, running on the Poly-88, a 1976 microcomputer.
In 1979, Alexander Zeno Cohen, researched fluid mechanics in the MIT pool, along with the 1978 Field Medallist, Daniel Quillen, a professor of mathematics at MIT. The ensuing joint publication in the MIT house newspaper, TechTalk, (reproduced below), automatically gave Alexander an Erdös’s Number of 4, just one more than Quillen's Erdös’s Number of 3.
Here is a copy of the joint publication:

Front page story of MIT house newspaper Tech Talk --
glowing report of the award of latest Field Medal
with accompanying pix of Alexander studying fluid
mechanics in MIT swimming pool
Dr Harvey Cohen supervises two-year old
 Alexander Zeno Cohen operating +- keyboard
 1975 microcomputer. Monitor is adapted TV Those who gain their knowledge of mathematics from that most reliable medium, the film, will learn from Good Will Hunting that publication in MIT TechTalk is the absolute pinnacle of mathematical achievement, if a little lower in stature than the actual award of a Fields Medal. Thus Alexander had it made within mathematics by the very publication of his exploits on the front page of TechTalk -- but it was nice that MIT's latest Field Medallist could assist him in gaining a low Erdös Number .
Does Joan Baez have an Erdös Number of 3 ?
Program cover for Joan Baez concert Quote from Email:
Lucy Kaplansky was the opening act at a recent concert given by Joan Baez.
Lucy Kaplansky's father is Izzy Kaplansky.
Izzy Kaplansky is a co-author of Erdos'.
Gerry Myerson (
Link to the Evidence for this claim. YOU be the Judge !

Do any animals have an Erdös Number ? Is it possible ?
A horse ponders its Erdos number Recent work by animal psychologists showing that not only primates but even birds have surprising intellectual capacities, opens the question as to whether non-humans can boast a Erdös Number. The answer is indeed yes; the story is however curious.

Jerry Grossman at Oakland University contributed an article to a Bridge magazine, jointly with Smarty, his wife's horse. As Grossman (Grossman, Jerrold Wayne) has an Erdös Number of 2, the horse achieved an Erdös Number of 3.

In keeping with the hard-edge, yet generous, approach taken on this site, here are the detailed facts re Smarty. A clue/entry in a crossword included in a magazine devoted to Bridge cast aspersion on the Arabian breed. Smarty, as was his style, expressed gross irritation, and was consoled by Jerry Grossman, who ghosted a letter of complaint to the magazine. The published letter only featured Smarty's name, but as this is common practice in "ghosted" books and articles, the joint authorship of this publication is accepted. And how could one dispute with the principal compiler of the official Erdös Number Project

Just what are the principles of Mathematical Genealogy ?

The key idea is that there has to be a path of joint publications, linking the awardee with Paul Erdös. The Erdös Number is the smallest number of links connecting a (joint) paper of the awardee with Paul Erdös. A full formal definition can be given using Graph Theory, but the idea is simple enough, to be explained by a simple example.

Alexander Zeno Cohen acquired an Erdös Number of four via the following path:

> 1,40c Erdos, Paul; Wintner, Aurel. Additive arithmetical functions and

> statistical independence. Amer. J. Math. 61, (1939). 713--721.
> 19,397e Sternberg, Shlomo; Wintner, Aurel On a class of analogies between
> differential equations and implicit equations. J. Analyse Math. 5  (1956/57), 34--46.
> 57 #1582 Guillemin, Victor W.; Quillen, Daniel; Sternberg, Shlomo. The
> integrability of characteristics. Comm. Pure Appl. Math. 23 no. 1 (1970),  39--77.

>> "American Academy Elects Quillen, Wunsch and Brown", TechTalk Vol 23 No 35 p1  May
16, 1979 -- including the pix to which Alexander contributed.

Starting from the classic Erdös Wintner paper, for which Wintner acquired a Erdös number 0f 1; an Analyse Math paper with Wintner sets Sternberg's Erdös number =2; while Quillen's collarative effort with Sternberg (and Guillemin) made his Erdös Number =3. In the case of Alexander Zeno Cohen, we need to note that invariably press articles re mathematicians were first written by the mathematicians themselves, then revised by journalists enroute to the presses. In this case the article re Quillen et al, has been typographically joined with the pictorial saga of Alexander's exercise in fluid dynamics, to produce the Erdös Number defining publication.

Did my Partner Acquire an Erdös Number on marriage ? If Not, How can he/she acquire a finite one?

What if one party to a marriage already has an assigned Erdös Number while the other has no finite Erdös Number. Does a marriage certificate signed by both parties, constitute a publication of those two parties, assigning Erdös Number + 1 to the spouse?

No -- a single copy does NOT constitute a publication. In our opinion only in the case of "serial marriage" -- repeated marriages of the same parties -- would the duplicated marriage certificate constitute a publication for these purposes. Its arguable that in the case of a bigamist, certificates each with different partners names constitute revised editions -- but we won't buy that.

Can Sophie Acquire an Erdös Number ?
Cover of Sophies World, a novel by Jostein Gaarder Can a character in a novel gain an Erdös Number ? Clearly the author of a novel can give one of his characters any such attribute he requires, but an Erdös Number bestowed by an author will NOT be recognised by this Project. The work of the author remains a fiction. We are more flexible than the Erdös Number Project, but not fanciful. In detail, the Erdös Number Project will only recognise an awardee whose act of collaboration involved an act of free will on their part. Few characters in novels possess the philosophical nouce required to escape the author's direction and to act for themselves. But in Sophies World the character Sophie, with devilish cunning, achieved an act of free-will, Sophie escaped from the tyranny of her author, The Major, himself a fictional construct of Jostein Gaarder.

There is a further question: in which world can Sophie -- or any other fictional character -- acquire an Erdös Number. For the answer to this question, we await further. presentations by Jostein Gaarder.

See also this Sophies's World site.
But can a mathematical Dragon gain an an Erdös Number ? This matter is being zealously researched.
Amazing scupture - the Quintrino of Bathesda Grossman Quintrino Assignment of an Erdös Number
There is a five-fold chain of collaborators linking the webmaster of this site, Harvey A. Cohen, with Paul Erdös,
In detail, the five chains of collaborators linking Cohen with Erdös are:
  • Cohen, H.A. - Bracken, A.J. --Doebner, H.-D.--Schott, R.--Janson, S.--Erdos
  • Cohen, H.A. - Bracken, A.J., --Barut, A.O.--Wilson, Raj--Macintyre, A.J.--Erdos
  • Cohen, H.A. - Bracken, A.J., --Rogers, C.--Swetits, J.J.--Kroo, A.--Erdos
  • Cohen, H.A. - Bracken, A.J., --Vyborny, R--Lee, P. Y.--Chen, C.C.--Erdos
  • Cohen, H.A. - Bracken, A.J., --Hughes, J.W.B.--Moshinsky, M.--Sharma, A.--Erdos
No further proof is required that the topology of this multiple fivefold linkage matches the sculpture Quintrino shown to the left:
But this publication is a joint publication of the webmaster, and of the mathematical sculptor Bathsheba Grossman
QED: By virtue of this joint publication, Bathsheba Grossman has gained an Erdös Number of 6.
Pix of Dr Harvey Cohen in cylindrical projection Link to Inside Harvey's Head
Comments, enquiries, and outlandish nominations of awardees to the Webmaster  Dr Harvey A. Cohen
Note that successful claims for Erdös Number assignment are invariably outrageous -- Like the claim that the sum of the (Babe) Ruth-Aron Numbers, 714 and 715, is a backwards-forwards-sideways prime:
In detail: 714 + 715 = 1429.
1429, 9241, 1249, 9421, 4129, 4219 are all prime numbers.
As to 1492? That couldn't be more prime in the dictionary sense, despite being an even number, as it was the year that Columbus 'discovered' America.
What's more, 714 x 715 = 2 x 3 x 5 x 7 x 11 x 13 x 17 -- the product of the first seven primes. This must be the clincher !!
So we accept Ivars Peterson's claim that 1429 is a backwards-forwards-sideways prime, as we apply the same principle in assigning Erdös Numbers.
Basic Rule for Assigning Erdös Numbers: Was enough Chutzbah involved in the claim for it to be taken seriously ???