The tables below shows upper bounds on the Erdös numbers of some famous scientists and mathematicians, including many Nobel laureates. Further details, including the paths that establish these numbers and many other people, can be found in Famous Trail to Paul Erdös by Rodrigo De Castro and Jerrold W. Grossman, available here in preprint form — in LATeX (118K), postscript (419K, 35 pages), and pdf (453K, 35 pages). It appears (somewhat abbreviated) in The Mathematical Intelligencer: vol. 21, no. 3 (Summer 1999), 51–63, and (in Spanish and updated) in the journal of the Colombian Academy of Sciences (Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales, vol. 23, no. 89 (December, 1999), 563–582).

In addition, we have listed on a separate page the collaboration paths from Erdös to each of the winners of the Fields Medal, the Nevanlinna Prize, the Abel Prize, the Wolf Prize in Mathematics, and the Steele Prize for Lifetime Achievement, as well as a few others.

Perhaps the most famous contemporary mathematician, Andrew Wiles, was too old to receive a Fields Medal (but was given a special tribute at the 1998 International Congress of Mathematicians). He has an Erdös number of at most 3, via Erdös to ANDREW ODLYZKO to Chris M. Skinner.

And surely the most famous contemporary "computer personality" with a small Erdös number is William H. (Bill) Gates, who published with Christos H. Papadimitriou in 1979, who published with Xiao Tie Deng, who published with Erdös coauthor PAVOL HELL, giving Gates Erdös number at most 4.

A prolific biologist, Eugene V. Koonin, at the National Center for Biotechnology Information, has an Erdös number of 2, through Laszlo A. Szekely. This gives many biologists small finite Erdös numbers, as well. (Another link to the biological sciences community is geneticist Eric Lander, who has Erdös number 2, via Dan Kleitman.) Indeed, it is probably possible to connect almost everyone who has published in the biological sciences to Erdös. With a couple of hours work on the Web, Grossman was able to establish an upper bound of 9 for the Erdös number of his brother, a practicing physician, who was a coauthor on a biology paper resulting from a summer internship. As Margaret Wilson at the University of California points out, the same is probably true for the fields of linguistics (via Noam Chomsky) and psychology (via Jean Piaget).

Here is a message from another biologist, Bruce Kristal, who has Erdös number 2 and lots of coauthors, which may provide useful hints for other searchers in this area: “I recently published with D Frank Hsu (Erdös number 1), and I am writing to briefly point out some potential implications of this that Frank and I found very interesting. Specifically, I am a biologist who works across several areas. Because of this, I have published with, among others, major figures in research on AIDS, aging, neurologic injury and neurodegeneration, and nutritional epidemiology. I believe that one of the neuroscientists I have published with, M. F. Beal, is among the most highly cited in this area. In the last area, nutritional epidemiology, I am on one (position) paper with many of the world leaders, including Walter Willett. Walt has over 1000 publications and was recently named as the most highly cited biomedical researcher in the last decade. Likewise, Frank is a computer scientist with ties in both mathematics and information retrieval as well as some biology citations. I mention these because Frank and I have discussed, among other issues, whether I may serve as a ‘weak link’ of sufficient breadth to impact the overall network structure both within biology and between biology and these other areas of math and computer science. Koonin is clearly more prolific than I am, but our fields may be sufficiently different to complement.” Interested people can contact him directly.

For other links in the neuroscience area (and clinical medicine), see Jonathan Victor's Erdös number page. For a nice discussion of Erdös numbers in physics, see Barbecue Joe Marasco's Erdös number page.

A person on the Erdös2 list, Kenneth Hodges, turned from mathematics to a totally different field. He is Associate Professor of English at the University of Oklahoma and has at least two English literature collaborators, whose Erdös numbers are therefore 3.

Felipe Voloch found what seems to be the oldest mathematicican known to have a finite Erdös number, Richard Dedekind (1831-1916). His number is at most 7, via this path: H. Weber – W. Jacobsthal – R. Fuchs – L.Hopf – A. Einstein – E. Straus – P. Erdös. Some of these collaborations might not meet the usual standard for mathematical research, however (education-oriented works or handbooks). On the other hand, there is a clear path of length 4 to David Hilbert (1862-1943), via R. Courant – K. Friedrichs – H. N. Shapiro – P. Erdös; and a path of length 3 to Georg Frobenius (1849-1917), via I. Schur – G. Szegö – P. Erdös.

We would like to acknowledge and thank the dozens of people, too numerous to mention by name, who have written in with suggestions, additions, and corrections to these lists. We would appreciate further help from anybody with relevant information.

Nobel Prize winners

NAME                         YEAR     SUBJECT        ERDÖS NUMBER

Max von Laue                 1914     Physics             4
William Henry Bragg          1915     Physics             7
William Laurence Bragg       1915     Physics             6
Albert Einstein              1921     Physics             2
Niels Bohr                   1922     Physics             5
Louis de Broglie             1929     Physics             5
Werner Heisenberg            1932     Physics             4
Paul A. Dirac                1933     Physics             4
Erwin Schrödinger            1933     Physics             8
Enrico Fermi                 1938     Physics             3
Ernest O. Lawrence           1939     Physics             6
Otto Stern                   1943     Physics             3
Isidor I. Rabi               1944     Physics             4
Wolfgang Pauli               1945     Physics             3
Frits Zernike                1953     Physics             6
Max Born                     1954     Physics             3
Willis E. Lamb               1955     Physics             3
John Bardeen                 1956     Physics             5
Walter H. Brattain           1956     Physics             6
William B. Shockley          1956     Physics             6
Chen Ning Yang               1957     Physics             4
Tsung-dao Lee                1957     Physics             5
Emilio Segrè                 1959     Physics             4
Owen Chamberlain             1959     Physics             5
Robert Hofstadter            1961     Physics             5
Eugene Wigner                1963     Physics             3
Richard P. Feynman           1965     Physics             3
Julian S. Schwinger          1965     Physics             4
Hans A. Bethe                1967     Physics             3
Luis W. Alvarez              1968     Physics             5
Murray Gell-Mann             1969     Physics             3
John Bardeen                 1972     Physics             5
Leon N. Cooper               1972     Physics             5
John R. Schrieffer           1972     Physics             4
Aage Bohr                    1975     Physics             5
Ben Mottelson                1975     Physics             5
Leo J. Rainwater             1975     Physics             7
Sheldon Lee Glashow          1979     Physics             2
Abdus Salam                  1979     Physics             3
Steven Weinberg              1979     Physics             3
Arthur L. Schawlow           1981     Physics             5
S. Chandrasekhar             1983     Physics             4
Klaus von Klitzing           1985     Physics             5
Gerd Binnig                  1986     Physics             6
Heinrich Rohrer              1986     Physics             7
Norman F. Ramsey             1989     Physics             3
Joseph Hooton Taylor, Jr.    1993     Physics             4
David M. Lee                 1996     Physics             6
Douglas D. Osheroff          1996     Physics             5
Robert C. Richardson         1996     Physics             6
Steven Chu                   1997     Physics             7
Gerardus 't Hooft            1999     Physics             6
Martinus J.G. Veltman        1999     Physics             7
Carl E. Wieman               2001     Physics             6
Anthony J. Leggett           2003     Physics             4
Frank Wilczek                2004     Physics             3
Theodor W. Hansch            2005     Physics             5
Andre K. Geim                2010     Physics             6
Konstantin Novoselov         2010     Physics             6
Serge Haroche                2012     Physics             4
David Wineland               2012     Physics             3

Paul A. Samuelson            1970     Economics           5
Kenneth J. Arrow             1972     Economics           3
Tjalling C. Koopmans         1975     Economics           4
Herbert A. Simon             1978     Economics           3
Gerard Debreu                1983     Economics           3
Franco Modigliani            1985     Economics           4
Robert M. Solow              1987     Economics           4
Harry M. Markowitz           1990     Economics           2
Merton H. Miller             1990     Economics           4
John C. Harsanyi             1994     Economics           8
John F. Nash                 1994     Economics           4
Reinhard Selten              1994     Economics           5
James Mirrlees               1996     Economics           3
Robert C. Merton             1997     Economics           6
Amartya Sen                  1998     Economics           4
James J. Heckman             2000     Economics           4
Joseph Stiglitz              2001     Economics           4
Daniel Kahneman              2002     Economics           3
Robert J. Aumann             2005     Economics           3
Edmund S. Phelps             2006     Economics           4
Alvin E. Roth                2012     Economics           3
Lloyd S. Shapley             2012     Economics           3

Peter J. Debye               1936     Chemistry           5
George De Hevesy             1943     Chemistry           7
Otto Diels                   1950     Chemistry           7
Kurt Alder                   1950     Chemistry           6
Edwin M. McMillan            1951     Chemistry           6
Glenn T. Seaborg             1951     Chemistry           5
Linus Pauling*               1954     Chemistry           4
       *Also received the 1962 Nobel Peace Prize
John C. Kendrew              1962     Chemistry           7
Max F. Perutz                1962     Chemistry           7
Robert B. Woodward           1965     Chemistry           7
Lars Onsager                 1968     Chemistry           3
Ilya Prigogine               1977     Chemistry           6
Walter Gilbert               1980     Chemistry           4
Kenichi Fukui                1981     Chemistry           3
Roald Hoffmann               1981     Chemistry           6
Robert Bruce Merrifield      1984     Chemistry           6
Herbert A. Hauptman          1985     Chemistry           3
Jerome Karle                 1985     Chemistry           4
Jean-Marie Lehn              1987     Chemistry           5
Hartmut Michel               1988     Chemistry           4
Johann  Deisenhofer          1988     Chemistry           5
Rudolph A. Marcus            1992     Chemistry           4
George A. Olah               1994     Chemistry           7
Robert F. Curl, Jr.          1996     Chemistry           8
Harold W. Kroto              1996     Chemistry           7
Richard E. Smalley           1996     Chemistry           8
Walter Kohn                  1998     Chemistry           3
John A. Pople                1998     Chemistry           5
Ahmed H. Zewail              1999     Chemistry           9
Alan J. Heeger               2000     Chemistry           5
Alan G. MacDiarmid           2000     Chemistry           6
Hideki Shirakawa             2000     Chemistry           6

Joshua Lederberg             1958     Medicine*           5
Edward Tatum                 1958     Medicine*          11
Francis H. C. Crick          1962     Medicine*           4
James D. Watson              1962     Medicine*           4
Sir John Carew Eccles        1963     Medicine*           3
David Baltimore              1975     Medicine*           5
Hamilton O. Smith            1978     Medicine*           3
Harold E. Varmus             1989     Medicine*           4
Richard J. Roberts           1993     Medicine*           4
Eric R. Kandel               2000     Medicine*           4
Sydney Brenner               2002     Medicine*           4
H. Robert Horvitz            2002     Medicine*           4
John E. Sulston              2002     Medicine*           3
Andrew Z. Fire               2006     Medicine*           4
Craig C. Mello               2006     Medicine*           5
Mario R. Capecchi            2007     Medicine*           4
Luc Montaigner               2008     Medicine*           5

*or Physiology

Fields Medal winners

NAME                      YEAR     COUNTRY      ERDÖS NUMBER

Lars Ahlfors              1936     Finland           4
Jesse Douglas             1936     USA               4
Laurent Schwartz          1950     France            4
Atle Selberg              1950     Norway            2
Kunihiko Kodaira          1954     Japan             2
Jean-Pierre Serre         1954     France            3
Klaus Roth                1958     Germany           2
Rene Thom                 1958     France            4
Lars Hormander            1962     Sweden            3
John Willard Milnor       1962     USA               3
Michael Atiyah            1966     Great Britain     4
Paul Cohen                1966     USA               5
Alexander Grothendieck    1966     Germany/France    5
Stephen Smale             1966     USA               4
Alan Baker                1970     Great Britain     2
Heisuke Hironaka          1970     Japan             4
Serge Novikov             1970     USSR              3
John G. Thompson          1970     USA               3
Enrico Bombieri           1974     Italy             2
David Mumford             1974     Great Britain     2
Pierre Deligne            1978     Belgium           3
Charles Fefferman         1978     USA               2
Gregory Margulis          1978     USSR              3
Daniel Quillen            1978     USA               3
Alain Connes              1982     France            3
William Thurston          1982     USA               2
Shing-Tung Yau            1982     China             2
Simon Donaldson           1986     Great Britain     4
Gerd Faltings             1986     Germany           4
Michael Freedman          1986     USA               3
Valdimir Drinfeld         1990     USSR              4
Vaughan Jones             1990     New Zealand       4
Shigemufi Mori            1990     Japan             3
Edward Witten             1990     USA               3
Pierre-Louis Lions        1994     France            4
Jean Christophe Yoccoz    1994     France            3
Jean Bourgain             1994     Belgium           2
Efim Zelmanov             1994     Russia            3
Richard  Borcherds        1998     S Afr/Gt Brtn     2
William T. Gowers         1998     Great Britain     4
Maxim L. Kontsevich       1998     Russia            4
Curtis McMullen           1998     USA               3
Laurent Lafforgue         2002     France            5
Vladimir A. Voevodsky     2002     Russia/USA        4
Andrei Okounkov           2006     Russia/USA        3
Grigory Perelman(refused) 2006     Russia            4
Terence C. Tao            2006     Australia/USA     2
Wendelin Werner           2006     Germany/France    3
Ngo Bau Chau              2010     Vietnam           4
Elon Lindenstrauss        2010     Israel            3
Stanislav Smirnov         2010     Russia            3
Cedric Villani            2010     France            3

Nevanlinna Prize winners

NAME                      YEAR     COUNTRY      ERDÖS NUMBER

Robert Tarjan             1982     USA               2
Leslie Valiant            1986     Hungary/Gt Brtn   3
Alexander Razborov        1990     Russia            2
Avi Wigderson             1994     Israel            2
Peter Shor                1998     USA               2
Madhu Sudan               2002     India/USA         2
Jon Kleinberg             2006     USA               3
Daniel Spielman           2010     USA               3

Abel Prize winners

NAME                      YEAR     COUNTRY      ERDÖS NUMBER

Jean-Pierre Serre         2003     France            3
Michael Atiyah            2004     Great Britain     4
Isadore M. Singer         2004     USA               3
Peter D. Lax              2005     Hungary/USA       3
Lennart Carleson          2006     Sweden            2
Srinivasa S. R. Varadhan  2007     India/USA         2
John G. Thompson          2008     USA               3
Jacques Tits              2008     Belgium           4
Mikhael Gromov            2009     Russia            3
John T. Tate              2010     USA               3
John Willard Milnor       2011     USA               3
Endre Szemeredi           2012     Hungary/USA       1
Pierre Deligne            2013     Belgium           3

Wolf Prize in Mathematics winners

NAME                      YEAR      COUNTRY      ERDÖS NUMBER

Izrail M. Gelfand         1978      USSR (Russia)       3
Carl L. Siegel            1978      Germany             3
Jean Leray                1979      France              3
André Weil                1979      France              4
Henri Cartan              1980      France              3
Andrei N. Kolmogorov      1980      Russia              4
Lars Ahlfors              1981      Finland             4
Oscar Zariski             1981      USA                 3
Hassler Whitney           1982      USA                 2
Mark G. Krein             1982      Ukranian SSR        4
Shiing Shen Chern         1983-84   China               2
Paul Erdös                1983-84   Hungary             0
Kunihiko Kodaira          1984-85   Japan               2
Hans Lewy                 1984-85   Germany             3
Samuel Eilenberg          1986      Poland              2
Atle Selberg              1986      Norway              2
Kiyoshi Ito               1987      Japan               3
Peter D. Lax              1987      Hungary/USA         3
Friedrich E. Hirzebruch   1988      Germany             3
Lars Hormander            1988      Sweden              3
Alberto Calderón          1989      Argentina           3
John Willard Milnor       1989      USA                 3
Ennio De Giorgi           1990      Italy               3
Ilya Piatetski-Shapiro    1990      Russia              3
Lennart A. Carleson       1992      Sweden              4
John G. Thompson          1992      USA                 3
Mikhael Gromov            1993      Russia              3
Jacques Tits              1993      Belgium             4
Jurgen K. Moser           1994-95   Germany             3
Robert Langlands          1995-96   Canada              2
Andrew Wiles              1995-96   Great Britain       3
Joseph B. Keller          1997      USA                 3
Yakov G. Sinai            1997      Russia              4
Laszlo Lovasz             1999      Hungary             1
Elias M. Stein            1999      Belgium/USA         2
Raoul Bott                2000      Hungary             3
Jean-Pierre Serre         2000      France              3
Vladimir I. Arnold        2001      Russia              6
Saharon Shelah            2001      Israel              1
Mikio Sato                2002/3    Japan               4
John T. Tate              2002/3    USA                 3
Gregory Margulis          2005      USSR                3
Serge Novikov             2005      USSR                3
Hillel Furstenberg        2006/7    Israel              2
Stephen Smale             2006/7    USA                 4
Pierre Deligne            2008      Belgium             3
David Mumford             2008      Great Britain       2
Phillip A. Griffiths      2008      USA                 3
Dennis Sullivan           2010      USA                 3
Shing-Tung Yau            2010      USA                 2
Michael Aschbacher        2012      USA                 2
Luis Caffarelli           2012      USA                 3

Steele Prize (Lifetime Achievement) winners

NAME                      YEAR     COUNTRY      ERDÖS NUMBER

Salomon Bochner           1979     Poland               2
Antoni Zygmund            1979     Poland               2
André Weil                1980     France               4
Gerhard P. Hochschild     1980     Germany              3
Oscar Zariski             1981     Poland               3
Fritz John                1982     Germany              4
Shiing Shen Chern         1983     China                2
Joseph L. Doob            1984     USA                  2
Hassler Whitney           1985     USA                  2
Saunders Mac Lane         1986     USA                  3
Samuel Eilenberg          1987     Poland               2
Deane Montgomery          1988     USA                  3
Irving Kaplansky          1989     Canada               1
Raoul Bott                1990     Hungary              3
Armand Borel              1991     Switzerland          3
Peter D. Lax              1992     Hungary/USA          3
Eugene B. Dynkin          1993     Russia/USA           3
Louis Nirenberg           1994     Canada               3
John T. Tate              1995     USA                  3
Goro Shimura              1996     Japan                2
Ralph S. Phillips         1997     USA                  2
Nathan Jacobson           1998     USA                  3
Richard V. Kadison        1999     USA                  3
Isadore M. Singer         2000     USA                  3
Harry Kesten              2001     Netherlands/USA      2
Elias M. Stein            2002     Belgium/USA          2
Michael Artin             2002     USA                  3
Ronald L. Graham          2003     USA                  1
Victor W. Guillemin       2003     USA                  3
Cathleen S. Morawetz      2004     USA                  3
Izrail M. Gelfand         2005     USSR (Russia)        3
Frederick W. Gehring      2006     USA                  2
Dennis P. Sullivan        2006     USA                  3
Henry P. Mckean, Jr.      2007     USA                  2
George Lusztig            2008     USA                  3
Luis Caffarelli           2009     Argentina            3
William Fulton            2010     USA                  2
John Willard Milnor       2011     USA                  3
Ivo Babuska               2012     Czech Rep./USA       3
Yakov G. Sinai            2013     Russia               4

Mathematics members of the National Academy of Sciences as of 2001

NAME                     ERDÖS NUMBER

Arnold, Vladimir I.             6
Artin, Michael                  3
Aschbacher, Michael             3
Askey, Richard A.               2
Atiyah, Michael                 4
Bass, Hyman                     3
Bloch, Spencer J.               3
Bombieri, Enrico                2
Borel, Armand                   3
Bott, Raoul                     3
Browder, Felix E.               4
Browder, William                3
Burkholder, Donald L.           3
Caffarelli, Luis A.             3
Calabi, Eugenio                 2
Cartan, Henri P.                3
Cheeger, Jeff                   3
Chern, Shiing-shen              2
Cohen, Paul J.                  5
Connes, Alain                   3
Cox, David R.                   3
Daubechies, Ingrid              3
Diaconis, Persi                 2
Donaldson, Simon K.             4
Doob, Joseph L.                 2
Dynkin, Eugene B.               3
Faddeev, Lyudvig Dmitrievich    7
Federer, Herbert                3
Fefferman, Charles L.           2
Feit, Walter                    3
Freedman, Michael H.            3
Friedman, Avner                 3
Fulton, William                 3
Furstenberg, Hillel H.          2
Gale, David                     2
Gehring, Frederick W.           2
Gelfand, Izrail M.              3
Gleason, Andrew M.              3
Glimm, James                    4
Graham, Ronald L.               1
Grenander, Ulf                  2
Griffiths, Phillip A.           3
Gromov, Mikhael L.              3
Guillemin, Victor               3
Hamilton, Richard S.            3
Hirzebruch, Friedrich           3
Hochschild, Gerhard P.          3
Hochster, Melvin                3
Hormander, Lars                 3
Howe, Roger                     2
Ito, Kiyosi                     3
Jaffe, Arthur M.                5
Jones, Vaughan F.               4
Kadison, Richard V.             3
Kalman, Rudolf E.               4
Kaplansky, Irving               1
Kazhdan, David                  3
Kirby, Robion C.                4
Kohn, Joseph J.                 3
Kostant, Bertram                2
Kruskal, Martin D.              6
Langlands, Robert P.            2
Lang, Serge                     3
Lawson, H. Blaine               3
Lax, Peter D.                   3
Lieb, Elliott H.                2
Lusztig, George                 3
Mac Lane, Saunders              3
Mackey, George W.               2
MacPherson, Robert              3
Margulis, Gregory A.            3
Mather, John N.                 3
Mazur, Barry C.                 2
McDuff, Dusa                    3
McKean, Henry P.                2
Milnor, John Willard            3
Mostow, George Daniel           3
Nash, John F., Jr.              4
Nelson, Edward                  5
Nirenberg, Louis                3
Novikov, Sergei P.              3
Ornstein, Donald S.             2
Palis, Jacob, Jr.               4
Quillen, Daniel G.              3
Rabinowitz, Paul H.             4
Ratner, Marina                  ∞
Ribet, Kenneth A.               3
Sato, Mikio                     4
Schoen, Richard M.              3
Serre, Jean-Pierre              3
Serrin, James B.                3
Shafarevich, Igor R.            4
Sinai, Yakov G.                 4
Singer, Isadore M.              3
Smale, Stephen                  4
Solovay, Robert                 2
Spencer, Donald C.              3
Stanley, Richard P.             2
Stein, Charles M.               3
Stein, Elias M.                 2
Steinberg, Robert               3
Sternberg, Shlomo               2
Stroock, Daniel W.              3
Sullivan, Dennis P.             3
Swan, Richard G.                3
Tate, John T.                   3
Taubes, Clifford H.             4
Thompson, John G.               3
Thurston, William P.            2
Tits, Jacques                   4
Uhlenbeck, Karen K.             3
Varadhan, Srinivasa S. R.       2
Whitehead, George W.            4
Wiles, Andrew J.                3
Yau, Shing-Tung                 2
Zelmanov, Efim I.               3

Other distinguished scholars and famous people

NAME                        FIELD OF RESEARCH            ERDÖS NUMBER

Walter Alvarez              geology                            5
David Blackwell             mathematics, statistics            2
Malcolm K. Brachman         nuclear physics, oil, bridge       6
Sergey Brin                 Google                             3
Rudolf Carnap               philosophy                         4
Gregory Chaitin             mathematics                        3
Ahmad Chalabi               Iraqi politics                     6
Jule G. Charney             meteorology                        4
Noam Chomsky                linguistics                        4
Freeman J. Dyson            quantum physics                    2
Paul R. Ehrlich             population studies                 4
Georg Frobenius             mathematics                        3
George Gamow                nuclear physics and cosmology      4
Kurt Gödel                  mathematics                        3
Stephen Hawking             relativity and cosmology           4
John L. Hennessey           comp. sci., Stanford U president   4
David Hilbert               mathematics                        4
Pascual Jordan              quantum physics                    4
Theodore von Kármán         aeronautical engineering           4
Ephraim Katchalski-Katzir   scientist and Israeli president    2
Tom Lehrer                  music performance                  4
Benoit Mandelbrot           mathematics (fractals)             3
John Maynard Smith          biology                            4
Oskar Morgenstern           economics                          4
Rolf Nevanlinna             mathematics                        5
J. Robert Oppenheimer       nuclear physics                    4
Larry Page                  Google                             3
Roger Penrose               relativity and cosmology           3
Jean Piaget                 psychology                         3
Karl Popper                 philosophy                         4
Srinivasa Ramanujan         mathematics                        3
Carl Sagan                  astronomy                          4
Edwin E. Salpeter           astrophysics                       5
Issai Schur                 mathematics                        2
Claude E. Shannon           electrical engineering             3
Waclaw Sierpinski           mathematics                        2
Ronald L. Smith             mathematics and bridge             3
Arnold Sommerfeld           atomic physics                     4
Ivar Stakgold               mathematics and bridge             4
Dirk Struik                 mathematics, history               4
Edward Teller               nuclear physics                    4
John Wilder Tukey           statistics                         2
Alan Turing                 computer science                   5
George Uhlenbeck            atomic physics                     2
John von Neumann            mathematics                        3
John A. Wheeler             nuclear physics                    3

It would have been nice to find an Erdös number for the great twentieth century mathematician, philosopher, and activist Bertrand Russell. However, he collaborated very little, as did his coauthor Alfred North Whitehead. Thus we can't find a path using research articles. However, Sachi Sri Kantha points out the following, which also would give small Erdös numbers to several other prominent scientists: "Both Russell and Albert Einstein have impeccable credentials as mathematicians; equally impeccable are their credentials as anti-establishment peace activists against militarism and warfare. They authored the Russell-Einstein Manifesto of 1955, which was the last public document authored by Einstein, before his death. Though it is not a mathematical paper. this Russell-Einstein Manifesto is a valid collaboration of two peace activist scientists, given the tenor of McCarthy era. It is also counted as one of Russell's publication [source: A Bibliography of Bertrand Russell, vol.II, Serial Publications 1890-1990, by K.Blackwell and H.Ruja, Routledge, London, 1994, pp.194-196]. The specific title is TEXTS OF SCIENTISTS' APPEAL FOR ABOLITION OF WAR, New York Times, 10 July 1955, p.25. This was the original citation, and it had been reproduced umpteen times in other journals, magazines and newspapers. The worth of this Russell-Einstein Manifesto was that according to the citation in the bibliography: 'The entire Rusell-Einstein manifesto with Russell's prefatory remarks. The other signatories, besides Einstein, were Max Born, P.W.Bridgman, L.Infeld, F.Joliot-Curie, Linus Pauling, H.J.Muller, C.F.Powell, J.Rotblat and Hideko Yukawa.' Among these, at the time of its release, all except Einstein's collaborator Infeld and Rotblat were Nobelists in science. Later in 1995, Rotblat received the Nobel Peace Prize. Thus other Nobelists like Bridgman (physics 1946), Joliot-Curie (chemistry, 1935), H.J.Muller (medicine, 1946), Powell (physics, 1950), Rotblat (peace, 1995) and Yukawa (physics, 1949), all of whom have not been included in your current list of Erdos Number Nobelists, receive an Erdos Number of 3, courtesy of Einstein. Since Russell was also the only mathematician who received the Nobel literature prize, this Russell-Einstein Manifesto of 1955 is also indicative of his eminent stature as a literateur."

Here is another interesting story, suggesting that Peter Lax should have a non-integer Erdös number. It comes from Istvan Hargittai.

"Abel-laureate Peter Lax is listed with Erdös number 3. I would like to suggest to correct this because Peter Lax, in fact, has a unique Erdös number of one and a half! Peter and I recorded three in-depth conversations during the past few years in Budapest and in New York. A composite version, translated into Hungarian, has appeared in Hungarian in November 2007 in the magazine of the Hungarian Academy of Sciences, called Magyar Tudomany. The original English-language version of the composite is awaiting publication in The Mathematical Intelligencer. Among many other topics, we talked about Paul Erdös, and Peter's Erdös number also came up in the conversation. How did Lax figure out that his Erdös number was 1.5? Lax never wrote a paper with Erdös, but Peter's first paper was on a conjecture of Erdös. That was in 1944. Even before that, a paper in 1943, by Erdös, which appeared in The Annals of Mathematics (volume 44, pages 643-646), had a footnote, which said, 'This proof is due to Mr. P. Lax. Oral communication.' This footnote accounts for Lax's Erdos number of 1.5. (At this time, Peter was 17 years old.)"

 URL = http://www.oakland.edu/enp/erdpaths.html