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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 by the Committee at the 1998 ICM). 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 has an Erdös number of 2, through Laszlo A. Szekely, Eugene V. Koonin, at the National Center for Biotechnology Information. This gives many biologists small finite Erdös numbers, as well. 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.

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.

NAME YEAR SUBJECT ERDÖS NUMBER Max von Laue 1914 Physics 4 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 4 Luis W. Alvarez 1968 Physics 5 Murray Gell-Mann 1969 Physics 3 John Bardeen 1972 Physics 5 Leon N. Cooper 1972 Physics 6 John R. Schrieffer 1972 Physics 5 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 Norman F. Ramsey 1989 Physics 3 David M. Lee 1996 Physics 6 Douglas D. Osheroff 1996 Physics 5 Robert C. Richardson 1996 Physics 6 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 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 7 Robert C. Merton 1997 Economics 6 James J. Heckman 2000 Economics 4 Robert J. Aumann 2005 Economics 3 Edmund S. Phelps 2006 Economics 4 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 Lars Onsager 1968 Chemistry 3 Ilya Prigogine 1977 Chemistry 6 Walter Gilbert 1980 Chemistry 4 Kenichi Fukui 1981 Chemistry 3 Robert Bruce Merrifield 1984 Chemistry 6 Jerome Karle 1985 Chemistry 4 Herbert A. Hauptman 1985 Chemistry 3 Jean-Marie Lehn 1987 Chemistry 5 Joshua Lederberg 1958 Medicine 10 Edward Tatum 1958 Medicine 11 Francis H. C. Crick 1962 Medicine 5 James D. Watson 1962 Medicine 6 Sir John Carew Eccles 1963 Medicine 3

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 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 infinite Vladimir A. Voevodsky 2002 Russia/USA 4 Andrei Okounkov 2006 Russia/USA 3 Grigory Perelman(refused) 2006 Russia 4 Terrence Tao 2006 Australia/USA 3 Wendelin Werner 2006 Germany/France 3

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

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

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 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

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 Gehring, Frederick W. 2006 USA 2 Sullivan, Dennis P. 2006 USA 3

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 W. 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

NAME FIELD OF RESEARCH ERDÖS NUMBER Walter Alvarez geology 5 David Blackwell mathematics, statistics 2 Malcolm K. Brachman nuclear physics, oil, bridge 6 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 5 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 John Kaczynski murder infinite Theodore von Kármán aeronautical engineering 4 Ephraim Katchalski-Katzir scientist and Israeli president 2 Benoit Mandelbrot mathematics (fractals) 3 John Maynard Smith biology 4 Oskar Morgenstern economics 4 Rolf Nevanlinna mathematics 5 J. Robert Oppenheimer nuclear physics 4 Roger Penrose relativity and cosmology 3 Jean Piaget psychology 3 Karl Popper philosophy 4 Srinivasa Ramanujan mathematics 3 Carl Sagan astronomy 6 Edwin E. Salpeter astrophysics 5 Issai Schur mathematics 2 Claude E. Shannon electrical engineering 3 Waclaw Sierpinski mathematics 2 Arnold Sommerfeld atomic physics 5 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."

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

This page was last updated on October 16, 2006.

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