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definition - erdos bacon number

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Erdős–Bacon number


A person's Erdős–Bacon number is the sum of one's Erdős number—which measures the "collaborative distance" in authoring mathematical papers between that person and Hungarian mathematician Paul Erdős—and one's Bacon number—which represents the number of links, through roles in films, by which the individual is separated from American actor Kevin Bacon. The lower the number, the closer a person is to Erdős and Bacon, and this reflects a small world phenomenon in academia and entertainment.

The idea of Erdős–Bacon numbers has been written about by Simon Singh in the British media[1][2] and Benjamin Rosenbaum,[3] among others,[4] in the blogosphere.

Roles as self, as a cameo appearance, or as an extra are often included for the Bacon component. The Erdős criterion technically refers to collaboration on mathematical papers, but it is often relaxed to include general research articles for the Erdős–Bacon number.[5]

In general, to have a defined Erdős–Bacon number, it is necessary (but not sufficient) for one to have both appeared in a film and co-authored an academic paper.

Notable scientists with defined Erdős–Bacon numbers include popular astronomer Carl Sagan. One of the best-known actors with a number is actress Natalie Portman, whose authorship of a psychology paper during her Harvard degree in psychology earned her an Erdős–Bacon number of 6 (see table below).



It is sometimes reported that Erdős himself has an Erdős–Bacon number of three. His Erdős number is zero by definition. His Bacon number is erroneously thought to be three since he appears in N Is a Number: A Portrait of Paul Erdős (1993) with a Gene Patterson, and a Gene Patterson was in Box of Moon Light (1996) with Sam Rockwell who was in Frost/Nixon (2008) with Kevin Bacon. However, this is incorrect, as the Gene Patterson in N Is a Number: A Portrait of Paul Erdős is not the same person as the one in Box of Moon Light (1996).

Bruce Reznick, a professor at University of Illinois at Urbana-Champaign has an Erdős number of 1 and a Bacon number (by virtue of being an extra in Pretty Maids All in a Row with Roddy McDowall) of 2, and thus has an Erdős–Bacon number of 3.[6]

For a time, the person with the lowest known Erdős–Bacon number was Dave Bayer, mathematical consultant to A Beautiful Mind who was on screen in a minor role in the movie. Rance Howard was also in A Beautiful Mind and in Apollo 13 with Kevin Bacon to give Bayer a Bacon number of 2. Bayer wrote a paper with Persi Diaconis, who has an Erdős number of 1 due to a jointly authored 1977 Stanford University technical report, later published in a 2004 compilation.[7] As such, Bayer's Erdős–Bacon number is 4. Diaconis himself has an Erdős–Bacon number of 5, and Bacon number of 4. He was in the documentary The Math Life[8] with Freeman Dyson, who was in A Glorious Accident[9] with Oliver Sacks. Sacks has a Bacon number of 2.[10]

Robin E. Harte, former professor of mathematics at University College, Cork, Ireland,[11] has an acting role in Tony Bill's Oliver Twist (1997). Elijah Wood, who appeared with Bacon in Beyond All Boundaries (2009), plays the Artful Dodger in the film, giving Professor Harte a Bacon number of 2. Professor Harte has co-authored with Mostafa Mbekhta, who has co-authored with Endre Makai Jr, who has co-authored with Paul Erdős, so has an Erdős number of 3. Harte's Erdős–Bacon number is 5.

Astronomer Carl Sagan has an Erdős number of no more than 4[12] via Steven J. Ostro and a Bacon number of 3,[13][14] for a total of 7. Physicist Richard Feynman has an Erdős number of 3[15] and a Bacon number of 3, having appeared in the film Anti-Clock alongside Tony Tang.[16] Physicist H. David Politzer has an Erdős number of 4 [15] and a Bacon number of 2. [17]

Karl Schaffer is a dancer/choreographer who appeared as a "Killer Klown" in the 1988 film Killer Klowns from Outer Space,[18] and is also a mathematician at De Anza College, with a Bacon number of 2[19] and an Erdős number of 3,[20] for a sum of 5.

Computer science Professor Marco Pedicini at University of Rome has an Erdős–Bacon number of 5; he has an Erdős number of 2 (through Professor Vilmos Komornik) and a Bacon Number of 3 (appearing in the Italian movie directed by Fausto Brizzi, Notte prima degli esami, Oggi with actress Alessandra Costanzo[21] who played in The Order (2003 film) and this gives her Bacon number of two).

Mathematician and Economics Nobel laureate John Nash, better known in popular culture as the subject of the unauthorized biography A Beautiful Mind and the Academy Award-winning film adaptation has an Erdős number of 4[22] and a Bacon number of 2,[23] resulting in an Bacon-Erdős number of 6.

Electrical engineer Robert J. Marks II appeared in Ben Stein's movie Expelled: No Intelligence Allowed. Stein appeared with Bacon in Planes, Trains and Automobiles giving Marks a Bacon number of two. Marks has published with Donald C. Wunch II [24] who published with Frank Harary[25] who has coauthored with Erdős. Marks therefore has an Erdős number of three and Erdős–Bacon number of five. Intelligent design proponent William A. Dembski also appeared in Expelled. He has published with Marks [26] and therefore has a Erdős–Bacon number of six.


Former NCAA gymnastics champion Kiralee Hayashi[27] may be the professional actress with the lowest Erdős number (3), having co-written a peer-reviewed mathematics paper on Riemannian manifolds with Fields medalist Shing-Tung Yau,[28] and having a Bacon number of 2,[29] giving her an Erdős–Bacon number of 5.[30]

Danica McKellar, most famous for her role as Winnie Cooper in The Wonder Years, has an Erdős–Bacon number of 6, having coauthored a mathematics paper published while an undergraduate at UCLA. Her paper gives her an Erdős number of 4, and a Bacon number of 2, both of them having worked with Margaret Easley.[31]

US actress Natalie Portman has an Erdős–Bacon number of 6. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,[32] who has a collaboration path[33][34][35] leading to Joseph Gillis, who has an Erdős number of 1.[36] Bacon and Portman both appear in New York, I Love You, giving Portman a Bacon number of 1 and an Erdős number of 5.

Mayim Bialik has an Erdős–Bacon number of at most 7, having worked on a book chapter[37] and having a 5 point Erdős path [38][39] connecting to Shing-Tung Yau. Her Bacon number is 2.[40]

British actor Colin Firth has an Erdős–Bacon number of 7. Firth is formally credited as co-author of a neuroscience paper, "Political Orientations Are Correlated with Brain Structure in Young Adults",[41] after he suggested on BBC Radio 4 that such a study could be done.[42] Another author of that paper, Geraint Rees, has an Erdős number of 5,[43][44][45] which gives Firth an Erdős number of 6. Firth appeared with Kevin Bacon in Where the Truth Lies, so his Bacon number is 1.

The movie What the Bleep Do We Know!?, which featured both persons published in the sciences and an actress with Bacon number 2 (Academy Award winner Marlee Matlin), gave Erdős–Bacon numbers to David Albert (Erdős 4,[46] [47][48][49] Erdős–Bacon 7), Fred Alan Wolf (Erdős 5, Erdős–Bacon 8), and Natural Law Party Presidential Candidate John Hagelin (Erdős 5 through frequent collaborator Dimitri Nanopoulos, Erdős–Bacon 8), all appearing as themselves.


Hank Aaron, a baseball player, is sometimes also considered to have an Erdős–Bacon number of 3, as he and Erdős both autographed the same baseball (for which he is jokingly referred to as having Erdős number of 1),[50] and he also appeared in Summer Catch with Susan Gardner, who was in In The Cut with Bacon.


For people listed in the Internet Movie Database who are connected to Kevin Bacon, the average Bacon number is 2.957.[51] For mathematicians listed in the American Mathematical Society's MR Collaboration Distance search engine who are connected to Erdős, the average Erdős number is 4.65.[52] There currently exists no exhaustive list of people with defined Erdős–Bacon numbers, but a select group is listed below.

Name Erdős number Bacon number Erdős–Bacon number
Albert, DavidDavid Albert 4[46][47][48][49] 3(b)(i) 7(b)
Bar-Natan, DrorDror Bar-Natan 2[53] 4(b) 6
Bayer, DaveDave Bayer 2(c) 2(d)(i) 4(c,d)
Billingsley, PatrickPatrick Billingsley 4[54][55][56][57] 2[58] 6
Bialik, MayimMayim Bialik 5 2 7
Blum, LenoreLenore Blum 4 3(b)(i) 7(b)
Dalrymple, DavidDavid Dalrymple 3[59][60][61] 2(b)(e)[62] 5(b)(e)
Davis, MartinMartin Davis 3 3(b)(i) 6(b)
Dembski, William A.William A. Dembski 4[citation needed] 2(b)(i) 6
Denef, JanJan Denef 3 3(b)(i) 6(b)
Diaconis, PersiPersi Diaconis 1(c) 4(b,e)(i) 5(b,c,e)
Feferman, SolomonSolomon Feferman 3 3(b)(i) 6(b)
Feynman, RichardRichard Feynman 3[15] 3[16] 6
Firth, ColinColin Firth 6(i) 1(i) 7
Hagelin, JohnJohn Hagelin 5 3(b)(i) 8(b)
Houh, HenryHenry Houh 5[63][64][65][66][67] 2[68][69] 7
Marks II, Robert J.Robert J. Marks II 3 2(b)(i) 5[70]
Matiyasevich, YuriYuri Matiyasevich 2 3(b)(i) 5(b)
McCallum, WilliamWilliam McCallum 4[71][72][73][74] 3[75][76][77] 7
McKellar, DanicaDanica McKellar 4[46][78][79][80] 2 6
Metropolis, NicholasNicholas Metropolis 2 [81] 2 [82] 4
Myers, P.Z.P.Z. Myers 4[citation needed] 2 6
Nash, JohnJohn Nash 4 2 6
Poonen, BjornBjorn Poonen 2 3(b)(i) 5(b)
Portman, NatalieNatalie Portman (Hershlag) 5[32][33][34][35][36] 1(i) 6
Putnam, HilaryHilary Putnam 3 3(b)(i) 6(b)
Sagan, CarlCarl Sagan 4[15] 3(b)[13][14] 7
Scott, DanaDana Scott 2 3(b)(i) 5(b)
Van Snellenberg, JaredJared Van Snellenberg 4[83] 2 6
Wandell, BrianBrian Wandell 3[15][84] 2[85][86] 5
Warwick, KevinKevin Warwick 4[87] 2(e)[88] 6(e)
Werner, WendelinWendelin Werner 3[89][90][91] 3[92] 6
Wolf, Fred AlanFred Alan Wolf 5 3(b)(i) 8(b)


(b) Includes role as self
(c) Includes technical report posthumously published in a book (otherwise Erdős number 3, Erdős–Bacon number 5)
(d) Includes role as extra
(e) Includes documentary credit
(g) Includes nonacademic paper
(h) Includes archival footage
(i) See discussion above.


  1. ^ Simon Singh (September 2005). "A Further Five Numbers, Programme 3: 6 degrees of separation". BBC. Also available at [1]. Retrieved 2006-12-01. 
  2. ^ Simon Singh (May 2002). "And the Winner Tonight Is". London: The Daily Telegraph. Retrieved 2006-12-01. 
  3. ^ Benjamin Rosenbaum (September 2004). "Bacon-Erdős numbers". Retrieved 2006-12-01. 
  4. ^ Cory Doctorow (September 2004). "Erdős-Bacon numbers". Boing Boing. Retrieved 2006-12-01. 
  5. ^ "There's not much separating her from Bacon, Erdos", USA Today, August 14, 2007: "As a UCLA undergraduate, McKellar co-wrote a theorem proving a magnetic field property [...] So McKellar's "Erdos-Bacon" number is 6. Some academics who have had film cameos have lower Erdos-Bacon numbers [...]"
  6. ^ "Items of Interest Related to Erdös Numbers". The Erdös Number Project. Oakland University. Retrieved December 29, 2011. 
  7. ^ Persi Diaconis and Paul Erdős. On the distribution of the greatest common divisor. Technical report 252. Stanford University. Dept. of Statistics. October 10, 1977. Also issued as Department of Statistics technical report no. 12 under ARO Grant DAAG29-77-G-0031. Republished; see [2].
  8. ^ "The Math Life". Retrieved December 29, 2011. 
  9. ^ A Glorious Accident
  10. ^ Oliver Sacks's Kevin Bacon connection[dead link]
  11. ^ Robin E. Harte
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  13. ^ a b "The Oracle of Bacon at Virginia". Retrieved 2007-05-20. [dead link]
  14. ^ a b "IMDb: Who's Out There?". Retrieved 2007-05-20. 
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  16. ^ a b "The Oracle of Bacon at Virginia". Retrieved 2006-12-05. [dead link]
  17. ^ "The Oracle of Bacon at Virginia". Retrieved 2009-06-23. 
  18. ^ "Full cast and crew for Killer Klowns from Outer Space". Internet Movie Database. Retrieved 2007-05-21.  Schaffer's name is misspelled in the credits as "Karl Shaeffer".
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  28. ^ "Paul Thompson's Erdos Number Page". 
  29. ^ " Kiralee Hayashi at the Oracle of Bacon
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  31. ^ "There's not much separating her from Bacon, Erdos", USA Today, August 14, 2007
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  37. ^ book chapter. Retrieved December 29, 2011. 
  38. ^ Luders E, Narr KL, Zaidel E, Thompson PM, Toga AW (Jul 2006). "Gender effects on callosal thickness in scaled and unscaled space". NeuroReport 17 (11): 1103–6. doi:10.1097/ PMID 16837835. 
  39. ^ Wang Y, Gu X, Hayashi KM, Chan TF, Thompson PM, Yau ST (2005). "Brain surface parameterization using Riemann surface structure". Med Image Comput Comput Assist Interv Int Conf Med Image Comput Comput Assist Interv 8 (Pt 2): 657–65. PMID 16686016. 
  40. ^ [6] Mayim Bialik at the Oracle of Bacon
  41. ^ Political Orientations Are Correlated with Brain Structure in Young Adults. 21. Current Biology. April 2011. pp. 677–680. doi:10.1016/j.cub.2011.03.017. PMID 21474316. Retrieved December 29, 2011. 
  42. ^ "Colin Firth credited in brain research". BBC News. 2011-06-05. 
  43. ^ Schwarzkopf, DS; Schindler, A; Rees, G (2010). Baker, Chris I.. ed. "Knowing with Which Eye We See: Utrocular Discrimination and Eye-Specific Signals in Human Visual Cortex". PLoS ONE 5 (10): e13775. doi:10.1371/journal.pone.0013775. PMC 2966441. PMID 21048942. // 
  44. ^ "Andreas Schindler". Max Planck Institutefor Biological Cybernetics. Retrieved December 29, 2011. 
  45. ^ "Can I help you find your Erdos number?". Retrieved December 29, 2011. 
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  51. ^ UVA Computer Science: The Oracle of Bacon at Virginia[dead link]
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  53. ^ [7]
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