Erdős–Bacon number

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A person's Erdős–Bacon number is the sum of one's Erdős number—which measures the "collaborative distance" in authoring academic 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 person is separated from American actor Kevin Bacon.[1][2] The lower the number, the closer a person is to Erdős and Bacon, which reflects a small world phenomenon in academia and entertainment.[3]

To have a defined Erdős–Bacon number, it is necessary to have both appeared in a film and co-authored an academic paper, although this in and of itself is not sufficient.

An extended definition named Erdős–Bacon-Sabbath includes the Sabbath number, an equivalent to Bacon number that connects musicians to the heavy metal band Black Sabbath.[4][5]


Mathematician Daniel Kleitman has an Erdős–Bacon number of 3. He co-authored papers with Erdős and has a Bacon number of 2 via Minnie Driver in Good Will Hunting; Driver and Bacon appeared together in Sleepers.[6]

Like Kleitman, mathematician Bruce Reznick has co-authored a paper with Erdős[7] and has a Bacon number of 2, via Roddy McDowall in the film Pretty Maids All in a Row, giving him an Erdős–Bacon number of 3 as well.[8]

Physicist Nicholas Metropolis has an Erdős number of 2,[9] and also a Bacon number of 2,[10] giving him an Erdős–Bacon number of 4.

Physicists Nicholas Metropolis and Richard Feynman both worked on the Manhattan Project at Los Alamos Laboratory. Via Metropolis, Feynman has an Erdős number of 3 and, from having appeared in the film Anti-Clock alongside Tony Tang, Feynman also has a Bacon number of 3. Richard Feynman thus has an Erdős–Bacon number of 6.[9]

Theoretical physicist Stephen Hawking has an Erdős–Bacon number of 6: his Bacon number of 2 (via his appearance alongside John Cleese in Monty Python Live (Mostly) who acted alongside Kevin Bacon in The Big Picture) is lower than his Erdős number of 4.[11]

Similarly to Stephen Hawking scientist Carl Sagan has an Erdős–Bacon number of 6, also from a Bacon number of 2 and an Erdős number of 4.[12]

Mathematician Jordan Ellenberg has an Erdős number of 3[13] and a Bacon number of 2 due to a cameo appearance in the film Gifted for which he was also the mathematical consultant[14]


Danica McKellar, who played Winnie Cooper in The Wonder Years, has an Erdős–Bacon number of 6. While an undergraduate at the University of California, Los Angeles McKellar coauthored a mathematics paper[15] with Lincoln Chayes who via his wife Jennifer Tour Chayes[16] has an Erdős number of 3, giving McKellar one of 4. Having worked with Margaret Easley, McKellar has a Bacon number of 2.[2]

Israeli-American actress Natalie Portman has an Erdős–Bacon number of 7.[17] She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,[18] who has a collaboration path[19][20][21] leading to Joseph Gillis, who has an Erdős number of 1.[22] Portman appeared in A Powerful Noise Live (2009) with Sarah Michelle Gellar, who appeared in The Air I Breathe (2007) with Bacon, giving Portman a Bacon number of 2 and an Erdős number of 5.

British actor Colin Firth has an Erdős–Bacon number of 6. Firth is credited as co-author of a neuroscience paper, "Political Orientations Are Correlated with Brain Structure in Young Adults",[23] after he suggested on BBC Radio 4 that such a study could be done.[24] Another author of that paper, Geraint Rees, has an Erdős number of 4,[25] which gives Firth an Erdős number of 5. Firth's Bacon number of 1 is due to his appearance in Where the Truth Lies.[26][27]

Kristen Stewart has an Erdős–Bacon number of 7; she is credited as a co-author on an artificial intelligence paper that was written after a technique was used for her short film Come Swim, giving her an Erdős number of 5,[28][29] and she co-starred with Michael Sheen in Twilight, who co-starred with Bacon in Frost/Nixon, giving her a Bacon number of 2.[30]


Elon Musk, who is neither an academic nor an actor, has an Erdős–Bacon number of 6. In 2010 Musk had a cameo in the film Iron Man 2.[31] Since actor Mickey Rourke played a role in both Iron Man 2 and in Diner where also Kevin Bacon played a role, Musk has a Bacon number of 2.[32] In 2021 Musk coauthored a peer-reviewed scientific paper on COVID-19 together with among others Pardis Sabeti.[33] Since Sabeti has an Erdős number of 3,[34] Musk has an Erdős number of 4[35] and consequently an Erdős–Bacon number of 6.


Name Erdős number Bacon number Erdős–Bacon number
Mayim Bialik 5 2 7[36]
Jordan Ellenberg 3[13] 2[14] 5
Richard Feynman 3 3 6[9]
Colin Firth 5[a][23] 1[26] 6
Stephen Hawking 4 2[b] 6[11]
Daniel Kleitman 1 2 3[6]
Danica McKellar 4[37][15][16][38] 2[a] 6
Nicholas Metropolis 2[9] 2[10] 4
Elon Musk 4 2[b] 6
Natalie Portman 5[18][19][20][21][22] 2[a] 7[17]
Bruce Reznick 1 2 3
Carl Sagan 4 2[b] 6[12]
Kristen Stewart 5[28] 2[39][40] 7
Richard Thaler 3 2 5[41]


  1. ^ a b c See discussion above (Actors).
  2. ^ a b c Includes role as self.


  1. ^ Singh, Simon (May 1, 2002). "And the winner tonight is". The Telegraph. Archived from the original on November 12, 2012. Retrieved September 26, 2013.
  2. ^ a b "There's not much separating her from Bacon, Erdos". USA Today. August 14, 2007. Archived from the original on November 4, 2012.
  3. ^ Collins, James J.; Chow, Carson C. (1998). "It's a small world". Nature. 393 (6684): 409–10. Bibcode:1998Natur.393..409C. doi:10.1038/30835. PMID 9623993. S2CID 6827605.
  4. ^ Len Fisher (2016-02-17). "What's your Erdös-Bacon-Sabbath number?". Times Higher Education. Retrieved 2020-12-21.
  5. ^ Nancy Duvergne Smith (2013-01-29). "Erdos-Bacon-Sabbath Numbers: MITers at the Center of the Creative Universe". Slice of MIT. Retrieved 2020-12-21.
  6. ^ a b Grossman, Jerry (January 27, 1999). "The Erdös Number Project". Oakland University. Archived from the original on 1999-02-03. Retrieved 2021-03-03.
  7. ^ Erdős, P.; Hildebrand, A.; Odlyzko, A.; Pudaite, P.; Reznick, B. (1987). "The asymptotic behavior of a family of sequences". Pacific J. Math. no. 2 (126): 227–241.
  8. ^ Grossman, Jerry (December 6, 2018). "The Erdös Number Project". Oakland University. Archived from the original on 2020-03-11. Retrieved 2021-03-03.
  9. ^ a b c d "Richard Feynman". Erdős Bacon Sabbath Project. Archived from the original on 2017-12-25. Retrieved 2015-12-26.
  10. ^ a b "The Oracle of Bacon".
  11. ^ a b "Stephen Hawking". Erdős Bacon Sabbath Project. Archived from the original on 2017-12-25. Retrieved 2018-11-10.
  12. ^ a b "Carl Sagan". Erdős Bacon Sabbath Project. Archived from the original on 2018-01-11. Retrieved 2018-11-10.
  13. ^ a b "MR: Search MSC database". Retrieved 2022-02-06. MR Erdos Number = 3 Jordan S. Ellenberg coauthored with Christopher M. Skinner MR1844206 Christopher M. Skinner coauthored with Andrew M. Odlyzko MR1210537 Andrew M. Odlyzko coauthored with Paul Erdős1 MR0535395
  14. ^ a b "The Oracle of Bacon". Retrieved 2022-02-14.
  15. ^ a b Chayes, L; McKellar, D; Winn, B (1998). "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on ". Journal of Physics A: Mathematical and General. 31 (45): 9055–9063. Bibcode:1998JPhA...31.9055C. doi:10.1088/0305-4470/31/45/005.
  16. ^ a b Chayes, J. T.; Chayes, L.; Kotecký, R. (1995). "The analysis of the Widom-Rowlinson model by stochastic geometric methods". Communications in Mathematical Physics. 172 (3): 551. Bibcode:1995CMaPh.172..551C. doi:10.1007/BF02101808. S2CID 15051914.
  17. ^ a b "MICHAEL'S ERDŐS-BACON NUMBER | The Liquid Narrative Research Group".
  18. ^ a b Baird, A; Kagan, J; Gaudette, T; Walz, KA; Hershlag, N; Boas, DA (2002). "Frontal Lobe Activation during Object Permanence: Data from Near-Infrared Spectroscopy". NeuroImage. 16 (4): 1120–5. doi:10.1006/nimg.2002.1170. PMID 12202098. S2CID 15630444.
  19. ^ a b Baird, Abigail A.; Colvin, Mary K.; Vanhorn, John D.; Inati, Souheil; Gazzaniga, Michael S. (2005). "Functional Connectivity: Integrating Behavioral, Diffusion Tensor Imaging, and Functional Magnetic Resonance Imaging Data Sets". Journal of Cognitive Neuroscience. 17 (4): 687–93. CiteSeerX doi:10.1162/0898929053467569. PMID 15829087. S2CID 4666737.
  20. ^ a b Victor, Jonathan D.; Maiese, Kenneth; Shapley, Robert; Sidtis, John; Gazzaniga, Michael S. (1989). "Acquired central dyschromatopsia: analysis of a case with preservation of color discrimination". Clinical Vision Sciences. 4: 183–96.
  21. ^ a b Azor, Ruth; Gillis, J.; Victor, J. D. (1982). "Combinatorial Applications of Hermite Polynomials". SIAM Journal on Mathematical Analysis. 13 (5): 879–90. doi:10.1137/0513062.
  22. ^ a b Erdos, P.; Gillis, J. (2009). "Note on the Transfinite Diameter". Journal of the London Mathematical Society. s1-12 (3): 185. doi:10.1112/jlms/s1-12.2.185.
  23. ^ a b Kanai, Ryota; Feilden, Tom; Firth, Colin; Rees, Geraint (2011). "Political Orientations Are Correlated with Brain Structure in Young Adults". Current Biology. 21 (8): 677–80. doi:10.1016/j.cub.2011.03.017. PMC 3092984. PMID 21474316.
  24. ^ "Colin Firth credited in brain research". BBC News. 2011-06-05. Retrieved 2021-03-13.
  25. ^ "From Geraint Rees 0001 to Paul Erdős in four papers". Archived from the original on 2021-03-13. Retrieved 2021-03-13.
  26. ^ a b Where the Truth Lies at IMDb
  27. ^ "The Oracle of Bacon". Retrieved 2021-03-13.
  28. ^ a b Gershgorn, Dave. "Kristen Stewart (yes, that Kristen Stewart) just released a research paper on artificial intelligence".
  29. ^ "From Paul Erdős to Kristen Stewart in five papers". Archived from the original on 2018-03-14. Retrieved 2021-03-13.
  30. ^ "The Oracle of Bacon". Retrieved 2021-03-13.
  31. ^ Tate, Ryan (2012-09-20). "10 Awkward Hollywood Cameos by Tech Founders". Wired. Archived from the original on 2017-12-01. Retrieved 2021-05-08.
  32. ^ "The Oracle of Bacon". Retrieved 2021-05-08. Elon Musk has a Bacon number of 2. Elon Musk was in Iron Man 2 with Mickey Rourke was in Diner with Kevin Bacon
  33. ^ Bartsch, Yannic C.; Fischinger, Stephanie; Siddiqui, Sameed M.; Chen, Zhilin; Yu, Jingyou; Gebre, Makda; Atyeo, Caroline; Gorman, Matthew J.; Zhu, Alex Lee; Kang, Jaewon; Burke, John S.; Slein, Matthew; Gluck, Matthew J.; Beger, Samuel; Hu, Yiyuan; Rhee, Justin; Petersen, Eric; Mormann, Benjamin; de St Aubin, Michael; Hasdianda, Mohammad A.; Jambaulikar, Guruprasad; Boyer, Edward W.; Sabeti, Pardis C.; Barouch, Dan H.; Julg, Boris D.; Musk, Elon R.; Menon, Anil S.; Lauffenburger, Douglas A.; Nilles, Eric J.; Alter, Galit (2021-02-15). "Discrete SARS-CoV-2 antibody titers track with functional humoral stability". Nature Communications. 12 (1): 1018. Bibcode:2021NatCo..12.1018B. doi:10.1038/s41467-021-21336-8. PMC 7884400. PMID 33589636.
  34. ^ "MR: Search MSC database". Retrieved 2021-05-08. MR Erdos Number = 3 Pardis C. Sabeti coauthored with Michael Mitzenmacher MR3595146 Michael Mitzenmacher coauthored with Joel H. Spencer MR2056083 Joel H. Spencer coauthored with Paul Erdős1 MR0382007
  35. ^ "Jerry Grossman's Web Page > The Erdös Number Project > Some Famous People with Finite Erdös Numbers >". Oakland University. Retrieved 2021-05-08. Elon Musk entrepreneur 4
  36. ^ "Mayim Bialik". Erdős Bacon Sabbath Project. Archived from the original on 2018-01-15. Retrieved 2014-02-09.
  37. ^ "The Erdős Number Project, Erdos1". Archived from the original on 2006-12-07. Retrieved 2006-12-20.
  38. ^ Kotecký, R.; Preiss, D. (1986). "Cluster expansion for abstract polymer models". Communications in Mathematical Physics. 103 (3): 491–8. Bibcode:1986CMaPh.103..491K. doi:10.1007/BF01211762. S2CID 121879006.
  39. ^ Twilight at IMDb co-starred Kristen Stewart and Michael Sheen
  40. ^ Frost/Nixon at IMDb co-starred Michael Sheen and Kevin Bacon
  41. ^ Thaler, Richard H. [@R_Thaler] (May 10, 2016). "Learned I have a Bacon-Erdos number=5! Wrote a paper with Peter Wakker an Erdos 2 via Fishburn, and am Bacon 2 via Ryan Gosling in Big Short" (Tweet) – via Twitter.