Editing Erdős number (section)

==Related fields==
{{As of|2022}}, all Fields Medalists have a finite Erdős number, with values that range between 2 and 6, and a median of 3. In contrast, the median Erdős number across all mathematicians (with a finite Erdős number) is 5, with an extreme value of 13.<ref>{{Cite web|url=http://wwwp.oakland.edu/enp/trivia/|title=Facts about Erdös Numbers and the Collaboration Graph - The Erdös Number Project- Oakland University|website=wwwp.oakland.edu|access-date=2016-10-27}}</ref> The table below summarizes the Erdős number statistics for [[Nobel Prize|Nobel prize]] laureates in Physics, Chemistry, Medicine, and Economics.<ref>{{Cite journal|last=López de Prado|first=Marcos|title=Mathematics and Economics: A reality check|journal=The Journal of Portfolio Management|volume=43|issue=1|pages=5–8|doi=10.3905/jpm.2016.43.1.005|year=2016| s2cid=219231926 }}</ref> The first column counts the number of laureates. The second column counts the number of winners with a finite Erdős number. The third column is the percentage of winners with a finite Erdős number. The remaining columns report the minimum, maximum, average, and median Erdős numbers among those laureates.

{| class="wikitable sortable"
|+ Statistics on Mathematical Collaboration, 1903–2016
!
! #Laureates
! #Erdős
! %Erdős
! Min 
! Max
! Average
! Median
|-
|Fields Medal
|56
|56
|100.0%
|2
|6
|3.36
|3
|-
|Nobel Economics
|76
|47
|61.84%
|2
|8
|4.11
|4
|-
|Nobel Chemistry
|172
|42
|24.42%
|3
|10
|5.48
|5
|-
|Nobel Medicine
|210
|58
|27.62%
|3
|12
|5.50
|5
|-
|Nobel Physics
|200
|159
|79.50%
|2
|12
|5.63
|5
|}

===Physics===
Among the Nobel Prize laureates in Physics, [[Albert Einstein]] and [[Sheldon Glashow]] have an Erdős number of 2. Nobel Laureates with an Erdős number of 3 include [[Enrico Fermi]], [[Otto Stern]], [[Wolfgang Pauli]], [[Max Born]], [[Willis E. Lamb]], [[Eugene Wigner]], [[Richard P. Feynman]], [[Hans A. Bethe]], [[Murray Gell-Mann]], [[Abdus Salam]], [[Steven Weinberg]], [[Norman F. Ramsey]], [[Frank Wilczek]], [[David Wineland]], and [[Giorgio Parisi]]. Fields Medal-winning physicist [[Ed Witten]] has an Erdős number of 3.<ref name="paths">{{Cite web |title = Some Famous People with Finite Erdős Numbers |url = http://www.oakland.edu/enp/erdpaths/ |publisher = [[Oakland University|oakland.edu]] |access-date = 4 April 2014 }}</ref>

===Biology===
[[computational biology|Computational biologist]] [[Lior Pachter]] has an Erdős number of 2.<ref name="erdos2">{{cite web |title=List of all people with Erdos number less than or equal to 2 |url=https://files.oakland.edu/users/grossman/enp/ErdosA.html |work=The Erdös Number Project |publisher=Oakland University |date=14 July 2015 |access-date=25 August 2015}}</ref> [[Evolutionary biology|Evolutionary biologist]] [[Richard Lenski]] has an Erdős number of 3, having co-authored a publication with Lior Pachter and with mathematician [[Bernd Sturmfels]], each of whom has an Erdős number of 2.<ref>{{cite web|url=http://telliamedrevisited.wordpress.com/2015/05/28/erdos-with-a-non-kosher-side-of-bacon|title=Erdös with a non-kosher side of Bacon|author=Richard Lenski|date=May 28, 2015}}</ref>

===Finance and economics===
There are at least two winners of the [[Nobel Memorial Prize in Economic Sciences|Nobel Prize in Economics]] with an Erdős number of 2: [[Harry M. Markowitz]] (1990) and [[Leonid Kantorovich]] (1975). Other financial mathematicians with Erdős number of 2 include [[David Donoho]], [[Marc Yor]], [[Henry McKean]], [[Daniel Stroock]], and [[Joseph Keller]].

Nobel Prize laureates in Economics with an Erdős number of 3 include [[Kenneth J. Arrow]] (1972), [[Milton Friedman]] (1976), [[Herbert A. Simon]] (1978), [[Gerard Debreu]] (1983), [[John Forbes Nash, Jr.]] (1994), [[James Mirrlees]] (1996), [[Daniel McFadden]] (2000), [[Daniel Kahneman]] (2002), [[Robert J. Aumann]] (2005), [[Leonid Hurwicz]] (2007), [[Roger Myerson]] (2007), [[Alvin E. Roth]] (2012), and [[Lloyd S. Shapley]] (2012) and [[Jean Tirole]] (2014).<ref>Grossman, J. (2015): "The Erdős Number Project." http://wwwp.oakland.edu/enp/erdpaths/</ref>

Some investment firms have been founded by mathematicians with low Erdős numbers, among them [[James Ax|James B. Ax]] of [[Renaissance Technologies#Medallion Fund|Axcom Technologies]], and [[James H. Simons]] of [[Renaissance Technologies]], both with an Erdős number of 3.<ref>{{Cite news|url=https://www.bloomberg.com/news/articles/2016-11-11/six-degrees-of-quant-kevin-bacon-and-the-erdos-number-mystery|title=Six Degrees of Quant: Kevin Bacon and the Erdős Number Mystery|last=Kishan|first=Saijel|date=2016-11-11|newspaper=Bloomberg.com|access-date=2016-11-12}}</ref><ref>{{Cite news|url=http://www.financial-math.org/blog/2016/11/erdos-numbers-in-finance/|title=Erdős Numbers: A True "Prince and the Pauper" story|last=Bailey|first=David H.|date=2016-11-06|newspaper=The Mathematical Investor|language=en-US|access-date=2016-11-12}}</ref>

===Philosophy===
Since the more formal versions of philosophy share reasoning with the basics of mathematics, these fields overlap considerably, and Erdős numbers are available for many philosophers.<ref>{{cite web |url=http://home.iprimus.com.au/than/toby/2013-researchnetwork-poster.pdf |title=Philosophy research networks |author=Toby Handfield |archive-url=https://web.archive.org/web/20160221161316/http://home.iprimus.com.au/than/toby/2013-researchnetwork-poster.pdf |archive-date=2016-02-21 }}</ref> Philosophers [[John P. Burgess]] and [[Brian Skyrms]] have an Erdős number of 2.<ref name="Erdős Number Project File Erdos2"/> [[Jon Barwise]] and [[Joel David Hamkins]], both with Erdős number 2, have also contributed extensively to philosophy, but are primarily described as mathematicians.

===Law===
Judge [[Richard Posner]], having coauthored with [[Alvin E. Roth]], has an Erdős number of at most 4. [[Roberto Mangabeira Unger]], a politician, philosopher, and legal theorist who teaches at Harvard Law School, has an Erdős number of at most 4, having coauthored with [[Lee Smolin]].

===Politics===
[[Angela Merkel]], [[Chancellor of Germany]] from 2005 to 2021, has an Erdős number of at most 5.<ref name="project"/>

===Engineering===
Some fields of engineering, in particular [[communication theory]] and [[cryptography]], make direct use of the discrete mathematics championed by Erdős. It is therefore not surprising that practitioners in these fields have low Erdős numbers. For example, [[Robert McEliece]], a professor of [[electrical engineering]] at [[California Institute of Technology|Caltech]], had an Erdős number of 1, having collaborated with Erdős himself.<ref>{{cite journal |last1=Erdős |first1=Paul |last2=McEliece |first2=Robert James|last3=Taylor |first3=Herbert|title=Ramsey bounds for graph products |journal=[[Pacific Journal of Mathematics]] |volume=37 |issue=1 |date=1971 |pages=45–46 |url=https://msp.org/pjm/1971/37-1/pjm-v37-n1-p07-p.pdf |doi=10.2140/pjm.1971.37.45|doi-access=free }}</ref> Cryptographers [[Ron Rivest]], [[Adi Shamir]], and [[Leonard Adleman]], inventors of the [[RSA (cryptosystem)|RSA]] cryptosystem, all have Erdős number 2.<ref name="erdos2"/>

===Linguistics===
The Romanian mathematician and computational linguist [[Solomon Marcus]] had an Erdős number of 1 for a paper in ''[[Acta Mathematica Hungarica]]'' that he co-authored with Erdős in 1957.<ref>{{cite journal|first1=Paul|last1= Erdős |author1-link=Paul Erdős|first2= Solomon|last2= Marcus|author2-link=Solomon Marcus| year=1957|title= Sur la décomposition de l'espace euclidien en ensembles homogènes |trans-title= On the decomposition of the Euclidean space into homogeneous sets|journal=[[Acta Mathematica Hungarica]]|volume=8|issue= 3–4 |pages=443–452|mr=0095456|doi=10.1007/BF02020326|doi-access=|s2cid= 121671198 }}</ref>