916:
31:
115:
141:
Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 509 direct collaborators; these are the people with Erdős number 1. The people who have collaborated with them (but not with Erdős himself) have an Erdős number of 2 (12,600 people as of 7 August 2020), those
76:
Paul Erdős (1913–1996) was an influential
Hungarian mathematician who in the latter part of his life spent a great deal of time writing papers with a large number of colleagues—over 500—working on solutions to outstanding mathematical problems. He published more papers during his lifetime (at least
81:
published more total pages of mathematics but fewer separate papers: about 800.) Erdős spent most of his career with no permanent home or job. He traveled with everything he owned in two suitcases, and would visit mathematicians he wanted to collaborate with, often unexpectedly, and expect to stay
947:
of mathematicians throughout the world for many years. Among all working mathematicians at the turn of the millennium who have a finite Erdős number, the numbers range up to 15, the median is 5, and the mean is 4.65; almost everyone with a finite Erdős number has a number less than 8. Due to the
396:
laureates in
Physics, Chemistry, Medicine, and Economics. 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,
127:
To be assigned an Erdős number, someone must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős himself is assigned an Erdős number of zero. A certain author's Erdős number is one greater than the lowest Erdős number of any of their collaborators; for
97:
is 3. Only 7,097 (about 5% of mathematicians with a collaboration path) have an Erdős number of 2 or lower. As time passes, the lowest Erdős number that can still be achieved will necessarily increase, as mathematicians with low Erdős numbers die and become unavailable for collaboration. Still,
85:
The idea of the Erdős number was originally created by the mathematician's friends as a tribute to his enormous output. Later it gained prominence as a tool to study how mathematicians cooperate to find answers to unsolved problems. Several projects are devoted to studying connectivity among
264:
While Erdős collaborated with hundreds of co-authors, there were some individuals with whom he co-authored dozens of papers. This is a list of the ten persons who most frequently co-authored with Erdős and their number of papers co-authored with Erdős (i.e. their number of collaborations).
391:
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. The table below summarizes the Erdős number statistics for
142:
who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an Erdős number of
1267:
173:
but excludes non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The "Erdős number of the second kind" restricts assignment of Erdős numbers to papers with only two collaborators.
122:
collaborates with Paul Erdős on one paper, and with Bob on another, but Bob never collaborates with Erdős himself, then Alice is given an Erdős number of 1 and Bob is given an Erdős number of 2, as he is two steps from
964:
have collaborated on papers, and since
Kleitman has an Erdős number of 1, a large fraction of the genetics and genomics community can be linked via Lander and his numerous collaborators. Similarly, collaboration with
1075:
captures the citation impact of the publications," and that "One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking."
948:
very high frequency of interdisciplinary collaboration in science today, very large numbers of non-mathematicians in many other fields of science also have finite Erdős numbers. For example, political scientist
1083:, hence providing the buyer with an Erdős number of 5. The winning bid of $ 1031 was posted by a Spanish mathematician, who refused to pay and only placed the bid to stop what he considered a mockery.
790:
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. Philosophers
169:... Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional co-authors is permitted,...
2425:
161:... One drawback of the MR system is that it considers all jointly authored works as providing legitimate links, even articles such as obituaries, which are not really joint research. ...
157:, which includes most mathematics journals but covers other subjects only in a limited way, and which also includes some non-research publications. The Erdős Number Project web site says:
1019:
Earlier mathematicians published fewer papers than modern ones, and more rarely published jointly written papers. The earliest person known to have a finite Erdős number is either
1065:
joint paper they have produced—form an electrical network with a one-ohm resistor on each edge. The total resistance between two nodes tells how "close" these two nodes are.
1038:
version of the Erdős number problem, by orienting edges of the collaboration graph from the alphabetically earlier author to the alphabetically later author and defining the
952:
has an Erdős number of 2. In biomedical research, it is common for statisticians to be among the authors of publications, and many statisticians can be linked to Erdős via
861:, 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,
1061:. From the collaboration multigraph of the second kind (although he also has a way to deal with the case of the first kind)—with one edge between two mathematicians for
2154:
153:
There is room for ambiguity over what constitutes a link between two authors. The
American Mathematical Society collaboration distance calculator uses data from
59:
1123:
Further extension is possible. For example, the "Erdős–Bacon–Sabbath number" is the sum of the Erdős–Bacon number and the collaborative distance to the band
2014:(1957). "Sur la décomposition de l'espace euclidien en ensembles homogènes" [On the decomposition of the Euclidean space into homogeneous sets].
673:
93:
Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers (i.e. high proximity). The median Erdős number of
2422:
1483:
1206:
2081:
Pachter, L; Batzoglou, S; Spitkovsky, VI; Banks, E; Lander, ES; Kleitman, DJ; Berger, B (1999). "A dictionary-based approach for gene annotation".
1895:
1945:
1068:
It has been argued that "for an individual researcher, a measure such as Erdős number captures the structural properties of network whereas the
2456:
2124:
62:. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers.
826:, a politician, philosopher, and legal theorist who teaches at Harvard Law School, has an Erdős number of at most 4, having coauthored with
1418:
1355:
870:
2190:
2488:
1235:
1201:
970:
181:
whose own Erdős number is 2. Goffman published his observations about Erdős' prolific collaboration in a 1969 article entitled "
2834:
1978:
1491:
806:, both with Erdős number 2, have also contributed extensively to philosophy, but are primarily described as mathematicians.
2659:
2620:
1868:
2704:
1682:
129:
90:
can tell us how authors cluster, how the number of co-authors per paper evolves over time, or how new theories propagate.
2300:
1103:
by a chain of joint appearances in films. It was created in 1994, 25 years after
Goffman's article on the Erdős number.
1050:
2748:
2725:
2839:
2271:
936:
2016:
1096:
903:
205:
132:
provides a free online tool to determine the collaboration distance between two mathematical authors listed in the
2593:
1107:
1217:
1028:
2829:
2779:
2312:
1151:
823:
779:
771:
2776:. Contains statistics and a complete list of all mathematicians with an Erdős number less than or equal to 2.
2578:
281:
2844:
2824:
2785:
2598:
2572:
1223:
920:
866:
2407:
1524:
842:
724:
647:
178:
147:
1952:
1920:
1780:"Facts about Erdös Numbers and the Collaboration Graph - The Erdös Number Project- Oakland University"
2626:
1189:
1173:
854:
654:
134:
660:
has an Erdős number of 3, having co-authored a publication with Lior
Pachter and with mathematician
150:
one). Since the death of Paul Erdős, the lowest Erdős number that a new researcher can obtain is 2.
1717:
1229:
1195:
1079:
In 2004 William Tozier, a mathematician with an Erdős number of 4 auctioned off a co-authorship on
128:
example an author who has coauthored a publication with Erdős would have an Erdős number of 1. The
99:
87:
2528:
2462:
2423:
Towards simultaneously exploiting structure and outcomes in interaction networks for node ranking
2388:
2361:
2171:
2041:
1820:
1766:
1699:
1667:
1565:
1516:
886:
803:
681:
677:
600:
50:
361:
341:
249:
1110:, which combines the two numbers by taking their sum. One example is the actress-mathematician
1091:
A number of variations on the concept have been proposed to apply to other fields, notably the
2798:
2791:
2484:
2452:
2098:
1424:
1414:
1296:
1020:
915:
321:
241:
233:
217:
2493:
1165:
number describes a player's connection to
Honinbo Shusaku, the strongest player of his time.
981:
have finite Erdős numbers, many due to chains of collaboration with such notable scholars as
766:
Some investment firms have been founded by mathematicians with low Erdős numbers, among them
2520:
2444:
2441:
Proceedings of the 19th ACM international conference on
Information and knowledge management
2380:
2353:
2163:
2090:
2025:
1987:
1812:
1756:
1691:
1589:
1500:
1402:
1286:
1276:
1116:
1046:
from Erdős to the author in this directed graph. He finds a path of this type of length 12.
1024:
1013:
966:
756:
740:
716:
708:
620:
608:
291:
221:
197:
94:
2037:
1841:
1543:
1512:
2558:
2550:
2429:
2194:
2142:
2116:
2033:
1540:
1508:
1162:
1132:
1128:
1111:
994:
961:
882:
862:
791:
775:
736:
732:
712:
661:
616:
572:
568:
237:
209:
98:
historical figures can have low Erdős numbers. For example, renowned Indian mathematician
30:
2481:
A Passion for
Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality
351:
2296:
2011:
1211:
1177:
1053:
suggests "rational Erdős numbers", generalizing the idea that a person who has written
1035:
898:
815:
744:
728:
697:
657:
632:
628:
592:
584:
331:
311:
225:
78:
2818:
2808:
2801:. A search engine for Erdős numbers and collaboration distance between other authors.
2138:
2045:
2007:
1970:
1824:
1520:
1407:
1291:
1262:
1143:
1124:
990:
986:
974:
873:, had an Erdős number of 1, having collaborated with Erdős himself. Cryptographers
838:
819:
752:
748:
720:
701:
624:
604:
596:
371:
301:
229:
213:
119:
71:
55:
34:
2466:
2392:
2365:
1374:
106:, Erdős number 2), even though Paul Erdős was only 7 years old when Ramanujan died.
2498:
2436:
2250:
1655:
1092:
1043:
1031:(born 1849, Erdős number 3), depending on the standard of publication eligibility.
1009:
982:
949:
932:
858:
795:
693:
685:
650:
576:
388:
193:
189:
2546:
2726:"Street Fighter's Ryu and Chun-Li join Ubisoft's take on Smash Bros., Brawlhalla"
1336:
1016:
winners during the three cycles in 1986 to 1994 have Erdős numbers of at most 9.
2648:
1390:
1258:
1169:
1147:
1106:
A small number of people are connected to both Erdős and Bacon and thus have an
1100:
978:
957:
924:
799:
760:
612:
393:
245:
103:
2554:
2146:
1268:
Proceedings of the
National Academy of Sciences of the United States of America
114:
2804:
2304:
1816:
1613:
1594:
1379:
953:
878:
874:
827:
580:
253:
201:
177:
The Erdős number was most likely first defined in print by Casper Goffman, an
1803:
López de Prado, Marcos (2016). "Mathematics and Economics: A reality check".
575:
have an Erdős number of 2. Nobel Laureates with an Erdős number of 3 include
2448:
2420:
Kashyap Dixit, S Kameshwaran, Sameep Mehta, Vinayaka Pandit, N Viswanadham,
2094:
1428:
1158:
1150:, widely considered the greatest chess player of his time and an unofficial
636:
17:
2435:
Kameshwaran, S.; Pandit, V.; Mehta, S.; Viswanadham, N.; Dixit, K. (2010).
2275:
2102:
1992:
1300:
1281:
2384:
2120:
1409:
Math and mathematicians: the history of math discoveries around the world
1226: – Experiments examining the average path length for social networks
998:
944:
767:
689:
588:
143:
2684:
2357:
1882:
2532:
2175:
2060:
2029:
1738:
1703:
1626:
1561:
1504:
1232: – Graph where most nodes are reachable in a small number of steps
1069:
2326:
1779:
1315:
684:(1975). Other financial mathematicians with Erdős number of 2 include
2208:
1461:
1356:"An Arbitrary Number of Years Since Mathematician Paul Erdős's Birth"
956:, who has an Erdős number of 2. Similarly, the prominent geneticist
707:
Nobel Prize laureates in Economics with an Erdős number of 3 include
2524:
2167:
1695:
1609:
1607:
1605:
86:
researchers, using the Erdős number as a proxy. For example, Erdős
2229:
2147:"On Collections of Subsets Containing No 4-Member Boolean Algebra"
1447:
1139:
914:
397:
maximum, average, and median Erdős numbers among those laureates.
113:
29:
1896:"Six Degrees of Quant: Kevin Bacon and the Erdős Number Mystery"
1192: – Metrics of the bibliometric impact of individual authors
1080:
1002:
928:
27:
Closeness of someone's association with mathematician Paul Erdős
2433:, IBM Research Report R109002, February 2009; also appeared as
2327:"Paths to Erdös - The Erdös Number Project- Oakland University"
248:. There are no Fields medalists with Erdős number 1; however,
54:) describes the "collaborative distance" between mathematician
1842:"List of all people with Erdos number less than or equal to 2"
2773:
1969:
Erdős, Paul; McEliece, Robert James; Taylor, Herbert (1971).
1761:
1663:
192:
is as low as 3. Fields medalists with Erdős number 2 include
1176:
number describes a video game character's connection to the
927:, who was then 10 years old. Tao became a math professor at
1220: – Concept of social inter-connectedness of all people
185:" See also some comments in an obituary by Michael Golomb.
1680:
Goffman, Casper (1969). "And what is your Erdős number?".
1057:
joint papers with Erdős should be assigned Erdős number 1/
2305:"Visualising Virtual Communities: From Erdős to the Arts"
1584:
1582:
2749:"Street Fighter's Ryu Is The Kevin Bacon Of Video Games"
1198: – Graph modeling collaboration in a social network
1114:, best known for playing Winnie Cooper on the TV series
2307:. In Dunn, Stuart; Bowen, Jonathan P.; Ng, Kia (eds.).
1462:"Facts about Erdös Numbers and the Collaboration Graph"
1448:"Facts about Erdös Numbers and the Collaboration Graph"
2371:
Tompa, Martin (1990). "Figures of merit: the sequel".
2309:
EVA London 2012: Electronic Visualisation and the Arts
1627:"Compute your Erdös number - The Erdös Number Project"
1442:
1440:
1438:
897:
The Romanian mathematician and computational linguist
1921:"Erdős Numbers: A True "Prince and the Pauper" story"
1660:
Facts about Erdős Numbers and the Collaboration Graph
1120:. Her Erdős number is 4, and her Bacon number is 2.
845:
from 2005 to 2021, has an Erdős number of at most 5.
2786:"On a Portion of the Well-Known Collaboration Graph"
1263:"The structure of scientific collaboration networks"
1131:
had an Erdős–Bacon–Sabbath number of 8, and actress
401:
Statistics on Mathematical Collaboration, 1903-2016
1406:
1214: – Quantitative study of scholarly literature
1881:Grossman, J. (2015): "The Erdős Number Project."
1482:De Castro, Rodrigo; Grossman, Jerrold W. (1999).
77:1,525) than any other mathematician in history. (
58:and another person, as measured by authorship of
2155:Proceedings of the American Mathematical Society
2437:"Outcome aware ranking in interaction networks"
1534:Rev. Acad. Colombiana Cienc. Exact. Fís. Natur.
167:
159:
2545:McKellar's co-author Lincoln Chayes published
2061:"Some Famous People with Finite Erdős Numbers"
1562:"Some Famous People with Finite Erdős Numbers"
2511:Klarreich, Erica (2004). "Theorem for Sale".
1238: – Study of science as a social activity
8:
2792:"Some Analyses of Erdős Collaboration Graph"
2788:, Jerrold W. Grossman and Patrick D. F. Ion.
1413:. Baker, Lawrence W. Detroit, Mich.: U X L.
1253:
1251:
567:Among the Nobel Prize laureates in Physics,
2344:Tompa, Martin (1989). "Figures of merit".
1733:
1731:
1373:Krauthammer, Charles (27 September 1996).
853:Some fields of engineering, in particular
399:
267:
2594:"What's your Erdős–Bacon–Sabbath number?"
1991:
1836:
1834:
1290:
1280:
1127:in terms of singing in public. Physicist
664:, each of whom has an Erdős number of 2.
110:Definition and application in mathematics
2724:McWhertor, Michael (November 22, 2021).
1556:
1554:
1552:
1477:
1475:
907:that he co-authored with Erdős in 1957.
901:had an Erdős number of 1 for a paper in
1869:"Erdös with a non-kosher side of Bacon"
1247:
1135:has one of 11 (her Erdős number is 5).
1008:According to Alex Lopez-Ortiz, all the
889:cryptosystem, all have Erdős number 2.
102:has an Erdős number of only 3 (through
2576:(2002) with James Kisicki, who was in
2121:"Publications Since 1980 more or less"
943:Erdős numbers have been a part of the
672:There are at least two winners of the
2799:MR free tools: collaboration distance
2794:, Vladimir Batagelj and Andrej Mrvar.
2311:. Electronic Workshops in Computing.
2125:Massachusetts Institute of Technology
1883:http://wwwp.oakland.edu/enp/erdpaths/
1207:List of things named after Paul Erdős
1001:(4). There are also connections with
49:
7:
2274:. Lingo.stanford.edu. Archived from
822:, has an Erdős number of at most 4.
1805:The Journal of Portfolio Management
1391:File available as HTML via Solipsys
1146:describes a player's connection to
1042:of an author to be the length of a
1971:"Ramsey bounds for graph products"
1848:. Oakland University. 14 July 2015
1099:), connecting actors to the actor
782:, both with an Erdős number of 3.
25:
2665:from the original on 13 June 2006
1236:Sociology of scientific knowledge
635:. Fields Medal-winning physicist
260:Most frequent Erdős collaborators
2780:New Erdős Number Project website
2193:. Semantics, Inc. Archived from
1656:Erdős numbers of the second kind
1598:. American Mathematical Society.
1354:Cofield, Calla (26 March 2013).
1027:(born 1831, Erdős number 7), or
2797:American Mathematical Society,
2251:"Christopher Potts: Miscellany"
1919:Bailey, David H. (2016-11-06).
1867:Richard Lenski (May 28, 2015).
1670:, USA. Retrieved July 25, 2009.
939:in 2007. His Erdős number is 2.
2782:Migration to new site in 2021.
2209:"Aaron Dinkin has a web site?"
1979:Pacific Journal of Mathematics
1946:"Philosophy research networks"
1616:, Version 2020, 7 August 2020.
1492:The Mathematical Intelligencer
1202:List of people by Erdős number
1023:(born 1743, Erdős number 13),
256:Laureate with Erdős number 1.
188:The median Erdős number among
183:And what is your Erdős number?
1:
2747:Walker, Ian (June 22, 2021).
2621:"Erdős–Bacon–Sabbath numbers"
1894:Kishan, Saijel (2016-11-11).
1683:American Mathematical Monthly
1484:"Famous trails to Paul Erdős"
977:research community, and many
130:American Mathematical Society
2619:Sear, Richard (2012-09-15).
2561:, a co-author of Paul Erdős.
1532:Original Spanish version in
1337:"Frequently Asked Questions"
1316:"Publications of Paul Erdős"
798:have an Erdős number of 2.
2811:on imaginary Erdős numbers.
2230:"Mark Liberman's Home Page"
937:Fellow of the Royal Society
935:in 2006, and was elected a
676:with an Erdős number of 2:
2861:
2649:"Your Morphy Number Is Up"
2592:Fisher, Len (2016-02-17).
2553:, who in turn co-authored
2017:Acta Mathematica Hungarica
1097:Six Degrees of Kevin Bacon
919:Paul Erdős in 1985 at the
904:Acta Mathematica Hungarica
653:has an Erdős number of 2.
639:has an Erdős number of 3.
69:
1925:The Mathematical Investor
1817:10.3905/jpm.2016.43.1.005
1218:Six degrees of separation
1029:Ferdinand Georg Frobenius
818:, having coauthored with
2774:The Erdős Number Project
2582:(1997) with Kevin Bacon.
2408:"Rational Erdős numbers"
2313:British Computer Society
2189:von Fintel, Kai (2004).
1846:The Erdös Number Project
1762:The Erdős Number Project
1743:The Erdös Number Project
1664:The Erdős Number Project
1590:"Collaboration Distance"
1034:Martin Tompa proposed a
824:Roberto Mangabeira Unger
780:Renaissance Technologies
674:Nobel Prize in Economics
2625:Department of Physics,
2579:Telling Lies in America
2570:Danica McKellar was in
2449:10.1145/1871437.1871470
2095:10.1089/106652799318364
1769:, US, October 20, 2010.
648:Computational biologist
2835:Mathematics literature
2599:Times Higher Education
2573:The Year That Trembled
2479:Clifford A. Pickover:
2191:"My Erdös Number is 8"
1993:10.2140/pjm.1971.37.45
1718:"Paul Erdös at Purdue"
1282:10.1073/pnas.021544898
1224:Small-world experiment
960:and the mathematician
940:
921:University of Adelaide
867:electrical engineering
655:Evolutionary biologist
171:
163:
124:
38:
2385:10.1145/101371.101376
1745:. Oakland University.
1468:. Oakland University.
1450:. Oakland University.
1040:monotone Erdős number
969:opened the door for
918:
843:Chancellor of Germany
725:John Forbes Nash, Jr.
668:Finance and economics
117:
33:
2627:University of Surrey
2443:. pp. 229–238.
2272:"Bob's Erdős Number"
1539:(89) 563–582, 1999,
1466:Erdös Number Project
1343:. Dartmouth College.
1190:Author-level metrics
1152:World Chess Champion
855:communication theory
155:Mathematical Reviews
135:Mathematical Reviews
88:collaboration graphs
2358:10.1145/65780.65782
2315:. pp. 238–244.
2303:(10–12 July 2012).
1722:www.math.purdue.edu
1386:The Washington Post
1360:Scientific American
1230:Small-world network
1196:Collaboration graph
885:, inventors of the
402:
100:Srinivasa Ramanujan
60:mathematical papers
2840:Separation numbers
2647:Kingston, Taylor.
2428:2011-11-10 at the
2297:Bowen, Jonathan P.
2197:on 23 August 2006.
2030:10.1007/BF02020326
1767:Oakland University
1668:Oakland University
1631:Oakland University
1505:10.1007/BF03025416
1259:Newman, Mark E. J.
1108:Erdős–Bacon number
985:(Erdős number 4),
941:
804:Joel David Hamkins
772:Axcom Technologies
682:Leonid Kantorovich
678:Harry M. Markowitz
601:Richard P. Feynman
400:
125:
39:
2805:Numberphile video
2705:"Shusaku Numbers"
2458:978-1-4503-0099-5
2059:Grossman, Jerry.
1759:, Version 2010,
1755:Grossman, Jerry,
1403:Bruno, Leonard C.
1341:The Euler Archive
1314:Grossman, Jerry.
1021:Antoine Lavoisier
865:, a professor of
560:
559:
380:
379:
322:Cecil C. Rousseau
242:Jean-Pierre Serre
234:Richard Borcherds
218:Charles Fefferman
51:[ˈɛrdøːʃ]
16:(Redirected from
2852:
2772:Jerry Grossman,
2761:
2760:
2758:
2756:
2744:
2738:
2737:
2735:
2733:
2721:
2715:
2714:
2712:
2711:
2701:
2695:
2694:
2692:
2691:
2685:"Shusaku Number"
2681:
2675:
2674:
2672:
2670:
2664:
2653:
2644:
2638:
2637:
2635:
2634:
2616:
2610:
2609:
2607:
2606:
2589:
2583:
2568:
2562:
2543:
2537:
2536:
2508:
2502:
2477:
2471:
2470:
2418:
2412:
2411:
2403:
2397:
2396:
2369:
2341:
2335:
2334:
2323:
2317:
2316:
2301:Wilson, Robin J.
2293:
2287:
2286:
2284:
2283:
2268:
2262:
2261:
2259:
2258:
2247:
2241:
2240:
2238:
2237:
2232:. Ling.upenn.edu
2226:
2220:
2219:
2217:
2216:
2211:. Ling.upenn.edu
2205:
2199:
2198:
2186:
2180:
2179:
2151:
2143:Kleitman, Daniel
2135:
2129:
2128:
2117:Kleitman, Daniel
2113:
2107:
2106:
2078:
2072:
2071:
2069:
2067:
2056:
2050:
2049:
2024:(3–4): 443–452.
2004:
1998:
1997:
1995:
1975:
1966:
1960:
1959:
1957:
1951:. Archived from
1950:
1944:Toby Handfield.
1941:
1935:
1934:
1932:
1931:
1916:
1910:
1909:
1907:
1906:
1891:
1885:
1879:
1873:
1872:
1864:
1858:
1857:
1855:
1853:
1838:
1829:
1828:
1800:
1794:
1793:
1791:
1790:
1784:wwwp.oakland.edu
1776:
1770:
1753:
1747:
1746:
1739:"Paths to Erdös"
1735:
1726:
1725:
1714:
1708:
1707:
1677:
1671:
1648:
1642:
1641:
1639:
1638:
1623:
1617:
1611:
1600:
1599:
1586:
1577:
1576:
1574:
1572:
1558:
1547:
1531:
1529:
1523:. Archived from
1488:
1479:
1470:
1469:
1458:
1452:
1451:
1444:
1433:
1432:
1412:
1399:
1393:
1389:
1383:
1370:
1364:
1363:
1351:
1345:
1344:
1333:
1327:
1326:
1324:
1322:
1311:
1305:
1304:
1294:
1284:
1255:
1117:The Wonder Years
1095:(as in the game
1025:Richard Dedekind
1014:Nevanlinna prize
967:Gustavus Simmons
757:Lloyd S. Shapley
741:Robert J. Aumann
717:Herbert A. Simon
709:Kenneth J. Arrow
621:Norman F. Ramsey
609:Murray Gell-Mann
483:Nobel Chemistry
457:Nobel Economics
403:
389:Fields Medalists
387:As of 2022, all
268:
222:William Thurston
198:Kunihiko Kodaira
190:Fields medalists
95:Fields Medalists
53:
48:
21:
2860:
2859:
2855:
2854:
2853:
2851:
2850:
2849:
2830:Social networks
2815:
2814:
2769:
2764:
2754:
2752:
2746:
2745:
2741:
2731:
2729:
2723:
2722:
2718:
2709:
2707:
2703:
2702:
2698:
2689:
2687:
2683:
2682:
2678:
2668:
2666:
2662:
2651:
2646:
2645:
2641:
2632:
2630:
2618:
2617:
2613:
2604:
2602:
2591:
2590:
2586:
2569:
2565:
2559:Daniel Kleitman
2551:Elliott H. Lieb
2544:
2540:
2525:10.2307/4015267
2519:(24): 376–377.
2510:
2509:
2505:
2483:. Wiley, 2011,
2478:
2474:
2459:
2434:
2430:Wayback Machine
2419:
2415:
2406:Barr, Michael.
2405:
2404:
2400:
2373:ACM SIGACT News
2370:
2346:ACM SIGACT News
2343:
2342:
2338:
2325:
2324:
2320:
2295:
2294:
2290:
2281:
2279:
2270:
2269:
2265:
2256:
2254:
2249:
2248:
2244:
2235:
2233:
2228:
2227:
2223:
2214:
2212:
2207:
2206:
2202:
2188:
2187:
2183:
2168:10.2307/2037762
2149:
2137:
2136:
2132:
2115:
2114:
2110:
2089:(3–4): 419–30.
2080:
2079:
2075:
2065:
2063:
2058:
2057:
2053:
2012:Marcus, Solomon
2006:
2005:
2001:
1973:
1968:
1967:
1963:
1955:
1948:
1943:
1942:
1938:
1929:
1927:
1918:
1917:
1913:
1904:
1902:
1893:
1892:
1888:
1880:
1876:
1866:
1865:
1861:
1851:
1849:
1840:
1839:
1832:
1802:
1801:
1797:
1788:
1786:
1778:
1777:
1773:
1754:
1750:
1737:
1736:
1729:
1716:
1715:
1711:
1696:10.2307/2317868
1679:
1678:
1674:
1649:
1645:
1636:
1634:
1625:
1624:
1620:
1612:
1603:
1588:
1587:
1580:
1570:
1568:
1560:
1559:
1550:
1527:
1486:
1481:
1480:
1473:
1460:
1459:
1455:
1446:
1445:
1436:
1421:
1401:
1400:
1396:
1377:
1372:
1371:
1367:
1353:
1352:
1348:
1335:
1334:
1330:
1320:
1318:
1313:
1312:
1308:
1257:
1256:
1249:
1245:
1186:
1180:character Ryu.
1133:Natalie Portman
1129:Stephen Hawking
1112:Danica McKellar
1089:
995:Geoffrey Pullum
962:Daniel Kleitman
931:, received the
913:
895:
883:Leonard Adleman
863:Robert McEliece
851:
836:
812:
792:John P. Burgess
788:
776:James H. Simons
737:Daniel Kahneman
733:Daniel McFadden
713:Milton Friedman
670:
662:Bernd Sturmfels
645:
617:Steven Weinberg
573:Sheldon Glashow
569:Albert Einstein
565:
509:Nobel Medicine
385:
362:Endre Szemerédi
276:collaborations
275:
262:
250:Endre Szemerédi
238:Manjul Bhargava
210:Enrico Bombieri
112:
74:
68:
46:
28:
23:
22:
15:
12:
11:
5:
2858:
2856:
2848:
2847:
2842:
2837:
2832:
2827:
2817:
2816:
2813:
2812:
2802:
2795:
2789:
2783:
2777:
2768:
2767:External links
2765:
2763:
2762:
2739:
2716:
2696:
2676:
2639:
2611:
2584:
2563:
2538:
2503:
2472:
2457:
2413:
2398:
2336:
2318:
2288:
2263:
2253:. Stanford.edu
2242:
2221:
2200:
2181:
2145:(April 1971).
2130:
2108:
2073:
2051:
1999:
1961:
1958:on 2016-02-21.
1936:
1911:
1886:
1874:
1859:
1830:
1795:
1771:
1748:
1727:
1709:
1672:
1643:
1618:
1601:
1578:
1548:
1530:on 2015-09-24.
1471:
1453:
1434:
1420:978-0787638139
1419:
1394:
1388:. p. A25.
1365:
1346:
1328:
1306:
1275:(2): 404–409.
1246:
1244:
1241:
1240:
1239:
1233:
1227:
1221:
1215:
1212:Scientometrics
1209:
1204:
1199:
1193:
1185:
1182:
1178:Street Fighter
1088:
1085:
1036:directed graph
912:
909:
899:Solomon Marcus
894:
891:
850:
847:
835:
832:
816:Richard Posner
811:
808:
787:
784:
745:Leonid Hurwicz
729:James Mirrlees
698:Daniel Stroock
669:
666:
658:Richard Lenski
644:
641:
633:Giorgio Parisi
629:David Wineland
593:Willis E. Lamb
585:Wolfgang Pauli
564:
561:
558:
557:
554:
551:
548:
545:
542:
539:
536:
535:Nobel Physics
532:
531:
528:
525:
522:
519:
516:
513:
510:
506:
505:
502:
499:
496:
493:
490:
487:
484:
480:
479:
476:
473:
470:
467:
464:
461:
458:
454:
453:
450:
447:
444:
441:
438:
435:
432:
428:
427:
424:
421:
418:
415:
412:
409:
406:
384:
383:Related fields
381:
378:
377:
374:
368:
367:
364:
358:
357:
354:
348:
347:
344:
338:
337:
334:
328:
327:
324:
318:
317:
314:
312:Richard Schelp
308:
307:
304:
298:
297:
294:
288:
287:
284:
282:András Sárközy
278:
277:
272:
261:
258:
226:Shing-Tung Yau
165:It also says:
111:
108:
79:Leonhard Euler
67:
64:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2857:
2846:
2845:Bibliometrics
2843:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2822:
2820:
2810:
2809:Ronald Graham
2806:
2803:
2800:
2796:
2793:
2790:
2787:
2784:
2781:
2778:
2775:
2771:
2770:
2766:
2750:
2743:
2740:
2727:
2720:
2717:
2706:
2700:
2697:
2686:
2680:
2677:
2661:
2657:
2650:
2643:
2640:
2629:
2628:
2622:
2615:
2612:
2601:
2600:
2595:
2588:
2585:
2581:
2580:
2575:
2574:
2567:
2564:
2560:
2556:
2552:
2548:
2542:
2539:
2534:
2530:
2526:
2522:
2518:
2514:
2507:
2504:
2500:
2496:
2495:
2490:
2489:9781118046074
2486:
2482:
2476:
2473:
2468:
2464:
2460:
2454:
2450:
2446:
2442:
2438:
2432:
2431:
2427:
2424:
2417:
2414:
2409:
2402:
2399:
2394:
2390:
2386:
2382:
2378:
2374:
2367:
2363:
2359:
2355:
2351:
2347:
2340:
2337:
2332:
2328:
2322:
2319:
2314:
2310:
2306:
2302:
2298:
2292:
2289:
2278:on 2016-04-05
2277:
2273:
2267:
2264:
2252:
2246:
2243:
2231:
2225:
2222:
2210:
2204:
2201:
2196:
2192:
2185:
2182:
2177:
2173:
2169:
2165:
2161:
2157:
2156:
2148:
2144:
2140:
2134:
2131:
2126:
2122:
2118:
2112:
2109:
2104:
2100:
2096:
2092:
2088:
2084:
2083:J Comput Biol
2077:
2074:
2062:
2055:
2052:
2047:
2043:
2039:
2035:
2031:
2027:
2023:
2019:
2018:
2013:
2009:
2003:
2000:
1994:
1989:
1985:
1981:
1980:
1972:
1965:
1962:
1954:
1947:
1940:
1937:
1926:
1922:
1915:
1912:
1901:
1900:Bloomberg.com
1897:
1890:
1887:
1884:
1878:
1875:
1870:
1863:
1860:
1847:
1843:
1837:
1835:
1831:
1826:
1822:
1818:
1814:
1810:
1806:
1799:
1796:
1785:
1781:
1775:
1772:
1768:
1764:
1763:
1758:
1752:
1749:
1744:
1740:
1734:
1732:
1728:
1723:
1719:
1713:
1710:
1705:
1701:
1697:
1693:
1689:
1685:
1684:
1676:
1673:
1669:
1665:
1661:
1657:
1653:
1647:
1644:
1632:
1628:
1622:
1619:
1615:
1610:
1608:
1606:
1602:
1597:
1596:
1591:
1585:
1583:
1579:
1567:
1563:
1557:
1555:
1553:
1549:
1545:
1542:
1538:
1535:
1526:
1522:
1518:
1514:
1510:
1506:
1502:
1498:
1494:
1493:
1485:
1478:
1476:
1472:
1467:
1463:
1457:
1454:
1449:
1443:
1441:
1439:
1435:
1430:
1426:
1422:
1416:
1411:
1410:
1404:
1398:
1395:
1392:
1387:
1381:
1376:
1369:
1366:
1361:
1357:
1350:
1347:
1342:
1338:
1332:
1329:
1317:
1310:
1307:
1302:
1298:
1293:
1288:
1283:
1278:
1274:
1270:
1269:
1264:
1260:
1254:
1252:
1248:
1242:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1216:
1213:
1210:
1208:
1205:
1203:
1200:
1197:
1194:
1191:
1188:
1187:
1183:
1181:
1179:
1175:
1171:
1166:
1164:
1160:
1155:
1153:
1149:
1145:
1144:Morphy number
1141:
1136:
1134:
1130:
1126:
1125:Black Sabbath
1121:
1119:
1118:
1113:
1109:
1104:
1102:
1098:
1094:
1086:
1084:
1082:
1077:
1074:
1072:
1066:
1064:
1060:
1056:
1052:
1047:
1045:
1041:
1037:
1032:
1030:
1026:
1022:
1017:
1015:
1011:
1006:
1004:
1000:
996:
992:
991:Mark Liberman
988:
987:William Labov
984:
980:
976:
975:cryptographic
972:
971:Erdős numbers
968:
963:
959:
955:
951:
946:
938:
934:
930:
926:
922:
917:
910:
908:
906:
905:
900:
892:
890:
888:
884:
880:
876:
872:
868:
864:
860:
856:
848:
846:
844:
840:
839:Angela Merkel
833:
831:
829:
825:
821:
820:Alvin E. Roth
817:
809:
807:
805:
801:
797:
793:
785:
783:
781:
777:
773:
769:
764:
762:
758:
754:
753:Alvin E. Roth
750:
749:Roger Myerson
746:
742:
738:
734:
730:
726:
722:
721:Gerard Debreu
718:
714:
710:
705:
703:
702:Joseph Keller
699:
695:
691:
687:
683:
679:
675:
667:
665:
663:
659:
656:
652:
649:
642:
640:
638:
634:
630:
626:
625:Frank Wilczek
622:
618:
614:
610:
606:
605:Hans A. Bethe
602:
598:
597:Eugene Wigner
594:
590:
586:
582:
578:
574:
570:
562:
555:
552:
549:
546:
543:
540:
537:
534:
533:
529:
526:
523:
520:
517:
514:
511:
508:
507:
503:
500:
497:
494:
491:
488:
485:
482:
481:
477:
474:
471:
468:
465:
462:
459:
456:
455:
451:
448:
445:
442:
439:
436:
433:
431:Fields Medal
430:
429:
425:
422:
419:
416:
413:
410:
407:
405:
404:
398:
395:
390:
382:
375:
373:
372:Ronald Graham
370:
369:
365:
363:
360:
359:
355:
353:
350:
349:
345:
343:
340:
339:
335:
333:
330:
329:
325:
323:
320:
319:
315:
313:
310:
309:
305:
303:
302:Ralph Faudree
300:
299:
295:
293:
292:András Hajnal
290:
289:
285:
283:
280:
279:
273:
270:
269:
266:
259:
257:
255:
251:
247:
243:
239:
235:
231:
230:Jean Bourgain
227:
223:
219:
215:
214:David Mumford
211:
207:
203:
199:
195:
191:
186:
184:
180:
175:
170:
166:
162:
158:
156:
151:
149:
145:
139:
137:
136:
131:
121:
116:
109:
107:
105:
101:
96:
91:
89:
83:
80:
73:
65:
63:
61:
57:
52:
44:
36:
32:
19:
2753:. Retrieved
2742:
2730:. Retrieved
2719:
2708:. Retrieved
2699:
2688:. Retrieved
2679:
2667:. Retrieved
2655:
2642:
2631:. Retrieved
2624:
2614:
2603:. Retrieved
2597:
2587:
2577:
2571:
2566:
2541:
2516:
2513:Science News
2512:
2506:
2499:Google Books
2497:, p. 33, at
2492:
2480:
2475:
2440:
2421:
2416:
2401:
2379:(4): 78–81.
2376:
2372:
2352:(1): 62–71.
2349:
2345:
2339:
2330:
2321:
2308:
2291:
2280:. Retrieved
2276:the original
2266:
2255:. Retrieved
2245:
2234:. Retrieved
2224:
2213:. Retrieved
2203:
2195:the original
2184:
2162:(1): 87–90.
2159:
2153:
2133:
2111:
2086:
2082:
2076:
2064:. Retrieved
2054:
2021:
2015:
2002:
1986:(1): 45–46.
1983:
1977:
1964:
1953:the original
1939:
1928:. Retrieved
1924:
1914:
1903:. Retrieved
1899:
1889:
1877:
1862:
1850:. Retrieved
1845:
1808:
1804:
1798:
1787:. Retrieved
1783:
1774:
1760:
1751:
1742:
1721:
1712:
1687:
1681:
1675:
1659:
1651:
1646:
1635:. Retrieved
1633:. 1999-02-22
1630:
1621:
1593:
1569:. Retrieved
1536:
1533:
1525:the original
1499:(3): 51–63.
1496:
1490:
1465:
1456:
1408:
1397:
1385:
1375:"Paul Erdos"
1368:
1359:
1349:
1340:
1331:
1319:. Retrieved
1309:
1272:
1266:
1167:
1156:
1137:
1122:
1115:
1105:
1093:Bacon number
1090:
1078:
1070:
1067:
1062:
1058:
1054:
1051:Michael Barr
1048:
1044:longest path
1039:
1033:
1018:
1007:
983:Noam Chomsky
950:Steven Brams
942:
933:Fields Medal
902:
896:
859:cryptography
852:
837:
813:
796:Brian Skyrms
789:
765:
755:(2012), and
706:
694:Henry McKean
686:David Donoho
671:
651:Lior Pachter
646:
577:Enrico Fermi
566:
386:
342:Alfréd Rényi
263:
194:Atle Selberg
187:
182:
176:
172:
168:
164:
160:
154:
152:
140:
133:
126:
92:
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43:Erdős number
42:
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18:Erdos number
2755:December 3,
2732:December 3,
2331:oakland.edu
2139:Erdős, Paul
2008:Erdős, Paul
1566:oakland.edu
1170:video games
1148:Paul Morphy
1101:Kevin Bacon
973:within the
958:Eric Lander
925:Terence Tao
893:Linguistics
849:Engineering
800:Jon Barwise
768:James B. Ax
761:Jean Tirole
759:(2012) and
680:(1990) and
613:Abdus Salam
408:#Laureates
394:Nobel prize
332:Vera T. Sós
246:Terence Tao
138:catalogue.
104:G. H. Hardy
82:with them.
2825:Paul Erdős
2819:Categories
2710:2023-04-07
2690:2023-04-07
2669:9 December
2633:2018-07-29
2605:2018-07-29
2282:2010-08-29
2257:2010-08-29
2236:2010-08-29
2215:2010-08-29
2066:1 February
1930:2016-11-12
1905:2016-11-12
1811:(1): 5–8.
1789:2016-10-27
1690:(7): 791.
1637:2022-10-15
1595:MathSciNet
1380:PostScript
1243:References
1087:Variations
954:John Tukey
879:Adi Shamir
875:Ron Rivest
828:Lee Smolin
786:Philosophy
581:Otto Stern
274:Number of
254:Abel Prize
206:Alan Baker
202:Klaus Roth
72:Paul Erdős
70:See also:
56:Paul Erdős
47:Hungarian:
35:Paul Erdős
2728:. Polygon
2656:Chesscafe
2491:, S. 33 (
2046:121671198
1852:25 August
1825:219231926
1650:Grossman
1521:120046886
1405:(2003) .
979:linguists
923:teaching
637:Ed Witten
352:Pál Turán
271:Co-author
148:undefined
2751:. Kotaku
2660:Archived
2467:16370569
2426:Archived
2393:14144008
2366:34277380
2103:10582576
1429:41497065
1301:11149952
1261:(2001).
1184:See also
1005:fields.
999:Ivan Sag
997:(3), or
945:folklore
834:Politics
763:(2014).
751:(2007),
747:(2007),
743:(2005),
739:(2002),
735:(2000),
731:(1996),
727:(1994),
723:(1983),
719:(1978),
715:(1976),
711:(1972),
690:Marc Yor
589:Max Born
423:Average
144:infinity
66:Overview
2555:a paper
2547:a paper
2533:4015267
2494:excerpt
2176:2037762
2038:0095456
1757:Erdos0p
1704:2317868
1571:4 April
1544:1744115
1513:1709679
1163:Shusaku
871:Caltech
643:Biology
563:Physics
544:79.50%
518:27.62%
492:24.42%
466:61.84%
440:100.0%
426:Median
414:%Erdős
411:#Erdős
179:analyst
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1073:-index
1049:Also,
1010:Fields
911:Impact
881:, and
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700:, and
631:, and
252:is an
123:Erdős.
2663:(PDF)
2652:(PDF)
2557:with
2549:with
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2463:S2CID
2389:S2CID
2362:S2CID
2172:JSTOR
2150:(PDF)
2042:S2CID
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1821:S2CID
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2757:2022
2734:2022
2671:2020
2485:ISBN
2453:ISBN
2099:PMID
2068:2011
1854:2015
1573:2014
1425:OCLC
1415:ISBN
1323:2011
1297:PMID
1081:eBay
1063:each
1012:and
1003:arts
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