Graph structure

In July 2016, Cosmin Ionita and Pat Quillen of MathWorks used MATLAB to analyze the Math Genealogy Project graph. At the time, the genealogy graph contained 200,037 vertices. There were 7639 (3.8%) isolated vertices and 1962 components of size two (advisor-advisee pairs where we have no information about the advisor). The largest component of the genealogy graph contained 180,094 vertices, accounting for 90% of all vertices in the graph. The main component has 7323 root vertices (individuals with no advisor) and 137,155 leaves (mathematicians with no students), accounting for 76.2% of the vertices in this component. The next largest component sizes were 81, 50, 47, 34, 34, 33, 31, 31, and 30.

For historical comparisonn, we also have data from June 2010, when Professor David Joyner of the United States Naval Academy asked for data from our database to analyze it as a graph. At the time, the genealogy graph had 142,688 vertices. Of these, 7,190 were isolated vertices (5% of the total). The largest component had 121,424 vertices (85% of the total number). The next largest component had 128 vertices. The next largest component sizes were 79, 61, 45, and 42. The most frequent size of a nontrivial component was 2; there were 1937 components of size 2. The component with 121,424 vertices had 4,639 root verticies, i.e., mathematicians for whom the advisor is currently unknown.

Top 25 Advisors

NameStudents
C.-C. Jay Kuo140
Roger Meyer Temam119
Andrew Bernard Whinston104
Pekka Neittaanmäki100
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky91
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Selim Grigorievich Krein81
Olivier Jean Blanchard80
Richard J. Eden80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Sergio Albeverio79
Arnold Zellner77
Johan F. A. K. van Benthem77
Charles Ehresmann77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Nasir al-Din al-Tusi142760
Shams ad-Din Al-Bukhari142759
Gregory Chioniadis142758
Manuel Bryennios142757
Theodore Metochites1427561315
Gregory Palamas142754
Nilos Kabasilas1427531363
Demetrios Kydones142752
Elissaeus Judaeus142729
Georgios Plethon Gemistos1427281380, 1393
Basilios Bessarion1427251436
Manuel Chrysoloras142701
Guarino da Verona1427001408
Vittorino da Feltre1426991416
Theodoros Gazes1426951433
Johannes Argyropoulos1426741444
Jan Standonck1426741490
Jan Standonck1426741474
Rudolf Agricola1426441478
Geert Gerardus Magnus Groote142644
Florens Florentius Radwyn Radewyns142644
Marsilio Ficino1426431462
Cristoforo Landino142643
Thomas von Kempen à Kempis142643
Alexander Hegius1426421474

Nonplanarity

The Mathematics Genealogy Project graph is nonplanar. Thanks to Professor Ezra Brown of Virginia Tech for assisting in finding the subdivision of K3,3 depicted below. The green vertices form one color class and the yellow ones form the other. Interestingly, Gauß is the only vertex that needs to be connected by paths with more than one edge.

K_{3,3} in the Genealogy graph

Frequency Counts

The table below indicates the values of number of students for mathematicians in our database along with the number of mathematicians having that many students.

Number of StudentsFrequency
0166138
122207
28272
34876
43375
52527
61859
71517
81214
91013
10819
11655
12616
13490
14442
15389
16322
17292
18252
19195
21175
20159
22157
23129
24116
25101
2691
2785
2880
2963
3453
3049
3142
3242
3339
3528
3827
3626
3922
4121
4321
3720
4020
4220
4519
5216
4415
5514
4613
5013
4811
5310
5610
479
498
617
516
606
636
545
575
585
654
623
673
683
713
763
773
793
823
592
692
722
732
752
802
1002
661
701
811
851
861
871
881
911
951
981
991
1041
1191
1401