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
Rudiger W. Dornbusch85
Kurt Mehlhorn84
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Bart De Moor82
Selim Grigorievich Krein81
Olivier Jean Blanchard80
Sergio Albeverio80
Richard J. Eden80
Bruce Ramon Vogeli79
Stefan Jähnichen79
Johan F. A. K. van Benthem77
Arnold Zellner77
Charles Ehresmann77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Nasir al-Din al-Tusi140739
Shams ad-Din Al-Bukhari140738
Gregory Chioniadis140737
Manuel Bryennios140736
Theodore Metochites1407351315
Gregory Palamas140733
Nilos Kabasilas1407321363
Demetrios Kydones140731
Elissaeus Judaeus140708
Georgios Plethon Gemistos1407071380, 1393
Basilios Bessarion1407041436
Manuel Chrysoloras140680
Guarino da Verona1406791408
Vittorino da Feltre1406781416
Theodoros Gazes1406741433
Jan Standonck1406531490
Jan Standonck1406531474
Johannes Argyropoulos1406531444
Florens Florentius Radwyn Radewyns140623
Rudolf Agricola1406231478
Geert Gerardus Magnus Groote140623
Cristoforo Landino140622
Thomas von Kempen à Kempis140622
Marsilio Ficino1406221462
Angelo Poliziano1406211477

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
0163586
121774
28104
34798
43314
52494
61826
71486
81200
91004
10794
11649
12603
13488
14437
15373
16323
17287
18243
19186
21170
20160
22155
23128
24114
25100
2786
2684
2882
2961
3449
3046
3342
3141
3241
3528
3627
3723
3923
4123
4323
3822
4221
4020
4518
5216
5514
4413
5013
4610
4710
5310
5610
489
499
547
577
617
516
606
635
593
623
713
753
773
803
823
582
652
662
672
682
692
722
732
762
792
1002
641
701
811
841
851
871
881
911
951
981
991
1041
1191
1401