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-Tusi140763
Shams ad-Din Al-Bukhari140762
Gregory Chioniadis140761
Manuel Bryennios140760
Theodore Metochites1407591315
Gregory Palamas140757
Nilos Kabasilas1407561363
Demetrios Kydones140755
Elissaeus Judaeus140732
Georgios Plethon Gemistos1407311380, 1393
Basilios Bessarion1407281436
Manuel Chrysoloras140704
Guarino da Verona1407031408
Vittorino da Feltre1407021416
Theodoros Gazes1406981433
Jan Standonck1406771474
Jan Standonck1406771490
Johannes Argyropoulos1406771444
Rudolf Agricola1406471478
Florens Florentius Radwyn Radewyns140647
Geert Gerardus Magnus Groote140647
Marsilio Ficino1406461462
Cristoforo Landino140646
Thomas von Kempen à Kempis140646
Alexander Hegius1406451474

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
0163617
121774
28102
34799
43317
52493
61825
71485
81203
91004
10795
11647
12604
13488
14437
15373
16324
17287
18243
19186
21170
20160
22155
23128
24114
25100
2786
2684
2882
2961
3449
3046
3342
3141
3241
3528
3627
3723
3923
4323
3822
4122
4222
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