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 Kuo134
Roger Meyer Temam119
Andrew Bernard Whinston104
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger97
Pekka Neittaanmäki96
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky89
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn84
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein81
Bart De Moor81
Richard J. Eden80
Bruce Ramon Vogeli78
Stefan Jähnichen78
Charles Ehresmann78
Johan F. A. K. van Benthem77
Arnold Zellner76
Egon Krause76
David Hilbert75
Wilhelm Magnus74

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari134653
Gregory Chioniadis134652
Manuel Bryennios134651
Theodore Metochites1346501315
Gregory Palamas134648
Nilos Kabasilas1346471363
Demetrios Kydones134646
Elissaeus Judaeus134623
Georgios Plethon Gemistos1346221380, 1393
Basilios Bessarion1346191436
Manuel Chrysoloras134595
Guarino da Verona1345941408
Vittorino da Feltre1345931416
Theodoros Gazes1345891433
Jan Standonck1345681474
Jan Standonck1345681490
Johannes Argyropoulos1345681444
Rudolf Agricola1345381478
Florens Florentius Radwyn Radewyns134538
Geert Gerardus Magnus Groote134538
Thomas von Kempen à Kempis134537
Cristoforo Landino134537
Marsilio Ficino1345371462
Angelo Poliziano1345361477
Alexander Hegius1345361474

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
0156498
120493
27738
34610
43118
52360
61728
71420
81174
9943
10771
11624
12572
13462
14412
15351
16314
17266
18213
19181
21164
20158
22152
23133
25108
24101
2680
2879
2774
2957
3046
3446
3141
3341
3236
3527
3625
4124
4224
3822
3921
4321
4019
4518
3715
5012
5212
5512
5311
5610
6010
449
469
489
499
476
516
546
636
575
615
593
673
733
783
652
682
702
712
742
762
812
822
581
621
641
661
721
751
771
801
841
871
881
891
951
961
971
991
1001
1041
1191
1341