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
Bart De Moor82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Charles Ehresmann78
Johan F. A. K. van Benthem77
Arnold Zellner77
Egon Krause76

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari139102
Gregory Chioniadis139101
Manuel Bryennios139100
Theodore Metochites1390991315
Gregory Palamas139097
Nilos Kabasilas1390961363
Demetrios Kydones139095
Elissaeus Judaeus139072
Georgios Plethon Gemistos1390711380, 1393
Basilios Bessarion1390681436
Manuel Chrysoloras139044
Guarino da Verona1390431408
Vittorino da Feltre1390421416
Theodoros Gazes1390381433
Jan Standonck1390171474
Johannes Argyropoulos1390171444
Jan Standonck1390171490
Rudolf Agricola1389871478
Florens Florentius Radwyn Radewyns138987
Geert Gerardus Magnus Groote138987
Marsilio Ficino1389861462
Cristoforo Landino138986
Thomas von Kempen à Kempis138986
Alexander Hegius1389851474
Angelo Poliziano1389851477

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
0161731
121418
28031
34740
43267
52458
61801
71466
81191
9976
10794
11639
12598
13484
14424
15366
16326
17283
18232
19193
21168
22151
20150
23136
24108
25102
2687
2881
2780
2958
3450
3046
3343
3242
3141
3527
3626
3825
4125
4224
4323
3922
3719
4018
4517
5216
5514
4411
4911
4710
5010
5310
5610
469
489
548
608
617
516
576
635
593
623
673
753
823
662
692
702
712
732
772
792
802
1002
581
641
651
681
721
741
761
781
811
841
851
871
881
911
951
981
991
1041
1191
1401