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 Kuo143
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
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Bart De Moor82
Selim Grigorievich Krein81
Olivier Jean Blanchard80
Richard J. Eden80
Stefan Jähnichen79
Sergio Albeverio79
Bruce Ramon Vogeli79
Arnold Zellner77
Charles Ehresmann77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Kamal al Din Ibn Yunus143386
Nasir al-Din al-Tusi143385
Shams ad-Din Al-Bukhari143384
Gregory Chioniadis143383
Manuel Bryennios143382
Theodore Metochites1433811315
Gregory Palamas143379
Nilos Kabasilas1433781363
Demetrios Kydones143377
Elissaeus Judaeus143354
Georgios Plethon Gemistos1433531380, 1393
Basilios Bessarion1433501436
Manuel Chrysoloras143326
Guarino da Verona1433251408
Vittorino da Feltre1433241416
Theodoros Gazes1433201433
Jan Standonck1432991490
Jan Standonck1432991474
Johannes Argyropoulos1432991444
Rudolf Agricola1432691478
Florens Florentius Radwyn Radewyns143269
Geert Gerardus Magnus Groote143269
Marsilio Ficino1432681462
Cristoforo Landino143268
Thomas von Kempen à Kempis143268

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
0166800
122375
28305
34888
43389
52534
61866
71534
81218
91025
10814
11670
12609
13494
14444
15385
16329
17292
18254
19197
21173
20161
22159
23127
24118
25102
2693
2785
2882
2963
3452
3048
3143
3242
3338
3528
3828
3627
3922
4122
3721
4321
4220
4019
4518
5216
4415
5515
4614
4812
5012
539
569
478
498
517
617
576
606
636
545
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
1431