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 Kuo144
Roger Meyer Temam119
Andrew Bernard Whinston104
Pekka Neittaanmäki101
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky92
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Sergio Albeverio79
Charles Ehresmann77
Arnold Zellner77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Kamal al Din Ibn Yunus144070
Nasir al-Din al-Tusi144069
Shams ad-Din Al-Bukhari144068
Gregory Chioniadis144067
Manuel Bryennios144066
Theodore Metochites1440651315
Gregory Palamas144063
Nilos Kabasilas1440621363
Demetrios Kydones144061
Elissaeus Judaeus144038
Georgios Plethon Gemistos1440371380, 1393
Basilios Bessarion1440341436
Manuel Chrysoloras144010
Guarino da Verona1440091408
Vittorino da Feltre1440081416
Theodoros Gazes1440041433
Jan Standonck1439831490
Jan Standonck1439831474
Johannes Argyropoulos1439831444
Rudolf Agricola1439531478
Geert Gerardus Magnus Groote143953
Florens Florentius Radwyn Radewyns143953
Thomas von Kempen à Kempis143952
Marsilio Ficino1439521462
Cristoforo Landino143952

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
0167794
122462
28326
34910
43404
52548
61884
71539
81208
91034
10815
11683
12611
13494
14452
15377
16339
17294
18255
19197
21178
20160
22156
23132
24119
25102
2692
2884
2783
2965
3455
3049
3143
3241
3338
3828
3527
3625
3924
3723
4222
4121
4321
4020
4519
5216
4615
5515
4413
5012
4911
4810
539
569
478
517
617
576
606
636
545
584
654
593
623
673
683
713
763
773
793
823
692
722
732
752
802
661
701
811
851
861
871
881
921
951
981
991
1001
1011
1041
1191
1441