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
Bart De Moor82
David Garvin Moursund82
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
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 Yunus144857
Nasir al-Din al-Tusi144856
Shams ad-Din Al-Bukhari144855
Gregory Chioniadis144854
Manuel Bryennios144853
Theodore Metochites1448521315
Gregory Palamas144850
Nilos Kabasilas1448491363
Demetrios Kydones144848
Elissaeus Judaeus144825
Georgios Plethon Gemistos1448241380, 1393
Basilios Bessarion1448211436
Manuel Chrysoloras144797
Guarino da Verona1447961408
Vittorino da Feltre1447951416
Theodoros Gazes1447911433
Johannes Argyropoulos1447701444
Jan Standonck1447701474
Jan Standonck1447701490
Rudolf Agricola1447401478
Geert Gerardus Magnus Groote144740
Florens Florentius Radwyn Radewyns144740
Cristoforo Landino144739
Thomas von Kempen à Kempis144739
Marsilio Ficino1447391462

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
0168468
122619
28397
34903
43435
52552
61890
71534
81222
91044
10815
11685
12611
13498
14451
15379
16337
17297
18256
19197
21177
20161
22159
23131
24119
25106
2692
2785
2885
2967
3455
3049
3141
3240
3340
3828
3527
3625
4224
4023
3722
3922
4321
4120
4520
5216
4614
4413
5513
5012
4811
5611
4910
479
539
517
617
576
606
545
635
584
654
593
623
673
683
713
733
763
773
793
823
692
752
802
641
661
701
721
811
851
861
871
881
921
951
981
991
1001
1011
1041
1191
1441