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 Kuo145
Roger Meyer Temam119
Pekka Neittaanmäki106
Andrew Bernard Whinston105
Willi Jäger100
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Shlomo Noach (Stephen Ram) Sawilowsky95
Leonard Salomon Ornstein95
Ludwig Prandtl88
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Bart De Moor82
Erol Gelenbe81
Richard J. Eden80
Olivier Jean Blanchard80
Stefan Jähnichen79
Sergio Albeverio79
Bruce Ramon Vogeli79
Charles Ehresmann77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī152523
Kamal al Din Ibn Yunus152522
Nasir al-Din al-Tusi152521
Shams ad-Din Al-Bukhari152520
Gregory Chioniadis1525191296
Manuel Bryennios152518
Theodore Metochites1525171315
Gregory Palamas152515
Nilos Kabasilas1525141363
Demetrios Kydones152513
Elissaeus Judaeus152490
Georgios Plethon Gemistos1524891380, 1393
Basilios Bessarion1524861436
Manuel Chrysoloras152459
Guarino da Verona1524581408
Vittorino da Feltre1524571416
Theodoros Gazes1524531433
Johannes Argyropoulos1524351444
Jan Standonck1524311474
Jan Standonck1524311490
Cristoforo Landino152404
Marsilio Ficino1524041462
Angelo Poliziano1524031477
Scipione Fortiguerra1524011493
Moses Perez152401

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
0177696
123909
28777
35164
43582
52691
62007
71628
81268
91103
10863
11730
12637
13528
14485
15378
16348
17336
18275
19204
20188
21177
22174
23143
24129
25104
2696
2794
2889
2974
3060
3452
3146
3342
3238
3535
3633
3929
3728
4024
4123
3822
4222
4319
4519
5014
5214
4413
4913
5512
4611
4711
4811
519
539
609
568
577
546
585
595
615
655
624
634
674
774
824
703
793
642
682
692
712
722
732
752
802
882
952
1002
661
741
761
811
851
861
991
1051
1061
1191
1451