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 Kuo147
Roger Meyer Temam119
Pekka Neittaanmäki106
Andrew Bernard Whinston105
Willi Jäger100
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Shlomo Noach (Stephen Ram) Sawilowsky96
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-Ṭūsī154058
Kamal al Din Ibn Yunus154057
Nasir al-Din al-Tusi154056
Shams ad-Din Al-Bukhari154055
Gregory Chioniadis1540541296
Manuel Bryennios154053
Theodore Metochites1540521315
Gregory Palamas154050
Nilos Kabasilas1540491363
Demetrios Kydones154048
Elissaeus Judaeus154025
Georgios Plethon Gemistos1540241380, 1393
Basilios Bessarion1540211436
Manuel Chrysoloras153994
Guarino da Verona1539931408
Vittorino da Feltre1539921416
Theodoros Gazes1539881433
Johannes Argyropoulos1539701444
Jan Standonck1539661474
Jan Standonck1539661490
Cristoforo Landino153939
Marsilio Ficino1539391462
Angelo Poliziano1539381477
Scipione Fortiguerra1539361493
Moses Perez153936

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
0178217
124027
28802
35168
43593
52725
62000
71634
81267
91112
10868
11736
12636
13531
14486
15379
16350
17338
18271
19210
20188
22176
21173
23146
24127
25103
2695
2893
2792
2977
3061
3452
3143
3342
3240
3635
3534
3930
3726
4024
4123
3822
4222
4319
4519
4914
5014
5214
4413
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
1002
661
741
761
811
851
861
951
961
991
1051
1061
1191
1471