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
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv100
Willi Jäger100
Shlomo Noach (Stephen Ram) Sawilowsky98
Leonard Salomon Ornstein95
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Bart De Moor82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Erol Gelenbe81
Richard J. Eden80
Olivier Jean Blanchard80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Sergio Albeverio79
Arnold Zellner77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī154537
Kamal al Din Ibn Yunus154536
Nasir al-Din al-Tusi154535
Shams ad-Din Al-Bukhari154534
Gregory Chioniadis1545331296
Manuel Bryennios154532
Theodore Metochites1545311315
Gregory Palamas154529
Nilos Kabasilas1545281363
Demetrios Kydones154527
Elissaeus Judaeus154504
Georgios Plethon Gemistos1545031380, 1393
Basilios Bessarion1545001436
Manuel Chrysoloras154473
Guarino da Verona1544721408
Vittorino da Feltre1544711416
Theodoros Gazes1544671433
Johannes Argyropoulos1544491444
Jan Standonck1544451474
Jan Standonck1544451490
Cristoforo Landino154418
Marsilio Ficino1544181462
Angelo Poliziano1544171477
Scipione Fortiguerra1544151493
Moses Perez154415

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
0178795
124105
28848
35167
43604
52756
62005
71631
81280
91113
10867
11741
12639
13534
14478
15385
16352
17342
18271
19204
20199
22175
21169
23148
24132
25101
2697
2895
2790
2978
3060
3452
3343
3141
3241
3635
3534
3928
3726
4025
4123
3822
4222
4320
4518
5014
5214
4613
4913
4412
4712
5512
4811
5110
539
609
568
577
546
585
595
615
655
634
674
774
824
623
643
703
793
1003
682
692
712
722
732
752
802
882
661
741
761
811
851
861
951
981
1051
1061
1191
1471