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 Kuo150
Roger Meyer Temam124
Andrew Bernard Whinston107
Pekka Neittaanmäki106
Shlomo Noach (Stephen Ram) Sawilowsky102
Willi Jäger100
Alexander Vasil'evich Mikhalëv100
Ronold Wyeth Percival King100
Leonard Salomon Ornstein95
Ludwig Prandtl89
Yurii Alekseevich Mitropolsky88
Erol Gelenbe86
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Bart De Moor82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard82
David Garvin Moursund82
Richard J. Eden80
Bruce Ramon Vogeli80
Stefan Jähnichen79
Sergio Albeverio79
Arnold Zellner77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī160487
Kamal al Din Ibn Yunus160486
Nasir al-Din al-Tusi160485
Shams ad-Din Al-Bukhari160484
Gregory Chioniadis1604831296
Manuel Bryennios160482
Theodore Metochites1604811315
Gregory Palamas160479
Nilos Kabasilas1604781363
Demetrios Kydones160477
Elissaeus Judaeus160454
Georgios Plethon Gemistos1604531380, 1393
Basilios Bessarion1604501436
Manuel Chrysoloras160423
Guarino da Verona1604221408
Vittorino da Feltre1604211416
Theodoros Gazes1604171433
Johannes Argyropoulos1603991444
Jan Standonck1603951474
Jan Standonck1603951490
Marsilio Ficino1603681462
Cristoforo Landino160368
Angelo Poliziano1603671477
Moses Perez160365
Scipione Fortiguerra1603651493

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
0186656
125400
29216
35378
43731
52843
62085
71705
81327
91160
10924
11783
12686
13587
14482
15394
16372
17364
18286
19226
20196
21187
22179
23153
24142
26111
25109
2896
2987
2785
3058
3458
3151
3244
3344
3536
3635
3828
3727
3926
4126
4225
4022
4322
4518
5016
4815
5214
5314
4612
4912
5512
4411
479
519
567
597
607
617
546
576
586
705
825
644
654
774
623
633
673
683
733
753
1003
692
722
792
802
862
711
741
761
851
881
891
951
1021
1061
1071
1241
1501