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 Whinston105
Pekka Neittaanmäki105
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Shlomo Noach (Stephen Ram) Sawilowsky95
Leonard Salomon Ornstein95
Ludwig Prandtl88
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Richard J. Eden80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
Erol Gelenbe79
Bruce Ramon Vogeli79
Arnold Zellner77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī148360
Kamal al Din Ibn Yunus148359
Nasir al-Din al-Tusi148358
Shams ad-Din Al-Bukhari148357
Gregory Chioniadis148356
Manuel Bryennios148355
Theodore Metochites1483541315
Gregory Palamas148352
Nilos Kabasilas1483511363
Demetrios Kydones148350
Elissaeus Judaeus148327
Georgios Plethon Gemistos1483261380, 1393
Basilios Bessarion1483231436
Manuel Chrysoloras148297
Guarino da Verona1482961408
Vittorino da Feltre1482951416
Theodoros Gazes1482911433
Johannes Argyropoulos1482701444
Jan Standonck1482701490
Jan Standonck1482701474
Rudolf Agricola1482401478
Florens Florentius Radwyn Radewyns148240
Geert Gerardus Magnus Groote148240
Cristoforo Landino148239
Thomas von Kempen à Kempis148239

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
0173078
123261
28588
35036
43523
52605
61975
71583
81247
91057
10835
11712
12621
13512
14467
15380
16345
17320
18268
19194
21184
20176
22164
23135
24115
25110
2699
2791
2885
2974
3454
3053
3342
3141
3238
3631
3527
3727
3826
3926
4225
4024
4120
4318
4518
4715
5215
4414
5014
5513
4812
4610
4910
5610
539
607
617
516
576
596
545
634
644
654
774
794
824
583
673
693
682
712
722
732
752
802
882
952
1052
621
661
701
741
761
851
861
981
991
1001
1191
1441