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 Kuo152
Roger Meyer Temam124
Pekka Neittaanmäki114
Andrew Bernard Whinston108
Shlomo Noach (Stephen Ram) Sawilowsky107
Willi Jäger101
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv100
Erol Gelenbe95
Leonard Salomon Ornstein95
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn88
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
David Garvin Moursund82
Olivier Jean Blanchard82
Bart De Moor82
Andrei Nikolayevich Kolmogorov82
Richard J. Eden80
Bruce Ramon Vogeli80
Stefan Jähnichen79
Sergio Albeverio79
Johan F. A. K. van Benthem77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī167915
Kamāl al-Dīn Ibn Yūnus167914
Nasir al-Dīn al-Ṭūsī167913
Shams al‐Dīn al‐Bukhārī167912
Gregory Chioniadis1679111296
Manuel Bryennios167910
Theodore Metochites1679091315
Gregory Palamas167907
Nilos Kabasilas1679061363
Demetrios Kydones167905
Elissaeus Judaeus167882
Georgios Plethon Gemistos1678811380, 1393
Basilios Bessarion1678781436
Manuel Chrysoloras167851
Guarino da Verona1678501408
Vittorino da Feltre1678491416
Theodoros Gazes1678451433
Johannes Argyropoulos1678271444
Jan Standonck1678231490
Jan Standonck1678231474
Cristoforo Landino167796
Marsilio Ficino1677961462
Angelo Poliziano1677951477
Moses Perez167793
Scipione Fortiguerra1677931493

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
0194920
126684
29650
35586
43818
52991
62179
71785
81386
91225
10962
11800
12729
13608
14520
15423
16393
17370
18294
19245
20210
21201
22190
23155
24149
26113
25108
28103
2996
2793
3072
3455
3154
3349
3244
3542
3636
3933
3729
3828
4325
4024
4122
4222
4521
5219
5015
4614
4813
4912
4711
5110
5310
5510
449
549
569
579
609
587
616
656
686
695
825
594
644
724
774
623
733
763
632
672
702
752
792
802
882
952
1002
741
851
901
1011
1071
1081
1141
1241
1521