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 Kuo153
Roger Meyer Temam124
Pekka Neittaanmäki114
Andrew Bernard Whinston108
Shlomo Noach (Stephen Ram) Sawilowsky108
Alexander Vasil'evich Mikhalëv101
Willi Jäger101
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Ludwig Prandtl90
Kurt Mehlhorn88
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Bart De Moor82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Richard J. Eden80
Bruce Ramon Vogeli80
Stefan Jähnichen79
Sergio Albeverio79
Arnold Zellner77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī169534
Kamāl al-Dīn Ibn Yūnus169533
Nasir al-Dīn al-Ṭūsī169532
Shams al‐Dīn al‐Bukhārī169531
Gregory Chioniadis1695301296
Manuel Bryennios169529
Theodore Metochites1695281315
Gregory Palamas169526
Nilos Kabasilas1695251363
Demetrios Kydones169524
Elissaeus Judaeus169501
Georgios Plethon Gemistos1695001380, 1393
Basilios Bessarion1694971436
Manuel Chrysoloras169470
Guarino da Verona1694691408
Vittorino da Feltre1694681416
Theodoros Gazes1694641433
Johannes Argyropoulos1694461444
Jan Standonck1694421490
Jan Standonck1694421474
Marsilio Ficino1694151462
Cristoforo Landino169415
Angelo Poliziano1694141477
Moses Perez169412
Scipione Fortiguerra1694121493

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
0196826
126965
29752
35608
43838
53030
62205
71787
81403
91233
10988
11807
12743
13604
14523
15422
16400
17372
18297
19246
20213
21200
22198
24156
23154
25115
26112
28103
2797
2996
3069
3158
3458
3348
3242
3538
3636
3936
3732
3828
4025
4325
4223
4121
4519
5219
4916
4615
4813
5013
5313
4710
5110
5610
6010
449
549
559
578
588
617
686
695
825
644
724
774
593
623
653
703
733
763
632
662
672
752
792
802
882
952
1012
1082
741
851
901
1001
1141
1241
1531