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
Shlomo Noach (Stephen Ram) Sawilowsky108
Andrew Bernard Whinston108
Willi Jäger101
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv100
Leonard Salomon Ornstein95
Erol Gelenbe95
Ludwig Prandtl90
Kurt Mehlhorn88
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard82
David Garvin Moursund82
Bart De Moor82
Richard J. Eden80
Bruce Ramon Vogeli80
Stefan Jähnichen79
Sergio Albeverio79
Johan F. A. K. van Benthem77
Arnold Zellner77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī168665
Kamāl al-Dīn Ibn Yūnus168664
Nasir al-Dīn al-Ṭūsī168663
Shams al‐Dīn al‐Bukhārī168662
Gregory Chioniadis1686611296
Manuel Bryennios168660
Theodore Metochites1686591315
Gregory Palamas168657
Nilos Kabasilas1686561363
Demetrios Kydones168655
Elissaeus Judaeus168632
Georgios Plethon Gemistos1686311380, 1393
Basilios Bessarion1686281436
Manuel Chrysoloras168601
Guarino da Verona1686001408
Vittorino da Feltre1685991416
Theodoros Gazes1685951433
Johannes Argyropoulos1685771444
Jan Standonck1685731490
Jan Standonck1685731474
Cristoforo Landino168546
Marsilio Ficino1685461462
Angelo Poliziano1685451477
Scipione Fortiguerra1685431493
Moses Perez168543

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
0195869
126821
29702
35591
43828
53007
62188
71795
81389
91231
10970
11808
12731
13611
14522
15421
16396
17375
18295
19241
20219
21200
22193
23154
24153
26111
25110
28100
2998
2797
3072
3456
3154
3351
3242
3539
3637
3934
3730
3827
4326
4025
4222
4121
4521
5218
4915
5015
4614
4812
4711
5311
5110
5410
5510
6010
569
448
578
587
617
686
655
695
825
644
724
774
593
623
733
763
632
672
702
752
792
802
882
952
1002
1082
661
741
851
901
1011
1141
1241
1521