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 Kuo164
Roger Meyer Temam128
Pekka Neittaanmäki123
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Leonard Salomon Ornstein95
Erol Gelenbe95
Kurt Mehlhorn93
Ludwig Prandtl90
Dimitris John Bertsimas90
Yurii Alekseevich Mitropolsky88
Bart De Moor86
Rudiger W. Dornbusch85
Olivier Jean Blanchard82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein82
Stefan Jähnichen81
Richard J. Eden80
Bruce Ramon Vogeli80
Sergio Albeverio80
Arnold Zellner79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī196832
Kamāl al-Dīn Ibn Yūnus196831
Nasir al-Dīn al-Ṭūsī196830
Shams al‐Dīn al‐Bukhārī196829
Gregory Chioniadis1968281296
Manuel Bryennios196827
Theodore Metochites1968261315
Gregory Palamas196824
Nilos Kabasilas1968231363
Demetrios Kydones196822
Elissaeus Judaeus196799
Georgios Plethon Gemistos1967981380, 1393
Basilios Bessarion1967951436
Manuel Chrysoloras196768
Guarino da Verona1967671408
Vittorino da Feltre1967661416
Theodoros Gazes1967621433
Johannes Argyropoulos1967441444
Jan Standonck1967401474
Jan Standonck1967401490
Cristoforo Landino196713
Marsilio Ficino1967131462
Angelo Poliziano1967121477
Moses Perez196710
Scipione Fortiguerra1967101493

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
0213398
129083
210484
36022
44269
53171
62457
71961
81563
91302
101064
11915
12806
13695
14558
15492
16432
17398
18319
20268
19266
22210
21207
23181
24161
25138
26119
27117
28110
2988
3084
3163
3253
3353
3451
3549
3638
3735
3832
3929
4229
4327
4026
4125
4617
5217
4416
4516
4916
4715
5114
5514
4813
5712
5011
5310
5410
6010
568
588
697
626
636
726
595
615
645
734
824
653
683
703
773
803
662
672
762
782
902
952
1002
741
751
791
811
851
861
881
931
1011
1081
1111
1231
1281
1641