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 Kuo156
Roger Meyer Temam124
Pekka Neittaanmäki119
Shlomo Noach (Stephen Ram) Sawilowsky110
Andrew Bernard Whinston108
Willi Jäger101
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Leonard Salomon Ornstein95
Erol Gelenbe95
Ludwig Prandtl90
Kurt Mehlhorn89
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
David Garvin Moursund82
Selim Grigorievich Krein82
Bart De Moor82
Olivier Jean Blanchard82
Andrei Nikolayevich Kolmogorov82
Stefan Jähnichen81
Richard J. Eden80
Bruce Ramon Vogeli80
Arnold Zellner79
Sergio Albeverio79
Johan F. A. K. van Benthem78

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī173395
Kamāl al-Dīn Ibn Yūnus173394
Nasir al-Dīn al-Ṭūsī173393
Shams al‐Dīn al‐Bukhārī173392
Gregory Chioniadis1733911296
Manuel Bryennios173390
Theodore Metochites1733891315
Gregory Palamas173387
Nilos Kabasilas1733861363
Demetrios Kydones173385
Elissaeus Judaeus173362
Georgios Plethon Gemistos1733611380, 1393
Basilios Bessarion1733581436
Manuel Chrysoloras173331
Guarino da Verona1733301408
Vittorino da Feltre1733291416
Theodoros Gazes1733251433
Johannes Argyropoulos1733071444
Jan Standonck1733031490
Jan Standonck1733031474
Marsilio Ficino1732761462
Cristoforo Landino173276
Angelo Poliziano1732751477
Scipione Fortiguerra1732731493
Moses Perez173273

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
0201147
127705
29969
35707
43969
53071
62272
71825
81457
91237
101005
11857
12735
13637
14526
15439
16412
17374
18309
19244
20230
21203
22192
23172
24148
25126
26108
27106
29102
2897
3069
3156
3453
3351
3249
3544
3738
3937
3631
4328
3827
4227
4024
4120
4618
4517
5216
5316
4915
5013
5113
4812
4411
5510
5610
479
589
619
548
578
687
606
645
695
825
624
634
724
593
653
703
733
763
672
752
772
792
802
952
1012
711
741
781
811
851
881
891
901
1001
1081
1101
1191
1241
1561