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 Neittaanmäki116
Shlomo Noach (Stephen Ram) Sawilowsky109
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Willi Jäger101
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Ludwig Prandtl90
Kurt Mehlhorn89
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Olivier Jean Blanchard82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Stefan Jähnichen81
Richard J. Eden80
Bruce Ramon Vogeli80
Sergio Albeverio79
Johan F. A. K. van Benthem78
Arnold Zellner78

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī172092
Kamāl al-Dīn Ibn Yūnus172091
Nasir al-Dīn al-Ṭūsī172090
Shams al‐Dīn al‐Bukhārī172089
Gregory Chioniadis1720881296
Manuel Bryennios172087
Theodore Metochites1720861315
Gregory Palamas172084
Nilos Kabasilas1720831363
Demetrios Kydones172082
Elissaeus Judaeus172059
Georgios Plethon Gemistos1720581380, 1393
Basilios Bessarion1720551436
Manuel Chrysoloras172028
Guarino da Verona1720271408
Vittorino da Feltre1720261416
Theodoros Gazes1720221433
Johannes Argyropoulos1720041444
Jan Standonck1720001490
Jan Standonck1720001474
Marsilio Ficino1719731462
Cristoforo Landino171973
Angelo Poliziano1719721477
Scipione Fortiguerra1719701493
Moses Perez171970

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
0199608
127416
29884
35700
43892
53052
62249
71816
81438
91234
101003
11834
12738
13622
14529
15429
16411
17371
18307
19243
20227
21203
22191
23166
24156
25120
29108
27106
26104
2894
3066
3156
3454
3350
3248
3541
3937
3736
3633
3827
4026
4226
4326
4119
4619
4517
5217
4916
5314
5013
5113
4411
4811
5511
4710
5710
569
588
618
547
606
686
645
695
825
594
634
724
623
653
673
703
733
763
752
772
782
802
952
1012
711
741
791
811
851
881
891
901
1001
1081
1091
1161
1241
1561