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
Willi Jäger101
Alexander Vasil'evich Mikhalëv100
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-Ṭūsī169347
Kamāl al-Dīn Ibn Yūnus169346
Nasir al-Dīn al-Ṭūsī169345
Shams al‐Dīn al‐Bukhārī169344
Gregory Chioniadis1693431296
Manuel Bryennios169342
Theodore Metochites1693411315
Gregory Palamas169339
Nilos Kabasilas1693381363
Demetrios Kydones169337
Elissaeus Judaeus169314
Georgios Plethon Gemistos1693131380, 1393
Basilios Bessarion1693101436
Manuel Chrysoloras169283
Guarino da Verona1692821408
Vittorino da Feltre1692811416
Theodoros Gazes1692771433
Johannes Argyropoulos1692591444
Jan Standonck1692551474
Jan Standonck1692551490
Marsilio Ficino1692281462
Cristoforo Landino169228
Angelo Poliziano1692271477
Scipione Fortiguerra1692251493
Moses Perez169225

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
0196628
126925
29748
35602
43831
53028
62202
71785
81401
91229
10983
11809
12741
13606
14522
15423
16397
17373
18297
19247
20212
21201
22198
24156
23153
25115
26110
28102
2798
2997
3069
3157
3457
3349
3242
3538
3636
3936
3732
3828
4025
4325
4122
4222
4519
5219
4615
4915
4813
5013
5312
4711
5111
5611
6010
449
549
559
588
577
617
685
695
825
644
654
724
774
593
623
703
733
763
632
662
672
752
792
802
882
952
1002
1082
741
851
901
1011
1141
1241
1531