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 Kuo144
Roger Meyer Temam119
Pekka Neittaanmäki105
Andrew Bernard Whinston105
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky93
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Bart De Moor82
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard80
Richard J. Eden80
Sergio Albeverio79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Erol Gelenbe77
Johan F. A. K. van Benthem77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī147548
Kamal al Din Ibn Yunus147547
Nasir al-Din al-Tusi147546
Shams ad-Din Al-Bukhari147545
Gregory Chioniadis147544
Manuel Bryennios147543
Theodore Metochites1475421315
Gregory Palamas147540
Nilos Kabasilas1475391363
Demetrios Kydones147538
Elissaeus Judaeus147515
Georgios Plethon Gemistos1475141380, 1393
Basilios Bessarion1475111436
Manuel Chrysoloras147486
Guarino da Verona1474851408
Vittorino da Feltre1474841416
Theodoros Gazes1474801433
Jan Standonck1474591490
Johannes Argyropoulos1474591444
Jan Standonck1474591474
Rudolf Agricola1474291478
Geert Gerardus Magnus Groote147429
Florens Florentius Radwyn Radewyns147429
Marsilio Ficino1474281462
Cristoforo Landino147428

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
0172081
123173
28564
35021
43494
52595
61958
71564
81241
91049
10836
11705
12622
13507
14463
15381
16349
17311
18270
19193
21180
20176
22163
23133
24120
25109
2698
2788
2884
2972
3455
3054
3141
3341
3237
3631
3526
3726
3926
3825
4225
4024
4120
4519
4318
5215
4414
5514
4713
5013
4612
4811
4911
539
569
597
617
516
576
606
636
545
775
654
824
583
673
693
793
642
682
712
722
732
752
802
1052
621
661
701
741
761
851
861
871
881
931
951
981
991
1001
1191
1441