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) Sawilowsky92
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Bart De Moor82
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Arnold Zellner77
Egon Krause77
Charles Ehresmann77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Kamal al Din Ibn Yunus145922
Nasir al-Din al-Tusi145921
Shams ad-Din Al-Bukhari145920
Gregory Chioniadis145919
Manuel Bryennios145918
Theodore Metochites1459171315
Gregory Palamas145915
Nilos Kabasilas1459141363
Demetrios Kydones145913
Elissaeus Judaeus145890
Georgios Plethon Gemistos1458891380, 1393
Basilios Bessarion1458861436
Manuel Chrysoloras145862
Guarino da Verona1458611408
Vittorino da Feltre1458601416
Theodoros Gazes1458561433
Jan Standonck1458351474
Jan Standonck1458351490
Johannes Argyropoulos1458351444
Florens Florentius Radwyn Radewyns145805
Geert Gerardus Magnus Groote145805
Rudolf Agricola1458051478
Thomas von Kempen à Kempis145804
Cristoforo Landino145804
Marsilio Ficino1458041462

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
0170026
122906
28480
34970
43462
52592
61911
71553
81223
91051
10827
11693
12616
13505
14452
15379
16338
17296
18264
19196
21176
20172
22166
23132
24116
25109
2690
2786
2886
2968
3455
3051
3342
3141
3237
3629
3826
3926
3525
4223
3722
4022
4121
4319
4519
5216
4615
4414
5513
5012
4811
4911
4710
5610
538
517
617
576
606
636
545
585
594
654
774
673
693
733
793
823
622
682
712
722
752
762
802
1052
641
661
701
811
851
861
871
881
921
951
981
991
1001
1191
1441