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
Andrew Bernard Whinston104
Pekka Neittaanmäki101
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
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard80
Stefan Jähnichen79
Sergio Albeverio79
Bruce Ramon Vogeli79
Arnold Zellner77
Charles Ehresmann77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Kamal al Din Ibn Yunus143926
Nasir al-Din al-Tusi143925
Shams ad-Din Al-Bukhari143924
Gregory Chioniadis143923
Manuel Bryennios143922
Theodore Metochites1439211315
Gregory Palamas143919
Nilos Kabasilas1439181363
Demetrios Kydones143917
Elissaeus Judaeus143894
Georgios Plethon Gemistos1438931380, 1393
Basilios Bessarion1438901436
Manuel Chrysoloras143866
Guarino da Verona1438651408
Vittorino da Feltre1438641416
Theodoros Gazes1438601433
Johannes Argyropoulos1438391444
Jan Standonck1438391474
Jan Standonck1438391490
Rudolf Agricola1438091478
Florens Florentius Radwyn Radewyns143809
Geert Gerardus Magnus Groote143809
Thomas von Kempen à Kempis143808
Marsilio Ficino1438081462
Cristoforo Landino143808

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
0167483
122449
28312
34907
43400
52547
61884
71535
81208
91035
10813
11682
12608
13498
14448
15379
16334
17294
18254
19200
21175
20161
22157
23130
24118
25102
2692
2885
2783
2965
3455
3048
3143
3240
3338
3828
3527
3625
3723
3923
4222
4121
4321
4020
4519
5216
5515
4414
4614
5012
4911
489
539
569
478
517
617
576
606
636
545
585
654
623
673
683
713
763
773
793
823
592
692
722
732
752
802
661
701
811
851
861
871
881
921
951
981
991
1001
1011
1041
1191
1441