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 Kuo140
Roger Meyer Temam119
Andrew Bernard Whinston104
Pekka Neittaanmäki100
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky91
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Rudiger W. Dornbusch85
Kurt Mehlhorn84
Bart De Moor82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Charles Ehresmann78
Johan F. A. K. van Benthem77
Arnold Zellner77
Egon Krause76

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari139189
Gregory Chioniadis139188
Manuel Bryennios139187
Theodore Metochites1391861315
Gregory Palamas139184
Nilos Kabasilas1391831363
Demetrios Kydones139182
Elissaeus Judaeus139159
Georgios Plethon Gemistos1391581380, 1393
Basilios Bessarion1391551436
Manuel Chrysoloras139131
Guarino da Verona1391301408
Vittorino da Feltre1391291416
Theodoros Gazes1391251433
Jan Standonck1391041474
Johannes Argyropoulos1391041444
Jan Standonck1391041490
Rudolf Agricola1390741478
Geert Gerardus Magnus Groote139074
Florens Florentius Radwyn Radewyns139074
Marsilio Ficino1390731462
Thomas von Kempen à Kempis139073
Cristoforo Landino139073
Angelo Poliziano1390721477
Alexander Hegius1390721474

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
0161817
121423
28035
34742
43266
52460
61805
71464
81195
9976
10797
11639
12599
13483
14425
15366
16325
17283
18232
19194
21168
22151
20150
23136
24108
25102
2686
2781
2881
2957
3450
3047
3343
3242
3140
3527
3627
3825
4125
4224
4323
3922
3719
4018
4517
5216
5515
4411
4911
4710
5010
5310
5610
469
489
608
547
617
516
576
635
593
623
673
753
823
662
692
702
712
732
772
792
802
1002
581
641
651
681
721
741
761
781
811
841
851
871
881
911
951
981
991
1041
1191
1401