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
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Bart De Moor81
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard79
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-Bukhari138357
Gregory Chioniadis138356
Manuel Bryennios138355
Theodore Metochites1383541315
Gregory Palamas138352
Nilos Kabasilas1383511363
Demetrios Kydones138350
Elissaeus Judaeus138327
Georgios Plethon Gemistos1383261380, 1393
Basilios Bessarion1383231436
Manuel Chrysoloras138299
Guarino da Verona1382981408
Vittorino da Feltre1382971416
Theodoros Gazes1382931433
Jan Standonck1382721490
Johannes Argyropoulos1382721444
Jan Standonck1382721474
Geert Gerardus Magnus Groote138242
Florens Florentius Radwyn Radewyns138242
Rudolf Agricola1382421478
Marsilio Ficino1382411462
Cristoforo Landino138241
Thomas von Kempen à Kempis138241
Alexander Hegius1382401474
Angelo Poliziano1382401477

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
0161038
121289
27995
34741
43254
52430
61794
71454
81196
9967
10778
11644
12594
13483
14420
15361
16328
17281
18233
19185
21173
20148
22148
23135
24111
25102
2688
2882
2776
2958
3448
3044
3244
3142
3341
3530
4225
3624
3824
4124
4322
3921
3720
4017
4517
5216
4912
5512
4411
4610
5310
5610
479
489
509
549
609
517
576
616
635
593
623
673
753
793
662
692
702
712
732
772
812
822
1002
581
641
651
681
721
741
761
781
801
841
851
871
881
911
951
981
991
1041
1191
1401