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 Kuo134
Roger Meyer Temam119
Andrew Bernard Whinston104
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger97
Pekka Neittaanmäki96
Leonard Salomon Ornstein95
Yurii Alekseevich Mitropolsky88
Shlomo Noach (Stephen Ram) Sawilowsky88
Ludwig Prandtl87
Kurt Mehlhorn84
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor81
Selim Grigorievich Krein81
Richard J. Eden80
Stefan Jähnichen78
Bruce Ramon Vogeli78
Charles Ehresmann78
Johan F. A. K. van Benthem77
Egon Krause76
David Hilbert75
Arnold Zellner75
Wilhelm Magnus74

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari134312
Gregory Chioniadis134311
Manuel Bryennios134310
Theodore Metochites1343091315
Gregory Palamas134307
Nilos Kabasilas1343061363
Demetrios Kydones134305
Elissaeus Judaeus134282
Georgios Plethon Gemistos1342811380, 1393
Basilios Bessarion1342781436
Manuel Chrysoloras134254
Guarino da Verona1342531408
Vittorino da Feltre1342521416
Theodoros Gazes1342481433
Jan Standonck1342271490
Jan Standonck1342271474
Johannes Argyropoulos1342271444
Rudolf Agricola1341971478
Geert Gerardus Magnus Groote134197
Florens Florentius Radwyn Radewyns134197
Marsilio Ficino1341961462
Cristoforo Landino134196
Thomas von Kempen à Kempis134196
Angelo Poliziano1341951477
Alexander Hegius1341951474

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
0156040
120446
27720
34597
43123
52343
61720
71408
81175
9947
10766
11623
12569
13457
14411
15345
16313
17271
18210
19181
21165
20155
22151
23132
25109
24100
2679
2879
2773
2958
3446
3045
3342
3141
3236
3528
3624
4124
4223
3821
3921
4321
4019
4518
3715
5012
5512
5211
5311
4410
5610
489
499
609
468
517
476
546
636
575
615
594
673
733
783
652
682
702
712
742
752
812
822
882
581
621
641
661
721
761
771
801
841
871
951
961
971
991
1001
1041
1191
1341