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
Ronold Wyeth Percival King100
Andrew Bernard Whinston98
Alexander Vasil'evich Mikhalëv98
Willi Jäger96
Pekka Neittaanmäki95
Leonard Salomon Ornstein95
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Shlomo Noach (Stephen Ram) Sawilowsky84
Kurt Mehlhorn83
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein81
Bart De Moor81
Richard J. Eden80
Arnold Zellner78
Stefan Jähnichen78
Bruce Ramon Vogeli78
Charles Ehresmann78
Johan F. A. K. van Benthem77
Egon Krause76
David Hilbert75
Wilhelm Magnus74

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari131927
Gregory Chioniadis131926
Manuel Bryennios131925
Theodore Metochites1319241315
Gregory Palamas131922
Nilos Kabasilas1319211363
Demetrios Kydones131920
Elissaeus Judaeus131897
Georgios Plethon Gemistos1318961380, 1393
Basilios Bessarion1318931436
Manuel Chrysoloras131869
Guarino da Verona1318681408
Vittorino da Feltre1318671416
Theodoros Gazes1318631433
Johannes Argyropoulos1318421444
Jan Standonck1318421474
Jan Standonck1318421490
Florens Florentius Radwyn Radewyns131812
Rudolf Agricola1318121478
Geert Gerardus Magnus Groote131812
Marsilio Ficino1318111462
Cristoforo Landino131811
Thomas von Kempen à Kempis131811
Angelo Poliziano1318101477
Alexander Hegius1318101474

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
0153290
120035
27604
34468
43096
52304
61670
71392
81159
9930
10744
11605
12551
13452
14410
15332
16311
17257
18210
19184
21167
20150
22148
23127
25109
2493
2684
2878
2767
2954
3143
3442
3041
3341
3239
3527
4127
3623
4223
3822
3920
4019
4319
3717
4514
5313
5513
5212
5011
4910
448
568
608
467
477
487
517
636
575
615
594
784
543
673
582
652
682
702
712
732
742
812
822
952
982
621
641
661
721
751
761
771
801
831
841
871
881
961
1001
1191
1341