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 Kuo137
Roger Meyer Temam119
Andrew Bernard Whinston104
Ronold Wyeth Percival King100
Pekka Neittaanmäki100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky90
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
Arnold Zellner77
Johan F. A. K. van Benthem77
Egon Krause76

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari137480
Gregory Chioniadis137479
Manuel Bryennios137478
Theodore Metochites1374771315
Gregory Palamas137475
Nilos Kabasilas1374741363
Demetrios Kydones137473
Elissaeus Judaeus137450
Georgios Plethon Gemistos1374491380, 1393
Basilios Bessarion1374461436
Manuel Chrysoloras137422
Guarino da Verona1374211408
Vittorino da Feltre1374201416
Theodoros Gazes1374161433
Jan Standonck1373951490
Jan Standonck1373951474
Johannes Argyropoulos1373951444
Rudolf Agricola1373651478
Florens Florentius Radwyn Radewyns137365
Geert Gerardus Magnus Groote137365
Thomas von Kempen à Kempis137364
Marsilio Ficino1373641462
Cristoforo Landino137364
Alexander Hegius1373631474
Angelo Poliziano1373631477

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
0159961
121085
27924
34697
43235
52420
61769
71453
81180
9964
10779
11637
12585
13489
14413
15358
16317
17282
18227
19186
21170
20152
22151
23134
24107
25100
2687
2882
2776
2957
3449
3047
3142
3342
3240
3530
4125
4225
3624
3823
3923
4321
3717
4517
4016
4913
5213
5312
5512
4410
4610
5610
479
489
509
609
518
548
617
636
575
593
753
793
662
672
682
702
712
732
772
812
822
1002
581
621
641
651
691
721
741
761
781
801
841
851
871
881
901
951
981
991
1041
1191
1371