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-Bukhari138460
Gregory Chioniadis138459
Manuel Bryennios138458
Theodore Metochites1384571315
Gregory Palamas138455
Nilos Kabasilas1384541363
Demetrios Kydones138453
Elissaeus Judaeus138430
Georgios Plethon Gemistos1384291380, 1393
Basilios Bessarion1384261436
Manuel Chrysoloras138402
Guarino da Verona1384011408
Vittorino da Feltre1384001416
Theodoros Gazes1383961433
Jan Standonck1383751474
Johannes Argyropoulos1383751444
Jan Standonck1383751490
Geert Gerardus Magnus Groote138345
Rudolf Agricola1383451478
Florens Florentius Radwyn Radewyns138345
Marsilio Ficino1383441462
Thomas von Kempen à Kempis138344
Cristoforo Landino138344
Alexander Hegius1383431474
Angelo Poliziano1383431477

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
0161146
121295
28007
34736
43263
52429
61797
71455
81191
9965
10787
11640
12598
13484
14418
15360
16329
17283
18234
19185
21174
22148
20147
23135
24111
25102
2687
2880
2777
2958
3449
3044
3244
3142
3342
3528
3825
4225
4124
3623
3922
4322
3721
4018
4517
5216
5513
4912
4411
4610
5610
479
489
509
539
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