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 Kuo144
Roger Meyer Temam119
Pekka Neittaanmäki105
Andrew Bernard Whinston105
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky92
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Bart De Moor82
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Arnold Zellner77
Egon Krause77
Charles Ehresmann77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Kamal al Din Ibn Yunus145709
Nasir al-Din al-Tusi145708
Shams ad-Din Al-Bukhari145707
Gregory Chioniadis145706
Manuel Bryennios145705
Theodore Metochites1457041315
Gregory Palamas145702
Nilos Kabasilas1457011363
Demetrios Kydones145700
Elissaeus Judaeus145677
Georgios Plethon Gemistos1456761380, 1393
Basilios Bessarion1456731436
Manuel Chrysoloras145649
Guarino da Verona1456481408
Vittorino da Feltre1456471416
Theodoros Gazes1456431433
Jan Standonck1456221490
Jan Standonck1456221474
Johannes Argyropoulos1456221444
Rudolf Agricola1455921478
Florens Florentius Radwyn Radewyns145592
Geert Gerardus Magnus Groote145592
Marsilio Ficino1455911462
Thomas von Kempen à Kempis145591
Cristoforo Landino145591

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
0169766
122881
28467
34967
43463
52586
61905
71551
81225
91045
10824
11692
12617
13503
14450
15377
16339
17296
18266
19195
21178
20167
22164
23130
24116
25109
2692
2886
2784
2968
3455
3051
3142
3341
3238
3629
3826
3525
3925
4223
3722
4022
4121
4520
4319
5216
4414
4614
5513
5012
4811
4911
4710
5610
538
517
617
576
606
545
585
635
594
654
774
623
673
683
733
793
823
692
712
722
752
762
802
1052
641
661
701
811
851
861
871
881
921
951
981
991
1001
1191
1441