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
Kurt Mehlhorn86
Rudiger W. Dornbusch85
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Bart De Moor82
Selim Grigorievich Krein81
Olivier Jean Blanchard80
Richard J. Eden80
Sergio Albeverio80
Bruce Ramon Vogeli79
Stefan Jähnichen79
Arnold Zellner77
Johan F. A. K. van Benthem77
Charles Ehresmann77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Nasir al-Din al-Tusi141697
Shams ad-Din Al-Bukhari141696
Gregory Chioniadis141695
Manuel Bryennios141694
Theodore Metochites1416931315
Gregory Palamas141691
Nilos Kabasilas1416901363
Demetrios Kydones141689
Elissaeus Judaeus141666
Georgios Plethon Gemistos1416651380, 1393
Basilios Bessarion1416621436
Manuel Chrysoloras141638
Guarino da Verona1416371408
Vittorino da Feltre1416361416
Theodoros Gazes1416321433
Jan Standonck1416111474
Johannes Argyropoulos1416111444
Jan Standonck1416111490
Geert Gerardus Magnus Groote141581
Florens Florentius Radwyn Radewyns141581
Rudolf Agricola1415811478
Thomas von Kempen à Kempis141580
Cristoforo Landino141580
Marsilio Ficino1415801462
Alexander Hegius1415791474

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
0164693
121876
28159
34837
43337
52498
61846
71505
81203
91007
10803
11656
12609
13486
14438
15381
16324
17290
18245
19193
21173
20159
22157
23130
24112
25102
2786
2684
2883
2962
3450
3045
3142
3242
3341
3529
3625
3825
3923
4123
3722
4322
4020
4219
4518
5217
5515
4414
5013
4612
4811
5310
5610
479
499
617
576
606
636
515
545
583
593
653
683
713
753
773
803
823
622
662
672
692
722
732
762
792
1002
701
811
851
861
871
881
911
951
981
991
1041
1191
1401