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 Kuo150
Roger Meyer Temam124
Andrew Bernard Whinston107
Pekka Neittaanmäki106
Shlomo Noach (Stephen Ram) Sawilowsky103
Alexander Vasil'evich Mikhalëv100
Willi Jäger100
Ronold Wyeth Percival King100
Leonard Salomon Ornstein95
Ludwig Prandtl89
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn88
Erol Gelenbe87
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Olivier Jean Blanchard82
Bart De Moor82
Richard J. Eden80
Bruce Ramon Vogeli80
Stefan Jähnichen79
Sergio Albeverio79
Egon Krause77
Arnold Zellner77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī162005
Kamāl al-Dīn Ibn Yūnus162004
Nasir al-Dīn al-Ṭūsī162003
Shams al‐Dīn al‐Bukhārī162002
Gregory Chioniadis1620011296
Manuel Bryennios162000
Theodore Metochites1619991315
Gregory Palamas161997
Nilos Kabasilas1619961363
Demetrios Kydones161995
Elissaeus Judaeus161972
Georgios Plethon Gemistos1619711380, 1393
Basilios Bessarion1619681436
Manuel Chrysoloras161941
Guarino da Verona1619401408
Vittorino da Feltre1619391416
Theodoros Gazes1619351433
Johannes Argyropoulos1619171444
Jan Standonck1619131474
Jan Standonck1619131490
Marsilio Ficino1618861462
Cristoforo Landino161886
Angelo Poliziano1618851477
Moses Perez161883
Scipione Fortiguerra1618831493

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
0188659
125748
29285
35418
43752
52870
62098
71731
81354
91186
10913
11784
12705
13580
14502
15399
16379
17363
18291
19235
20195
21190
22178
23153
24142
26115
25107
2892
2990
2789
3062
3462
3152
3246
3342
3635
3534
3929
3828
3727
4124
4224
4023
4323
4519
4814
5014
5214
4613
5113
5313
4912
4410
5510
479
569
608
577
587
546
595
615
625
655
825
644
674
704
774
683
693
723
1003
632
712
732
752
762
792
802
882
741
851
871
891
951
1031
1061
1071
1241
1501