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 Kuo147
Roger Meyer Temam119
Pekka Neittaanmäki106
Andrew Bernard Whinston105
Ronold Wyeth Percival King100
Willi Jäger100
Alexander Vasil'evich Mikhalëv99
Shlomo Noach (Stephen Ram) Sawilowsky98
Leonard Salomon Ornstein95
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Bart De Moor82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Erol Gelenbe81
Richard J. Eden80
Olivier Jean Blanchard80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Sergio Albeverio79
Arnold Zellner77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī154391
Kamal al Din Ibn Yunus154390
Nasir al-Din al-Tusi154389
Shams ad-Din Al-Bukhari154388
Gregory Chioniadis1543871296
Manuel Bryennios154386
Theodore Metochites1543851315
Gregory Palamas154383
Nilos Kabasilas1543821363
Demetrios Kydones154381
Elissaeus Judaeus154358
Georgios Plethon Gemistos1543571380, 1393
Basilios Bessarion1543541436
Manuel Chrysoloras154327
Guarino da Verona1543261408
Vittorino da Feltre1543251416
Theodoros Gazes1543211433
Johannes Argyropoulos1543031444
Jan Standonck1542991490
Jan Standonck1542991474
Marsilio Ficino1542721462
Cristoforo Landino154272
Angelo Poliziano1542711477
Scipione Fortiguerra1542691493
Moses Perez154269

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
0178626
124083
28824
35175
43597
52747
62008
71629
81280
91110
10868
11739
12635
13533
14480
15384
16354
17339
18272
19206
20194
22178
21169
23147
24129
25102
2696
2895
2791
2977
3060
3452
3343
3141
3241
3635
3534
3929
3726
4024
4124
3822
4222
4319
4518
4914
5014
5214
4613
4412
4712
5512
4811
519
539
609
568
577
546
585
595
615
655
624
634
674
774
824
703
793
642
682
692
712
722
732
752
802
882
1002
661
741
761
811
851
861
951
981
991
1051
1061
1191
1471