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 Kuo145
Roger Meyer Temam119
Pekka Neittaanmäki106
Andrew Bernard Whinston105
Willi Jäger100
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky95
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-Ṭūsī152393
Kamal al Din Ibn Yunus152392
Nasir al-Din al-Tusi152391
Shams ad-Din Al-Bukhari152390
Gregory Chioniadis1523891296
Manuel Bryennios152388
Theodore Metochites1523871315
Gregory Palamas152385
Nilos Kabasilas1523841363
Demetrios Kydones152383
Elissaeus Judaeus152360
Georgios Plethon Gemistos1523591380, 1393
Basilios Bessarion1523561436
Manuel Chrysoloras152329
Guarino da Verona1523281408
Vittorino da Feltre1523271416
Theodoros Gazes1523231433
Johannes Argyropoulos1523051444
Jan Standonck1523011474
Jan Standonck1523011490
Cristoforo Landino152274
Marsilio Ficino1522741462
Angelo Poliziano1522731477
Scipione Fortiguerra1522711493
Moses Perez152271

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
0177521
123886
28753
35161
43570
52694
62006
71622
81268
91103
10861
11728
12636
13528
14484
15380
16346
17335
18277
19203
20187
21178
22172
23143
24129
25105
2696
2793
2890
2973
3060
3452
3146
3342
3238
3536
3632
3728
3928
4024
3823
4123
4222
4319
4519
5014
5214
4413
4812
4912
5512
4611
4711
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
952
1002
661
741
761
811
851
861
991
1051
1061
1191
1451