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
Ronold Wyeth Percival King100
Willi Jäger99
Alexander Vasil'evich Mikhalëv99
Shlomo Noach (Stephen Ram) Sawilowsky95
Leonard Salomon Ornstein95
Ludwig Prandtl88
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Bart De Moor82
David Garvin Moursund82
Erol Gelenbe81
Richard J. Eden80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Charles Ehresmann77
Arnold Zellner77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī151395
Kamal al Din Ibn Yunus151394
Nasir al-Din al-Tusi151393
Shams ad-Din Al-Bukhari151392
Gregory Chioniadis1513911296
Manuel Bryennios151390
Theodore Metochites1513891315
Gregory Palamas151387
Nilos Kabasilas1513861363
Demetrios Kydones151385
Elissaeus Judaeus151362
Georgios Plethon Gemistos1513611380, 1393
Basilios Bessarion1513581436
Manuel Chrysoloras151331
Guarino da Verona1513301408
Vittorino da Feltre1513291416
Theodoros Gazes1513251433
Johannes Argyropoulos1513071444
Jan Standonck1513031490
Jan Standonck1513031474
Marsilio Ficino1512761462
Cristoforo Landino151276
Angelo Poliziano1512751477
Scipione Fortiguerra1512731493
Moses Perez151273

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
0176157
123680
28720
35117
43551
52679
61990
71602
81258
91095
10847
11722
12635
13518
14484
15380
16352
17328
18273
19202
20183
21181
22167
23145
24122
25106
2699
2891
2790
2974
3057
3454
3144
3341
3238
3534
3630
3730
3928
3823
4123
4022
4222
4319
4519
4415
5014
4813
5213
4912
5512
4711
4610
5310
569
518
577
597
607
617
545
655
584
634
774
824
673
793
622
642
662
682
692
702
712
722
732
752
802
882
952
992
741
761
811
851
861
1001
1051
1061
1191
1451