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
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky95
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl88
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
Stefan Jähnichen79
Bruce Ramon Vogeli79
Sergio Albeverio79
Charles Ehresmann77
Arnold Zellner77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī151590
Kamal al Din Ibn Yunus151589
Nasir al-Din al-Tusi151588
Shams ad-Din Al-Bukhari151587
Gregory Chioniadis1515861296
Manuel Bryennios151585
Theodore Metochites1515841315
Gregory Palamas151582
Nilos Kabasilas1515811363
Demetrios Kydones151580
Elissaeus Judaeus151557
Georgios Plethon Gemistos1515561380, 1393
Basilios Bessarion1515531436
Manuel Chrysoloras151526
Guarino da Verona1515251408
Vittorino da Feltre1515241416
Theodoros Gazes1515201433
Johannes Argyropoulos1515021444
Jan Standonck1514981490
Jan Standonck1514981474
Marsilio Ficino1514711462
Cristoforo Landino151471
Angelo Poliziano1514701477
Scipione Fortiguerra1514681493
Moses Perez151468

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
0176386
123712
28724
35123
43562
52687
61995
71604
81262
91094
10850
11723
12633
13522
14482
15380
16352
17331
18271
19202
21183
20182
22167
23144
24124
25106
2699
2790
2890
2973
3059
3454
3145
3341
3238
3533
3631
3730
3928
4124
3823
4222
4021
4319
4519
4414
5214
4813
5013
4912
5512
4611
4710
5310
518
568
578
607
617
546
596
655
584
634
774
824
673
683
793
622
642
662
692
702
712
722
732
752
802
882
952
992
741
761
811
851
861
1001
1051
1061
1191
1451