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 Kuo144
Roger Meyer Temam119
Andrew Bernard Whinston105
Pekka Neittaanmäki105
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Shlomo Noach (Stephen Ram) Sawilowsky95
Leonard Salomon Ornstein95
Ludwig Prandtl88
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Erol Gelenbe80
Richard J. Eden80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Arnold Zellner77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī150354
Kamal al Din Ibn Yunus150353
Nasir al-Din al-Tusi150352
Shams ad-Din Al-Bukhari150351
Gregory Chioniadis1503501296
Manuel Bryennios150349
Theodore Metochites1503481315
Gregory Palamas150346
Nilos Kabasilas1503451363
Demetrios Kydones150344
Elissaeus Judaeus150321
Georgios Plethon Gemistos1503201380, 1393
Basilios Bessarion1503171436
Manuel Chrysoloras150290
Guarino da Verona1502891408
Vittorino da Feltre1502881416
Theodoros Gazes1502841433
Jan Standonck1502621474
Jan Standonck1502621490
Johannes Argyropoulos1502611444
Rudolf Agricola1502301478
Cristoforo Landino150230
Geert Gerardus Magnus Groote150230
Marsilio Ficino1502301462
Florens Florentius Radwyn Radewyns150230

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
0174766
123549
28663
35093
43544
52656
61992
71577
81257
91076
10840
11723
12625
13512
14473
15390
16342
17331
18269
19199
21185
20180
22167
23140
24115
25106
26102
2790
2888
2974
3056
3453
3343
3142
3237
3532
3630
3728
3927
3825
4024
4222
4321
4120
4518
4414
4714
5214
5013
5512
4611
4811
4911
5310
569
518
608
577
616
545
595
655
584
634
774
824
673
793
803
622
642
662
682
692
702
712
722
732
752
882
952
1052
741
761
851
861
981
991
1001
1191
1441