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
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Selim Grigorievich Krein82
Richard J. Eden80
Erol Gelenbe80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Arnold Zellner77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī150269
Kamal al Din Ibn Yunus150268
Nasir al-Din al-Tusi150267
Shams ad-Din Al-Bukhari150266
Gregory Chioniadis1502651296
Manuel Bryennios150264
Theodore Metochites1502631315
Gregory Palamas150261
Nilos Kabasilas1502601363
Demetrios Kydones150259
Elissaeus Judaeus150236
Georgios Plethon Gemistos1502351380, 1393
Basilios Bessarion1502321436
Manuel Chrysoloras150205
Guarino da Verona1502041408
Vittorino da Feltre1502031416
Theodoros Gazes1501991433
Jan Standonck1501771490
Jan Standonck1501771474
Johannes Argyropoulos1501761444
Florens Florentius Radwyn Radewyns150145
Rudolf Agricola1501451478
Cristoforo Landino150145
Marsilio Ficino1501451462
Geert Gerardus Magnus Groote150145

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
0174660
123534
28653
35094
43537
52653
61991
71579
81248
91077
10847
11715
12626
13510
14475
15391
16342
17329
18269
19200
21184
20180
22166
23140
24115
25107
26101
2790
2889
2973
3057
3455
3343
3142
3237
3530
3630
3928
3727
3825
4023
4222
4321
4120
4518
5215
4414
4714
5013
5512
4611
4811
4911
539
569
518
608
577
616
545
595
584
634
654
774
824
643
673
713
793
803
622
662
682
692
722
732
752
882
952
1052
701
741
761
851
861
981
991
1001
1191
1441