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 Kuo159
Roger Meyer Temam124
Pekka Neittaanmäki120
Shlomo Noach (Stephen Ram) Sawilowsky110
Andrew Bernard Whinston108
Willi Jäger101
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Ludwig Prandtl90
Kurt Mehlhorn89
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Bart De Moor83
Selim Grigorievich Krein82
David Garvin Moursund82
Olivier Jean Blanchard82
Andrei Nikolayevich Kolmogorov82
Stefan Jähnichen81
Bruce Ramon Vogeli80
Richard J. Eden80
Sergio Albeverio80
Arnold Zellner79
Johan F. A. K. van Benthem78

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī186550
Kamāl al-Dīn Ibn Yūnus186549
Nasir al-Dīn al-Ṭūsī186548
Shams al‐Dīn al‐Bukhārī186547
Gregory Chioniadis1865461296
Manuel Bryennios186545
Theodore Metochites1865441315
Gregory Palamas186542
Nilos Kabasilas1865411363
Demetrios Kydones186540
Elissaeus Judaeus186517
Georgios Plethon Gemistos1865161380, 1393
Basilios Bessarion1865131436
Manuel Chrysoloras186486
Guarino da Verona1864851408
Vittorino da Feltre1864841416
Theodoros Gazes1864801433
Johannes Argyropoulos1864621444
Jan Standonck1864581490
Jan Standonck1864581474
Marsilio Ficino1864311462
Cristoforo Landino186431
Angelo Poliziano1864301477
Moses Perez186428
Scipione Fortiguerra1864281493

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
0202338
127939
210072
35756
43983
53096
62296
71837
81474
91229
101018
11861
12760
13636
14530
15459
16407
17380
18301
19249
20231
21204
22199
23174
24148
25124
27109
26107
29101
28100
3069
3156
3353
3452
3249
3543
3736
3634
3932
3829
4328
4027
4226
4121
5218
4516
4616
4915
5315
4414
5013
5112
4711
5511
4810
5410
569
579
589
607
687
616
646
635
695
624
724
824
593
653
703
733
763
803
672
772
782
952
1012
711
741
751
791
811
831
851
881
891
901
1001
1081
1101
1201
1241
1591