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 Kuo160
Roger Meyer Temam124
Pekka Neittaanmäki119
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
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard82
David Garvin Moursund82
Stefan Jähnichen81
Bruce Ramon Vogeli80
Richard J. Eden80
Dimitris John Bertsimas80
Sergio Albeverio80
Arnold Zellner79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī188556
Kamāl al-Dīn Ibn Yūnus188555
Nasir al-Dīn al-Ṭūsī188554
Shams al‐Dīn al‐Bukhārī188553
Gregory Chioniadis1885521296
Manuel Bryennios188551
Theodore Metochites1885501315
Gregory Palamas188548
Nilos Kabasilas1885471363
Demetrios Kydones188546
Elissaeus Judaeus188523
Georgios Plethon Gemistos1885221380, 1393
Basilios Bessarion1885191436
Manuel Chrysoloras188492
Guarino da Verona1884911408
Vittorino da Feltre1884901416
Theodoros Gazes1884861433
Johannes Argyropoulos1884681444
Jan Standonck1884641490
Jan Standonck1884641474
Marsilio Ficino1884371462
Cristoforo Landino188437
Angelo Poliziano1884361477
Moses Perez188434
Scipione Fortiguerra1884341493

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
0204590
128284
210184
35816
44038
53109
62337
71860
81478
91238
101022
11873
12776
13642
14546
15463
16411
17379
18313
19250
20240
22205
21199
23170
24149
25132
26113
27104
28104
2995
3075
3160
3352
3452
3250
3545
3636
3733
3933
4329
3828
4026
4124
4223
4618
5218
4416
4515
4915
4812
5012
5112
5312
5612
5411
5511
4710
579
609
588
688
616
635
645
725
624
654
694
804
824
593
733
763
672
702
772
952
1012
711
741
751
781
791
811
831
851
881
891
901
1001
1081
1101
1191
1241
1601