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 Kuo161
Roger Meyer Temam128
Pekka Neittaanmäki123
Shlomo Noach (Stephen Ram) Sawilowsky110
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Dimitris John Bertsimas87
Rudiger W. Dornbusch85
Bart De Moor84
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Stefan Jähnichen81
Richard J. Eden80
Bruce Ramon Vogeli80
Sergio Albeverio80
Arnold Zellner79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī192116
Kamāl al-Dīn Ibn Yūnus192115
Nasir al-Dīn al-Ṭūsī192114
Shams al‐Dīn al‐Bukhārī192113
Gregory Chioniadis1921121296
Manuel Bryennios192111
Theodore Metochites1921101315
Gregory Palamas192108
Nilos Kabasilas1921071363
Demetrios Kydones192106
Elissaeus Judaeus192083
Georgios Plethon Gemistos1920821380, 1393
Basilios Bessarion1920791436
Manuel Chrysoloras192052
Guarino da Verona1920511408
Vittorino da Feltre1920501416
Theodoros Gazes1920461433
Johannes Argyropoulos1920281444
Jan Standonck1920241490
Jan Standonck1920241474
Cristoforo Landino191997
Marsilio Ficino1919971462
Angelo Poliziano1919961477
Moses Perez191994
Scipione Fortiguerra1919941493

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
0208301
128798
210292
35942
44146
53123
62386
71926
81518
91270
101033
11886
12795
13669
14550
15474
16419
17390
18305
19257
20249
22215
21209
23173
24146
25141
26115
27108
28106
2999
3074
3161
3453
3352
3250
3545
3735
3634
3830
4329
3928
4126
4226
4025
4419
5218
4917
4616
4514
4713
4813
5012
5112
5311
5511
5711
5410
5610
608
618
697
586
636
595
625
645
654
684
724
824
703
733
763
803
672
752
772
952
1002
711
741
781
791
811
841
851
871
881
901
931
1011
1081
1101
1231
1281
1611