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 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
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Stefan Jähnichen81
Bruce Ramon Vogeli80
Richard J. Eden80
Sergio Albeverio80
Arnold Zellner79
Dimitris John Bertsimas79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī187647
Kamāl al-Dīn Ibn Yūnus187646
Nasir al-Dīn al-Ṭūsī187645
Shams al‐Dīn al‐Bukhārī187644
Gregory Chioniadis1876431296
Manuel Bryennios187642
Theodore Metochites1876411315
Gregory Palamas187639
Nilos Kabasilas1876381363
Demetrios Kydones187637
Elissaeus Judaeus187614
Georgios Plethon Gemistos1876131380, 1393
Basilios Bessarion1876101436
Manuel Chrysoloras187583
Guarino da Verona1875821408
Vittorino da Feltre1875811416
Theodoros Gazes1875771433
Johannes Argyropoulos1875591444
Jan Standonck1875551490
Jan Standonck1875551474
Marsilio Ficino1875281462
Cristoforo Landino187528
Angelo Poliziano1875271477
Scipione Fortiguerra1875251493
Moses Perez187525

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
0203578
128114
210125
35800
44013
53099
62325
71836
81476
91236
101025
11865
12774
13638
14537
15461
16408
17378
18312
19247
20234
21202
22202
23171
24156
25121
26113
27108
28101
2998
3072
3157
3353
3251
3450
3546
3735
3633
3931
3830
4329
4027
4223
4122
5218
4517
4617
4415
4915
5014
5513
5112
5312
4811
4710
5410
5810
569
579
607
687
616
646
635
695
725
624
824
593
653
703
733
763
803
672
772
792
952
1012
741
751
781
811
831
851
881
891
901
1001
1081
1101
1201
1241
1601