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 Kuo165
Roger Meyer Temam128
Pekka Neittaanmäki126
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Ludwig Prandtl90
Dimitris John Bertsimas88
Yurii Alekseevich Mitropolsky88
Bart De Moor86
Rudiger W. Dornbusch85
David Garvin Moursund82
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Stefan Jähnichen81
Bruce Ramon Vogeli80
Richard J. Eden80
Sergio Albeverio80
Wolfgang Karl Härdle79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Saraf al-Dīn Muhammad al-Masʿūdī202463
Fakhr al-Dīn Muhammad al-Rēzī202461
Sharaf al-Dīn al-Ṭūsī202461
Kamāl al-Dīn Ibn Yūnus202460
Qutb al-Dīn Ibrāhīm al-Mīṣrī2024601222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2024591264
Nasir al-Dīn al-Ṭūsī202458
Shams al‐Dīn al‐Bukhārī202455
Gregory Chioniadis2024541296
Manuel Bryennios202453
Theodore Metochites2024521315
Gregory Palamas202449
Nilos Kabasilas2024481363
Demetrios Kydones202447
Elissaeus Judaeus202424
Georgios Plethon Gemistos2024231380, 1393
Basilios Bessarion2024201436
Manuel Chrysoloras202393
Guarino da Verona2023921408
Vittorino da Feltre2023911416
Theodoros Gazes2023871433
Johannes Argyropoulos2023691444
Jan Standonck2023651474
Jan Standonck2023651490
Cristoforo Landino202338

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
0217144
129731
210761
36133
44376
53257
62478
72014
81596
91341
101092
11927
12830
13685
14582
15508
16447
17401
18315
19287
20267
21219
22217
23186
24160
25147
26118
28117
27114
2996
3077
3168
3254
3354
3454
3550
3641
3733
3930
3829
4228
4027
4327
4125
4619
4418
4918
4517
4716
5216
5115
4814
5514
5712
5411
6011
5010
5310
568
588
647
697
636
595
614
624
654
684
724
734
774
824
673
703
803
662
742
792
882
952
1002
711
751
761
781
811
851
861
901
931
1011
1081
1111
1261
1281
1651