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 Kuo144
Roger Meyer Temam119
Andrew Bernard Whinston105
Pekka Neittaanmäki105
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky95
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Richard J. Eden80
Olivier Jean Blanchard80
Erol Gelenbe80
Sergio Albeverio79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Arnold Zellner77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī149193
Kamal al Din Ibn Yunus149192
Nasir al-Din al-Tusi149191
Shams ad-Din Al-Bukhari149190
Gregory Chioniadis149189
Manuel Bryennios149188
Theodore Metochites1491871315
Gregory Palamas149185
Nilos Kabasilas1491841363
Demetrios Kydones149183
Elissaeus Judaeus149160
Georgios Plethon Gemistos1491591380, 1393
Basilios Bessarion1491561436
Manuel Chrysoloras149130
Guarino da Verona1491291408
Vittorino da Feltre1491281416
Theodoros Gazes1491241433
Jan Standonck1491031490
Jan Standonck1491031474
Johannes Argyropoulos1491031444
Florens Florentius Radwyn Radewyns149073
Rudolf Agricola1490731478
Geert Gerardus Magnus Groote149073
Marsilio Ficino1490721462
Cristoforo Landino149072

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
0173985
123389
28601
35075
43540
52635
61976
71575
81261
91065
10837
11712
12621
13515
14474
15383
16345
17326
18271
19191
21184
20178
22170
23136
24113
25109
2699
2792
2884
2972
3056
3455
3345
3142
3237
3529
3629
3728
3826
3926
4024
4224
4320
4119
4518
5215
4414
4714
5013
5512
4611
4911
4810
5610
539
518
577
607
596
616
545
634
654
774
824
583
643
673
793
803
622
662
682
692
702
712
722
732
752
882
952
1052
741
761
851
861
981
991
1001
1191
1441