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-Ṭūsī149303
Kamal al Din Ibn Yunus149302
Nasir al-Din al-Tusi149301
Shams ad-Din Al-Bukhari149300
Gregory Chioniadis149299
Manuel Bryennios149298
Theodore Metochites1492971315
Gregory Palamas149295
Nilos Kabasilas1492941363
Demetrios Kydones149293
Elissaeus Judaeus149270
Georgios Plethon Gemistos1492691380, 1393
Basilios Bessarion1492661436
Manuel Chrysoloras149240
Guarino da Verona1492391408
Vittorino da Feltre1492381416
Theodoros Gazes1492341433
Jan Standonck1492131474
Johannes Argyropoulos1492131444
Jan Standonck1492131490
Cristoforo Landino149182
Marsilio Ficino1491821462
Rudolf Agricola1491811478
Angelo Poliziano1491811477
Florens Florentius Radwyn Radewyns149181

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
0174174
123414
28614
35072
43544
52639
61976
71580
81260
91061
10842
11715
12621
13514
14475
15384
16343
17327
18270
19193
21182
20181
22170
23136
24115
25108
26100
2791
2886
2972
3056
3455
3345
3142
3237
3529
3629
3727
3927
3826
4024
4223
4321
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