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 Kuo137
Roger Meyer Temam119
Andrew Bernard Whinston104
Ronold Wyeth Percival King100
Pekka Neittaanmäki99
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky90
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn84
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein81
Bart De Moor81
Richard J. Eden80
Bruce Ramon Vogeli79
Stefan Jähnichen78
Charles Ehresmann78
Johan F. A. K. van Benthem77
Egon Krause76
Arnold Zellner76
David Hilbert75
Wilhelm Magnus75

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari136502
Gregory Chioniadis136501
Manuel Bryennios136500
Theodore Metochites1364991315
Gregory Palamas136497
Nilos Kabasilas1364961363
Demetrios Kydones136495
Elissaeus Judaeus136472
Georgios Plethon Gemistos1364711380, 1393
Basilios Bessarion1364681436
Manuel Chrysoloras136444
Guarino da Verona1364431408
Vittorino da Feltre1364421416
Theodoros Gazes1364381433
Jan Standonck1364171490
Johannes Argyropoulos1364171444
Jan Standonck1364171474
Rudolf Agricola1363871478
Florens Florentius Radwyn Radewyns136387
Geert Gerardus Magnus Groote136387
Cristoforo Landino136386
Marsilio Ficino1363861462
Thomas von Kempen à Kempis136386
Alexander Hegius1363851474
Angelo Poliziano1363851477

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
0158901
120889
27884
34681
43198
52399
61756
71443
81176
9954
10777
11642
12583
13475
14409
15357
16312
17284
18223
19186
21167
22155
20153
23130
24109
25101
2687
2881
2775
2955
3449
3046
3242
3140
3340
3530
3626
4124
3923
4223
3822
4321
4017
4517
5216
3714
4912
4411
5511
4610
5610
479
489
509
539
609
548
517
617
636
575
593
683
733
753
662
672
702
712
762
782
812
822
992
581
621
641
651
721
741
771
791
801
841
871
881
901
951
981
1001
1041
1191
1371