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 Kuo134
Roger Meyer Temam119
Ronold Wyeth Percival King100
Andrew Bernard Whinston98
Alexander Vasil'evich Mikhalëv98
Willi Jäger96
Pekka Neittaanmäki95
Leonard Salomon Ornstein95
Yurii Alekseevich Mitropolsky88
Shlomo Noach (Stephen Ram) Sawilowsky88
Ludwig Prandtl87
Kurt Mehlhorn83
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein81
Bart De Moor81
Richard J. Eden80
Charles Ehresmann78
Stefan Jähnichen78
Arnold Zellner78
Bruce Ramon Vogeli78
Johan F. A. K. van Benthem77
Egon Krause76
David Hilbert75
Wilhelm Magnus74

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari132901
Gregory Chioniadis132900
Manuel Bryennios132899
Theodore Metochites1328981315
Gregory Palamas132896
Nilos Kabasilas1328951363
Demetrios Kydones132894
Elissaeus Judaeus132871
Georgios Plethon Gemistos1328701380, 1393
Basilios Bessarion1328671436
Manuel Chrysoloras132843
Guarino da Verona1328421408
Vittorino da Feltre1328411416
Theodoros Gazes1328371433
Johannes Argyropoulos1328161444
Jan Standonck1328161474
Jan Standonck1328161490
Rudolf Agricola1327861478
Geert Gerardus Magnus Groote132786
Florens Florentius Radwyn Radewyns132786
Thomas von Kempen à Kempis132785
Cristoforo Landino132785
Marsilio Ficino1327851462
Alexander Hegius1327841474
Angelo Poliziano1327841477

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
0154151
120156
27666
34501
43114
52313
61686
71403
81166
9935
10753
11613
12557
13448
14404
15342
16311
17264
18209
19181
21170
20151
22147
23131
25109
2496
2680
2879
2767
2957
3445
3042
3141
3341
3238
3527
3624
4224
4123
3921
3820
4020
4320
3716
4516
5313
5012
5512
5211
499
569
448
488
608
467
477
517
636
575
595
615
544
784
673
652
682
702
712
732
742
812
822
882
952
982
581
621
641
661
721
751
761
771
801
831
871
961
1001
1191
1341