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 Kuo164
Roger Meyer Temam128
Pekka Neittaanmäki124
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Leonard Salomon Ornstein95
Erol Gelenbe95
Kurt Mehlhorn93
Ludwig Prandtl90
Dimitris John Bertsimas88
Yurii Alekseevich Mitropolsky88
Bart De Moor86
Rudiger W. Dornbusch85
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Stefan Jähnichen81
Richard J. Eden80
Sergio Albeverio80
Bruce Ramon Vogeli80
Arnold Zellner79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī200662
Kamāl al-Dīn Ibn Yūnus200661
Nasir al-Dīn al-Ṭūsī200659
Shams al‐Dīn al‐Bukhārī200656
Gregory Chioniadis2006551296
Manuel Bryennios200654
Theodore Metochites2006531315
Gregory Palamas200650
Nilos Kabasilas2006491363
Demetrios Kydones200648
Elissaeus Judaeus200625
Georgios Plethon Gemistos2006241380, 1393
Basilios Bessarion2006211436
Manuel Chrysoloras200594
Guarino da Verona2005931408
Vittorino da Feltre2005921416
Theodoros Gazes2005881433
Johannes Argyropoulos2005701444
Jan Standonck2005661474
Jan Standonck2005661490
Marsilio Ficino2005391462
Cristoforo Landino200539
Angelo Poliziano2005381477
Moses Perez200536
Scipione Fortiguerra2005361493

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
0215709
129481
210621
36087
44322
53222
62477
71976
81594
91329
101079
11923
12818
13696
14572
15497
16443
17397
18323
20273
19272
22221
21205
23180
24163
25144
26117
28117
27114
2990
3083
3163
3255
3455
3352
3547
3641
3736
3932
4228
3827
4026
4126
4326
4418
4518
4618
4917
5216
4715
5115
4814
5513
5712
5010
5310
5410
6010
569
588
637
697
595
625
645
655
725
614
684
734
774
824
703
803
662
672
742
782
882
952
1002
751
761
791
811
851
861
901
931
1011
1081
1111
1241
1281
1641