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 Kuo165
Roger Meyer Temam128
Pekka Neittaanmäki126
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Ludwig Prandtl90
Dimitris John Bertsimas88
Yurii Alekseevich Mitropolsky88
Bart De Moor86
Rudiger W. Dornbusch85
David Garvin Moursund82
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Stefan Jähnichen81
Bruce Ramon Vogeli80
Richard J. Eden80
Sergio Albeverio80
Arnold Zellner79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Saraf al-Dīn Muhammad al-Masʿūdī202264
Fakhr al-Dīn Muhammad al-Rēzī202262
Sharaf al-Dīn al-Ṭūsī202262
Qutb al-Dīn Ibrāhīm al-Mīṣrī2022611222
Kamāl al-Dīn Ibn Yūnus202261
Athīr al-Dīn al-Mufaḍḍal al-Abharī2022601264
Nasir al-Dīn al-Ṭūsī202259
Shams al‐Dīn al‐Bukhārī202256
Gregory Chioniadis2022551296
Manuel Bryennios202254
Theodore Metochites2022531315
Gregory Palamas202250
Nilos Kabasilas2022491363
Demetrios Kydones202248
Elissaeus Judaeus202225
Georgios Plethon Gemistos2022241380, 1393
Basilios Bessarion2022211436
Manuel Chrysoloras202194
Guarino da Verona2021931408
Vittorino da Feltre2021921416
Theodoros Gazes2021881433
Johannes Argyropoulos2021701444
Jan Standonck2021661474
Jan Standonck2021661490
Cristoforo Landino202139

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
0216916
129716
210752
36117
44366
53242
62482
72010
81597
91339
101091
11924
12832
13684
14583
15505
16446
17402
18316
19285
20267
21218
22216
23187
24160
25145
26118
27116
28115
2996
3079
3167
3354
3454
3253
3550
3641
3733
3830
3929
4228
4328
4027
4125
4518
4618
4417
4917
4716
5216
4815
5115
5514
5712
5411
5010
5310
6010
589
568
647
697
636
595
614
624
654
684
724
734
774
824
673
703
803
662
742
792
882
952
1002
711
751
761
781
811
851
861
901
931
1011
1081
1111
1261
1281
1651