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 Kuo171
Roger Meyer Temam130
Pekka Neittaanmäki127
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Leonard Salomon Ornstein95
Erol Gelenbe95
Kurt Mehlhorn93
Dimitris John Bertsimas91
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Bart De Moor86
Rudiger W. Dornbusch85
Wolfgang Karl Härdle83
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard82
David Garvin Moursund82
Sergio Albeverio81
Stefan Jähnichen81
Richard J. Eden80
Bruce Ramon Vogeli80

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu ʿAli al-Husayn (Avicenna) ibn Sina214157
Bahmanyār ibn al-Marzubān214156
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2141551068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī214154
Fakhr al-Dīn Muhammad al-Rēzī214152
Sharaf al-Dīn al-Ṭūsī214152
Kamāl al-Dīn Ibn Yūnus214151
Qutb al-Dīn Ibrāhīm al-Mīṣrī2141511222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2141501264
Nasir al-Dīn al-Ṭūsī214149
Shams al‐Dīn al‐Bukhārī214146
Gregory Chioniadis2141451296
Manuel Bryennios2141441300
Theodore Metochites2141431315
Gregory Palamas2141401316
Nilos Kabasilas2141391363
Demetrios Kydones214138
Elissaeus Judaeus214113
Georgios Plethon Gemistos2141121380, 1393
Basilios Bessarion2141091436
Manuel Chrysoloras214100
Giovanni Conversini214100
Gasparino da Barzizza214099
Guarino da Verona2140991408
Vittorino da Feltre2140981416

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
0226715
131084
211350
36463
44536
53383
62591
72124
81702
91426
101135
11965
12886
13729
14614
15540
16477
17409
18338
19307
20276
22238
21236
23197
24168
25168
26138
28123
27117
29100
3087
3174
3360
3459
3255
3653
3550
3736
3935
3832
4230
4326
4025
4123
4421
4521
5119
4618
4917
5217
5316
5414
4713
4812
5012
5511
5711
6011
569
587
617
637
647
687
596
696
725
654
704
744
824
623
733
783
672
712
752
772
802
812
952
1002
661
761
791
831
851
861
881
901
911
931
1011
1081
1111
1271
1301
1711