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 Kuo179
Egbert Havinga143
Pekka Neittaanmäki133
Roger Meyer Temam130
Ramalingam Chellappa127
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Dimitris John Bertsimas98
Johan Pieter Wibaut97
Erol Gelenbe96
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Bart De Moor91
Ludwig Prandtl90
Rutger Anthony van Santen90
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle85
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
David Garvin Moursund82
Olivier Jean Blanchard82

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi233638
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili233638
Abu Mansur al-Hasan ibn Nuh al-Qumri233638
Abu ʿAli al-Husayn (Avicenna) ibn Sina233637
Bahmanyār ibn al-Marzubān233636
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2336351068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī233634
Sharaf al-Dīn al-Ṭūsī233632
Fakhr al-Dīn Muhammad al-Rēzī233632
Kamāl al-Dīn Ibn Yūnus233631
Qutb al-Dīn Ibrāhīm al-Mīṣrī2336311222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2336301264
Nasir al-Dīn al-Ṭūsī233629
Shams al‐Dīn al‐Bukhārī233626
Gregory Chioniadis2336251296
Manuel Bryennios2336241300
Theodore Metochites2336231315
Gregory Palamas2336201316
Nilos Kabasilas2336191363
Demetrios Kydones233618
Elissaeus Judaeus233593
Georgios Plethon Gemistos2335921380, 1393
Basilios Bessarion2335891436
Manuel Chrysoloras233580
Giovanni Conversini2335801363

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
0243598
133193
212193
36988
44763
53626
62757
72232
81876
91537
101253
111049
12948
13801
14660
15591
16526
17455
18369
19325
20325
22253
23242
21239
24187
25180
26175
27129
28126
29107
3098
3178
3370
3268
3668
3563
3462
3744
3837
3936
4234
4331
4029
4128
4528
4625
4420
5220
4918
5417
5016
5115
4714
5314
4813
5513
5713
5612
6010
589
729
618
648
687
596
706
736
635
655
624
694
754
824
663
743
803
813
712
762
782
792
852
902
1002
671
771
881
911
931
951
961
971
981
1011
1091
1111
1271
1301
1331
1431
1791