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 Kuo175
Egbert Havinga143
Roger Meyer Temam130
Pekka Neittaanmäki129
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Dimitris John Bertsimas92
Ludwig Prandtl90
Bart De Moor89
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle83
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Olivier Jean Blanchard82
David Garvin Moursund82
Stefan Jähnichen81
Sergio Albeverio81
Richard J. Eden81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi220408
Abu ʿAli al-Husayn (Avicenna) ibn Sina220407
Bahmanyār ibn al-Marzubān220406
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2204051068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī220404
Fakhr al-Dīn Muhammad al-Rēzī220402
Sharaf al-Dīn al-Ṭūsī220402
Kamāl al-Dīn Ibn Yūnus220401
Qutb al-Dīn Ibrāhīm al-Mīṣrī2204011222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2204001264
Nasir al-Dīn al-Ṭūsī220399
Shams al‐Dīn al‐Bukhārī220396
Gregory Chioniadis2203951296
Manuel Bryennios2203941300
Theodore Metochites2203931315
Gregory Palamas2203901316
Nilos Kabasilas2203891363
Demetrios Kydones220388
Elissaeus Judaeus220363
Georgios Plethon Gemistos2203621380, 1393
Basilios Bessarion2203591436
Giovanni Conversini2203501363
Manuel Chrysoloras220350
Gasparino da Barzizza220349
Guarino da Verona2203491408

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
0232222
131829
211620
36648
44615
53481
62637
72151
81769
91460
101182
11990
12895
13758
14632
15552
16500
17404
18350
19320
20291
22240
21238
23222
24176
25166
26143
27128
28120
29103
3087
3178
3465
3263
3655
3354
3552
3741
3935
3832
4231
4328
4126
4025
4524
4622
5220
4419
5418
5116
4915
5315
4813
5013
5713
4712
5510
569
608
618
638
688
587
727
596
646
655
695
705
824
623
713
733
753
783
813
672
742
762
772
952
1002
661
791
801
831
851
881
891
901
921
931
1011
1091
1111
1291
1301
1431
1751