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
Rutger Anthony van Santen90
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle85
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Olivier Jean Blanchard82
David Garvin Moursund82

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi233536
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili233536
Abu Mansur al-Hasan ibn Nuh al-Qumri233536
Abu ʿAli al-Husayn (Avicenna) ibn Sina233535
Bahmanyār ibn al-Marzubān233534
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2335331068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī233532
Sharaf al-Dīn al-Ṭūsī233530
Fakhr al-Dīn Muhammad al-Rēzī233530
Qutb al-Dīn Ibrāhīm al-Mīṣrī2335291222
Kamāl al-Dīn Ibn Yūnus233529
Athīr al-Dīn al-Mufaḍḍal al-Abharī2335281264
Nasir al-Dīn al-Ṭūsī233527
Shams al‐Dīn al‐Bukhārī233524
Gregory Chioniadis2335231296
Manuel Bryennios2335221300
Theodore Metochites2335211315
Gregory Palamas2335181316
Nilos Kabasilas2335171363
Demetrios Kydones233516
Elissaeus Judaeus233491
Georgios Plethon Gemistos2334901380, 1393
Basilios Bessarion2334871436
Manuel Chrysoloras233478
Giovanni Conversini2334781363

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
0243431
133165
212189
36982
44760
53624
62763
72230
81869
91539
101252
111048
12946
13803
14662
15587
16525
17457
18367
19327
20325
22253
23241
21238
24187
25179
26175
27129
28127
29106
3097
3178
3370
3268
3668
3563
3462
3744
3837
3937
4234
4331
4028
4128
4528
4625
5221
4420
4918
5416
5015
5115
4714
5314
4813
5513
5713
5612
6010
589
618
648
688
728
707
596
736
635
655
624
694
754
824
663
743
803
813
762
782
792
852
902
1002
671
711
771
881
911
931
951
961
971
981
1011
1091
1111
1271
1301
1331
1431
1791