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
Pekka Neittaanmäki130
Roger Meyer Temam130
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Erol Gelenbe96
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Dimitris John Bertsimas92
Ludwig Prandtl90
Bart De Moor89
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle83
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
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-Masihi221960
Abu ʿAli al-Husayn (Avicenna) ibn Sina221959
Bahmanyār ibn al-Marzubān221958
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2219571068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī221956
Sharaf al-Dīn al-Ṭūsī221954
Fakhr al-Dīn Muhammad al-Rēzī221954
Kamāl al-Dīn Ibn Yūnus221953
Qutb al-Dīn Ibrāhīm al-Mīṣrī2219531222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2219521264
Nasir al-Dīn al-Ṭūsī221951
Shams al‐Dīn al‐Bukhārī221948
Gregory Chioniadis2219471296
Manuel Bryennios2219461300
Theodore Metochites2219451315
Gregory Palamas2219421316
Nilos Kabasilas2219411363
Demetrios Kydones221940
Elissaeus Judaeus221915
Georgios Plethon Gemistos2219141380, 1393
Basilios Bessarion2219111436
Manuel Chrysoloras221902
Giovanni Conversini2219021363
Gasparino da Barzizza221901
Guarino da Verona2219011408

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
0233556
131947
211698
36692
44643
53504
62647
72160
81776
91477
101186
111003
12893
13759
14639
15553
16507
17406
18352
19324
20295
22247
21233
23224
24176
25169
26145
27129
28120
29100
3089
3179
3465
3263
3357
3657
3552
3742
3834
3934
4232
4328
4026
4126
4526
4621
5221
4418
5418
4916
5115
5315
4714
5013
4812
5712
5510
569
609
689
588
618
638
646
696
726
595
654
704
734
824
623
713
743
753
783
813
662
762
772
1002
1302
671
791
801
831
851
881
891
901
921
931
951
961
1011
1091
1111
1431
1751