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 Kuo178
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
Dimitris John Bertsimas97
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
Olivier Jean Blanchard82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein82
Richard J. Eden81
Stefan Jähnichen81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Mansur al-Hasan ibn Nuh al-Qumri228834
Abu Sahl 'Isa ibn Yahya al-Masihi228834
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili228834
Abu ʿAli al-Husayn (Avicenna) ibn Sina228833
Bahmanyār ibn al-Marzubān228832
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2288311068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī228830
Sharaf al-Dīn al-Ṭūsī228828
Fakhr al-Dīn Muhammad al-Rēzī228828
Kamāl al-Dīn Ibn Yūnus228827
Qutb al-Dīn Ibrāhīm al-Mīṣrī2288271222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2288261264
Nasir al-Dīn al-Ṭūsī228825
Shams al‐Dīn al‐Bukhārī228822
Gregory Chioniadis2288211296
Manuel Bryennios2288201300
Theodore Metochites2288191315
Gregory Palamas2288161316
Nilos Kabasilas2288151363
Demetrios Kydones228814
Elissaeus Judaeus228789
Georgios Plethon Gemistos2287881380, 1393
Basilios Bessarion2287851436
Giovanni Conversini2287761363
Manuel Chrysoloras228776

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
0239180
132721
212011
36868
44723
53556
62716
72225
81819
91519
101221
111048
12915
13767
14662
15578
16525
17428
18361
19329
20304
22245
21243
23242
24182
25170
26168
28132
27122
29102
3089
3179
3267
3367
3563
3662
3461
3742
3937
3832
4232
4129
4329
4529
4026
4623
4421
5220
5419
4917
5115
5315
4714
5014
4812
5512
5712
5611
5810
609
688
617
647
706
726
595
635
655
695
624
734
754
824
663
713
743
783
803
672
762
792
812
852
902
1002
1302
771
881
911
931
951
961
971
1011
1091
1111
1431
1781