Dear Matthew, 

Alsdorf’s article is indeed on combinatorics in the metrical literature, not in mathematics…
as for combinatorics in music there is notably in French

Patte, François. 2012. “Rythmes et Algorithmes.” In Astronomy and Mathematics in Ancient India - Astronomie et Mathématiques de l’Inde Ancienne Actes de La Journée d’études Organisée Le 24 Avril 2009 à l’Université Libre de Bruxelles, edited by Jean-Michel Delire, 159–174. Peeters.

and recently
Petrocchi Alessandra. 2018. “Music Theory, Mathematics, and Patterns of Innovation in the Saṅgītaratnākara.” Asiatische Studien - Études Asiatiques 72 (2): 395. https://doi.org/10.1515/asia-2016-0003.

best

Agathe

From: Matthew Kapstein <mkapstei@uchicago.edu>
Reply: Matthew Kapstein <mkapstei@uchicago.edu>
Date: 9 April 2019 at 15:25:13
To: Agathe Keller <kelleragathe600@gmail.com>, Paolo Eugenio Rosati <paoloe.rosati@gmail.com>, Indology <indology@list.indology.info>
Subject:  Re: [INDOLOGY] Sciences and Tantra

Thank you Agathe,


I wasn't intending to refer to Indian mathematics broadly, but just to the application outside of mathematics per se. Besides poetic metrics and "tantric geometry", I imagine that the musicological literature offers some other examples, but i do not know them off hand.


best,

Matthew


Matthew Kapstein
Directeur d'études,
Ecole Pratique des Hautes Etudes

Numata Visiting Professor of Buddhist Studies,
The University of Chicago
From: Agathe Keller <kelleragathe600@gmail.com>
Sent: Tuesday, April 9, 2019 8:19:23 AM
To: Paolo Eugenio Rosati; Matthew Kapstein; Indology
Subject: Re: [INDOLOGY] Sciences and Tantra
 
Dear Matthew,

On the topic of combinatorics (including Pascal triangle), Piṅgala and his commentators  there is a classical article by Ludwig Alsdorf

 Die Pratyayas. Ein Beitrag zur indischen Mathematik". Zeitschrift fur Indologie und Iranistik, 9 (1933), pp. 97-157; reprinted in: Albrecht Wezler (ed.), Ludwig Alsdorf: Kleine Schriften, Wiesbaden, 1974, pp. 600-660.

This paper was translated into English by  Sarma, S. R. 1991. “The Pratyayas: Indian Contributions to Combinatorics.” Indian Journal of History of Science 26: 17–61. 


although much still needs to be investigated, there are quite a number of publications on this topic  actually…

best

Agathe

From: Matthew Kapstein via INDOLOGY <indology@list.indology.info>
Reply: Matthew Kapstein <mkapstei@uchicago.edu>
Date: 9 April 2019 at 14:49:06
To: Paolo Eugenio Rosati <paoloe.rosati@gmail.com>, Indology <indology@list.indology.info>
Subject:  Re: [INDOLOGY] Sciences and Tantra

Dear Paolo,


Although it is not quite on tantra, there is a highly interesting article in modern Sanskrit on the relationship between Sanskrit analysis of poetic metre and Pascal's triangle. I do not have the full reference available in my present location, but it may be found in the introduction to the late Michael Hahn's edition of the ChandoratnAkara, which may be available on his academia page, if that is still accessible.



In Buddhist tantra, quite a lot has been written on the mathematics of the KAlacakratantra. The late Edward Henning's webpage kalacakra.org has some useful material on this, as does Henning's book, KAlacakra and the Tibetan Calendar.


There is also quite a lot on this in German, by Dieter Schuh, but exclusively concerned with the Tibetan legacy of the Indian sources and not with the Indian materials themselves.


best,

Matthew


Matthew Kapstein
Directeur d'études,
Ecole Pratique des Hautes Etudes

Numata Visiting Professor of Buddhist Studies,
The University of Chicago
From: INDOLOGY <indology-bounces@list.indology.info> on behalf of Paolo Eugenio Rosati via INDOLOGY <indology@list.indology.info>
Sent: Tuesday, April 9, 2019 4:47:07 AM
To: Indology
Subject: [INDOLOGY] Sciences and Tantra
 
Dear indologists,

Can anyone points me out any study on Tantra in connection to sciences, mathematics and more specifically geometry?

With the best wishes,
Paolo

--
Paolo E. Rosati
PhD in Asian and African Studies
(South Asia Section)
Italian Institute of Oriental Studies
'Sapienza' University of Rome
 

Skype: paoloe.rosati
Mobile: (+39) 338 73 83 472


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Agathe Keller

tel : +33 1 57 27 68 87

Université Paris 7 Laboratoire SPHERE UMR 7219 
Bâtiment Condorcet
Parcels: 3è étage bureau 387A
Office: 6th floor 688 A
 10 rue A.Domont et L.Duquet
75013 PARIS

Postal Address :
Université Paris 7 - CNRS
Laboratoire SPHERE UMR 7219
Equipe Sphere
Case 7093
5 rue Thomas Mann
75205 PARIS CEDEX 13
France