“There is only one other survey, Datta and Singh’s 1938 History of Hindu Mathematics, recently reprinted but very hard to obtain in the West (I found a copy in a small specialized bookstore in Chennai). They describe in some detail the Indian work in arithmetic and algebra and, supplemented by the equally hard to find Geometry in Ancient and Medieval India by Sarasvati Amma (1979), one can get an overview of most topics.”

— David Mumford

[David Mumford, Book Review, Notices of the AMS, March 2010, 57, 3, http://www.ams.org/notices/201003/rtx100300385p.pdf]

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David Mumford 5

American mathematician 1937

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 59

“The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematics. Ideas that seem remarkably simple once explained were thousands of years in the making.”

Morris Kline (1908–1992) American mathematician

Morris Kline, p.22.
Mathematics for the Nonmathematician (1967)

“You see, some mathematicians have clear and far-ranging. "programs". For instance, Grothendieck had such a program for algebraic geometry; now Langlands has one for representation theory, in relation to modular forms and arithmetic. I never had such a program, not even a small size one.”

Jean-Pierre Serre (1926) French mathematician

An Interview with Jean-Pierre Serre - Singapore Mathematical Society https://sms.math.nus.edu.sg/smsmedley/Vol-13-1/An%20interview%20with%20Jean-Pierre%20Serre(CT%20Chong%20&%20YK%20Leong).pdf

“An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry.”

Joseph Louis Lagrange (1736–1813) Italian mathematician and mathematical physicist

Dans Les Leçons Élémentaires sur les Mathématiques (1795) Leçon cinquiéme, Tr. McCormack, cited in Moritz, Memorabilia mathematica or, The philomath's quotation-book (1914) Ch. 15 Arithmetic, p. 261. https://archive.org/stream/memorabiliamathe00moriiala#page/260/mode/2up

“In the winter of 2008, Jenifer and I visited Chennai Mathematical Institute. This remarkable Institute is the creation of Seshadri. It is a unique blend of an American style liberal arts college with traditional Indian guru one-on-one teaching, adding physics, computer science, history and music to its maths curriculum. Only in India could an intellectual with no business or management experience, who spends all his spare time singing classical south Indian music, have been the catalyst for such a unique educational experiment.”

David Mumford (1937) American mathematician

[David Mumford, Passages to India, Mathematics Intelligencer, 2010, Hyderabad edition, 51-55, http://www.dam.brown.edu/people/mumford/beyond/papers/2010c--PassagesIndia-journal.pdf]

“Contrary to what is sometimes claimed in the press, there are many fine historians in India. From my own generation of scholars, I can strongly recommend — to student and lay reader alike — the work of Upinder Singh on ancient India, of Nayanjot Lahiri on the history of archaeology, of Vijaya Ramaswamy on the bhakti movement, of Sanjay Subrahmanyam on the early history of European expansion, of Chetan Singh on the decline of the Mughal State, of Sumit Guha on the social history of Western India, of Seema Alavi on the social history of medicine, of Niraja Gopal Jayal on the history of citizenship, of Tirthankar Roy on the economic consequences of colonialism, of Mahesh Rangarajan on the history of forests and wildlife, and of A. R. Venkatachalapathy on South Indian cultural history.”

Ramachandra Guha (1958) historian and writer from India

[Guha, Ramachandra, Captive ideologues, http://ramachandraguha.in/archives/history-beyond-marxism-and-hindutva-the-telegraph.html, The Telegraph, July 26, 2014]