Ifrah 2000，第346頁 harvnb模板錯誤: 無指向目標: CITEREFIfrah2000 (幫助): "The measure of the genius of Indian civilisation, to which we owe our modern (number) system, is all the greater in that it was the only one in all history to have achieved this triumph. Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat. But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own."
Bourbaki 1998，第46頁: "...our decimal system, which (by the agency of the Arabs) is derived from Hindu mathematics, where its use is attested already from the first centuries of our era. It must be noted moreover that the conception of zero as a number and not as a simple symbol of separation) and its introduction into calculations, also count amongst the original contribution of the Hindus."
Bourbaki 1998，第49頁: Modern arithmetic was known during medieval times as "Modus Indorum" or method of the Indians. Leonardo of Pisa wrote that compared to method of the Indians all other methods is a mistake. This method of the Indians is none other than our very simple arithmetic of addition, subtraction, multiplication and division. Rules for these four simple procedures was first written down by Brahmagupta during 7th century AD. "On this point, the Hindus are already conscious of the interpretation that negative numbers must have in certain cases (a debt in a commercial problem, for instance). In the following centuries, as there is a diffusion into the West (by intermediary of the Arabs) of the methods and results of Greek and Hindu mathematics, one becomes more used to the handling of these numbers, and one begins to have other "representation" for them which are geometric or dynamic."
"algebra" 2007. Britannica Concise Encyclopedia （頁面存檔備份，存於網際網路檔案館）. Encyclopædia Britannica Online. 16 May 2007. Quote: "A full-fledged decimal, positional system certainly existed in India by the 9th century (AD), yet many of its central ideas had been transmitted well before that time to China and the Islamic world. Indian arithmetic, moreover, developed consistent and correct rules for operating with positive and negative numbers and for treating zero like any other number, even in problematic contexts such as division. Several hundred years passed before European mathematicians fully integrated such ideas into the developing discipline of algebra."
(Pingree 2003，第45頁) Quote: "Geometry, and its branch trigonometry, was the mathematics Indian astronomers used most frequently. Greek mathematicians used the full chord and never imagined the half chord that we use today. Half chord was first used by Aryabhata which made trigonometry much more simple. In fact, the Indian astronomers in the third or fourth century, using a pre-Ptolemaic Greek table of chords, produced tables of sines and versines, from which it was trivial to derive cosines. This new system of trigonometry, produced in India, was transmitted to the Arabs in the late eighth century and by them, in an expanded form, to the Latin West and the Byzantine East in the twelfth century."
(Bourbaki 1998，第126頁): "As for trigonometry, it is disdained by geometers and abandoned to surveyors and astronomers; it is these latter (Aristarchus, Hipparchus, Ptolemy) who establish the fundamental relations between the sides and angles of a right angled triangle (plane or spherical) and draw up the first tables (they consist of tables giving the chord of the arc cut out by an angle on a circle of radius r, in other words the number ; the introduction of the sine, more easily handled, is due to Hindu mathematicians of the Middle Ages)."
Bressoud 2002，第12頁 Quote: "There is no evidence that the Indian work on series was known beyond India, or even outside Kerala, until the nineteenth century. Gold and Pingree assert [4] that by the time these series were rediscovered in Europe, they had, for all practical purposes, been lost to India. The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use."
Plofker 2001，第293頁 Quote: "It is not unusual to encounter in discussions of Indian mathematics such assertions as that 「the concept of differentiation was understood [in India] from the time of Manjula (... in the 10th century)」 [Joseph 1991, 300], or that "we may consider Madhava to have been the founder of mathematical analysis" (Joseph 1991, 293), or that Bhaskara II may claim to be "the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus" (Bag 1979, 294). ... The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)). ... It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit (or Malayalam) and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian "discovery of the principle of the differential calculus" somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. The differential "principle" was not generalised to arbitrary functions—in fact, the explicit notion of an arbitrary function, not to mention that of its
derivative or an algorithm for taking the derivative, is irrelevant here"
Pingree 1992，第562頁 Quote:"One example I can give you relates to the Indian Mādhava's demonstration, in about 1400 A.D., of the infinite power series of trigonometrical functions using geometrical and algebraic arguments. When this was first described in English by Charles Matthew Whish, in the 1830s, it was heralded as the Indians' discovery of the calculus. This claim and Mādhava's achievements were ignored by Western historians, presumably at first because they could not admit that an Indian discovered the calculus, but later because no one read anymore the Transactions of the Royal Asiatic Society, in which Whish's article was published. The matter resurfaced in the 1950s, and now we have the Sanskrit texts properly edited, and we understand the clever way that Mādhava derived the series without the calculus; but many historians still find it impossible to conceive of the problem and its solution in terms of anything other than the calculus and proclaim that the calculus is what Mādhava found. In this case the elegance and brilliance of Mādhava's mathematics are being distorted as they are buried under the current mathematical solution to a problem to which he discovered an alternate and powerful solution."
Katz 1995，第173–174頁 Quote:"How close did Islamic and Indian scholars come to inventing the calculus? Islamic scholars nearly developed a general formula for finding integrals of polynomials by A.D. 1000—and evidently could find such a formula for any polynomial in which they were interested. But, it appears, they were not interested in any polynomial of degree higher than four, at least in any of the material that has come down to us. Indian scholars, on the other hand, were by 1600 able to use ibn al-Haytham's sum formula for arbitrary integral powers in calculating power series for the functions in which they were interested. By the same time, they also knew how to calculate the differentials of these functions. So some of the basic ideas of calculus were known in Egypt and India many centuries before Newton. It does not appear, however, that either Islamic or Indian mathematicians saw the necessity of connecting some of the disparate ideas that we include under the name calculus. They were apparently only interested in specific cases in which these ideas were needed. ... There is no danger, therefore, that we will have to rewrite the history texts to remove the statement that Newton and Leibniz invented calculus. They were certainly the ones who were able to combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between them, and turn the calculus into the great problem-solving tool we have today."
Bisht, R. S., Excavations at Banawali: 1974–77, Possehl, Gregory L. (編), Harappan Civilisation: A Contemporary Perspective, New Delhi: Oxford and IBH Publishing Co.: 113–124, 1982
Bressoud, David, Was Calculus Invented in India?, The College Mathematics Journal (Math. Assoc. Amer.), 2002, 33 (1): 2–13, JSTOR 1558972, doi:10.2307/1558972.
Bronkhorst, Johannes, Panini and Euclid: Reflections on Indian Geometry, Journal of Indian Philosophy (Springer Netherlands), 2001, 29 (1–2): 43–80, doi:10.1023/A:1017506118885.
Burnett, Charles, The Semantics of Indian Numerals in Arabic, Greek and Latin, Journal of Indian Philosophy (Springer-Netherlands), 2006, 34 (1–2): 15–30, doi:10.1007/s10781-005-8153-z.
Burton, David M., The History of Mathematics: An Introduction, The McGraw-Hill Companies, Inc.: 193–220, 1997.
Cooke, Roger, The History of Mathematics: A Brief Course, New York: Wiley-Interscience, 632 pages, 2005, ISBN 978-0-471-44459-6.
Datta, Bibhutibhusan, Early Literary Evidence of the Use of the Zero in India, The American Mathematical Monthly, December 1931, 38 (10): 566–572, JSTOR 2301384, doi:10.2307/2301384.
Datta, Bibhutibhusan; Singh, Avadesh Narayan, History of Hindu Mathematics : A source book, Bombay: Asia Publishing House, 1962.
De Young, Gregg, Euclidean Geometry in the Mathematical Tradition of Islamic India, Historia Mathematica, 1995, 22 (2): 138–153, doi:10.1006/hmat.1995.1014.
Encyclopædia Britannica (Kim Plofker), mathematics, South Asian, Encyclopædia Britannica Online, 2007: 1–12 [18 May 2007].
Fowler, David, Binomial Coefficient Function, The American Mathematical Monthly, 1996, 103 (1): 1–17, JSTOR 2975209, doi:10.2307/2975209.
Hayashi, Takao, The Bakhshali Manuscript, An ancient Indian mathematical treatise, Groningen: Egbert Forsten, 596 pages, 1995, ISBN 978-90-6980-087-5.
Hayashi, Takao, Aryabhata's Rule and Table of Sine-Differences, Historia Mathematica, 1997, 24 (4): 396–406, doi:10.1006/hmat.1997.2160.
Hayashi, Takao, Indian Mathematics, Grattan-Guinness, Ivor (編), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, 1, pp. 118–130, Baltimore, MD: The Johns Hopkins University Press, 976 pages, 2003, ISBN 978-0-8018-7396-6.
Hayashi, Takao, Indian Mathematics, Flood, Gavin (編), The Blackwell Companion to Hinduism, Oxford: Basil Blackwell, 616 pages, pp. 360–375: 360–375, 2005, ISBN 978-1-4051-3251-0.
Katz, Victor J., Ideas of Calculus in Islam and India, Mathematics Magazine (Math. Assoc. Amer.), 1995, 68 (3): 163–174, JSTOR 2691411, doi:10.2307/2691411.
Katz, Victor J. (編), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press, 685 pages, pp 385–514, 2007, ISBN 978-0-691-11485-9.
Keller, Agathe, Making diagrams speak, in Bhāskara I's commentary on the Aryabhaṭīya, Historia Mathematica, 2005, 32 (3): 275–302, doi:10.1016/j.hm.2004.09.001.
Kichenassamy, Satynad, Baudhāyana's rule for the quadrature of the circle, Historia Mathematica, 2006, 33 (2): 149–183, doi:10.1016/j.hm.2005.05.001.
Pingree, David, On the Greek Origin of the Indian Planetary Model Employing a Double Epicycle, Journal of Historical Astronomy, 1971, 2 (1): 80–85, doi:10.1177/002182867100200202.
Pingree, David, The Mesopotamian Origin of Early Indian Mathematical Astronomy, Journal of Historical Astronomy, 1973, 4 (1): 1–12, doi:10.1177/002182867300400102.
Pingree, David; Staal, Frits, Reviewed Work(s): The Fidelity of Oral Tradition and the Origins of Science by Frits Staal, Journal of the American Oriental Society, 1988, 108 (4): 637–638, JSTOR 603154, doi:10.2307/603154.
Plofker, Kim, An Example of the Secant Method of Iterative Approximation in a Fifteenth-Century Sanskrit Text, Historia Mathematica, 1996, 23 (3): 246–256, doi:10.1006/hmat.1996.0026.
Plofker, Kim, The "Error" in the Indian "Taylor Series Approximation" to the Sine, Historia Mathematica, 2001, 28 (4): 283–295, doi:10.1006/hmat.2001.2331.
Plofker, K., Mathematics of India, Katz, Victor J. (編), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press, 685 pages, pp 385–514: 385–514, 2007, ISBN 978-0-691-11485-9.
Plofker, Kim, Mathematics in India: 500 BCE–1800 CE, Princeton, NJ: Princeton University Press. Pp. 384., 2009, ISBN 978-0-691-12067-6.
Price, John F., Applied geometry of the Sulba Sutras(PDF), Gorini, Catherine A. (編), Geometry at Work: Papers in Applied Geometry, 53, pp. 46–58, Washington DC: Mathematical Association of America Notes, 236 pages: 46–58, 2000 [2019-08-11], ISBN 978-0-88385-164-7, （原始內容(PDF)存檔於2007-09-27）.
Roy, Ranjan, Discovery of the Series Formula for by Leibniz, Gregory, and Nilakantha, Mathematics Magazine (Math. Assoc. Amer.), 1990, 63 (5): 291–306, JSTOR 2690896, doi:10.2307/2690896.
Staal, Frits, The Fidelity of Oral Tradition and the Origins of Science, Mededelingen der Koninklijke Nederlandse Akademie von Wetenschappen, Afd. Letterkunde, NS 49, 8. Amsterdam: North Holland Publishing Company, 40 pages, 1986.
Staal, Frits, The Sanskrit of science, Journal of Indian Philosophy (Springer Netherlands), 1995, 23 (1): 73–127, doi:10.1007/BF01062067.
Staal, Frits, Greek and Vedic Geometry, Journal of Indian Philosophy, 1999, 27 (1–2): 105–127, doi:10.1023/A:1004364417713.
Staal, Frits, Squares and oblongs in the Veda, Journal of Indian Philosophy (Springer Netherlands), 2001, 29 (1–2): 256–272, doi:10.1023/A:1017527129520.
Staal, Frits, Artificial Languages Across Sciences and Civilisations, Journal of Indian Philosophy (Springer Netherlands), 2006, 34 (1): 89–141, doi:10.1007/s10781-005-8189-0.
Thibaut, George, Mathematics in the Making in Ancient India: reprints of 'On the Sulvasutras' and 'Baudhyayana Sulva-sutra', Calcutta and Delhi: K. P. Bagchi and Company (orig. Journal of Asiatic Society of Bengal), 133 pages, 1984 [1875].
van der Waerden, B. L., Geometry and Algebra in Ancient Civilisations, Berlin and New York: Springer, 223 pages, 1983, ISBN 978-0-387-12159-8
van der Waerden, B. L., On the Romaka-Siddhānta, Archive for History of Exact Sciences, 1988, 38 (1): 1–11, doi:10.1007/BF00329976
van der Waerden, B. L., Reconstruction of a Greek table of chords, Archive for History of Exact Sciences, 1988, 38 (1): 23–38, doi:10.1007/BF00329978
Van Nooten, B., Binary numbers in Indian antiquity, Journal of Indian Philosophy (Springer Netherlands), 1993, 21 (1): 31–50, doi:10.1007/BF01092744
Whish, Charles, On the Hindú Quadrature of the Circle, and the infinite Series of the proportion of the circumference to the diameter exhibited in the four S'ástras, the Tantra Sangraham, Yucti Bháshá, Carana Padhati, and Sadratnamála, Transactions of the Royal Asiatic Society of Great Britain and Ireland, 1835, 3 (3): 509–523, JSTOR 25581775, doi:10.1017/S0950473700001221
Yano, Michio, Oral and Written Transmission of the Exact Sciences in Sanskrit, Journal of Indian Philosophy (Springer Netherlands), 2006, 34 (1–2): 143–160, doi:10.1007/s10781-005-8175-6
梵語文獻
Keller, Agathe, Expounding the Mathematical Seed. Vol. 1: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya, Basel, Boston, and Berlin: Birkhäuser Verlag, 172 pages, 2006, ISBN 978-3-7643-7291-0.
Keller, Agathe, Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya, Basel, Boston, and Berlin: Birkhäuser Verlag, 206 pages, 2006, ISBN 978-3-7643-7292-7.
Neugebauer, Otto; Pingree, David (編), The Pañcasiddhāntikā of Varāhamihira, New edition with translation and commentary, (2 Vols.), Copenhagen, 1970.
Pingree, David (編), The Yavanajātaka of Sphujidhvaja, edited, translated and commented by D. Pingree, Cambridge, MA: Harvard Oriental Series 48 (2 vols.), 1978.
Sarma, K. V. (編), Āryabhaṭīya of Āryabhaṭa with the commentary of Sūryadeva Yajvan, critically edited with Introduction and Appendices, New Delhi: Indian National Science Academy, 1976.
Sen, S. N.; Bag, A. K. (編), The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava, with Text, English Translation and Commentary, New Delhi: Indian National Science Academy, 1983.
Shukla, K. S. (編), Āryabhaṭīya of Āryabhaṭa with the commentary of Bhāskara I and Someśvara, critically edited with Introduction, English Translation, Notes, Comments and Indexes, New Delhi: Indian National Science Academy, 1976.
Shukla, K. S. (編), Āryabhaṭīya of Āryabhaṭa, critically edited with Introduction, English Translation, Notes, Comments and Indexes, in collaboration with K.V. Sarma, New Delhi: Indian National Science Academy, 1988.
InSIGHT 2009（頁面存檔備份，存於網際網路檔案館）, a workshop on traditional Indian sciences for school children conducted by the Computer Science department of Anna University, Chennai, India.
on a circle of radius r, in other words the number 
; the introduction of the sine, more easily handled, is due to Hindu mathematicians of the Middle Ages)."
by Leibniz, Gregory, and Nilakantha, Mathematics Magazine (Math. Assoc. Amer.), 1990, 63 (5): 291–306, JSTOR 2690896, doi:10.2307/2690896.
