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Footnotes

1. Friberg, J. "Methods and traditions of Babylonian mathematics. Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations", Historia Mathematica, 8, 1981, pp. 277-318.
2. Neugebauer, Otto (1969) [1957]. The Exact Sciences in Antiquity. Acta Historica Scientiarum Naturalium et Medicinalium. Vol. 9 (2 ed.). Dover Publications. pp. 1-191. ISBN 978-0-486-22332-2. PMID 14884919. Chap. IV "Egyptian Mathematics and Astronomy", pp. 71-96.
3. Turnbull (1931). "A Manual of Greek Mathematics". Nature. 128 (3235): 5. Bibcode:1931Natur.128..739T. doi:10.1038/128739a0. S2CID 3994109.
4. Heath, Thomas L. (1963). A Manual of Greek Mathematics, Dover, p. 1: "In the case of mathematics, it is the Greek contribution which it is most essential to know, for it was the Greeks who first made mathematics a science."
5. Joseph, George Gheverghese (1991). The Crest of the Peacock: Non-European Roots of Mathematics. Penguin Books, London, pp. 140-48.
6. Kaplan, Robert (1999). The Nothing That Is: A Natural History of Zero. Allen Lane/The Penguin Press, London.
7. Juschkewitsch, A. P. (1964). Geschichte der Mathematik im Mittelalter. Teubner, Leipzig.
8. Eves, Howard (1990). History of Mathematics, 6th Edition, "After Pappus, Greek mathematics ceased to be a living study, ..." p. 185; "The Athenian school struggled on against growing opposition from Christians until the latter finally, in A.D. 529, obtained a decree from Emperor Justinian that closed the doors of the school forever." p. 186; "The period starting with the fall of the Roman Empire, in the middle of the fifth century, and extending into the eleventh century is known in Europe as the Dark Ages ... . Schooling became almost nonexistent." p. 258.
9. Duncan J. Melville (2003). Third Millennium Chronology, Third Millennium Mathematics. St. Lawrence University.
10. Maor, Eli (1998). Trigonometric Delights. Princeton University Press. p. 20. ISBN 0-691-09541-8.
11. Prestini, Elena (2004). The evolution of applied harmonic analysis: models of the real world. Birkhauser. ISBN 978-0-8176-4125-2., p. 62
12. Boyer, C.B. (1991) [1989], A History of Mathematics (2nd ed.), New York: Wiley , ISBN 978-0-471-54397-8, p. 25.
13. Boyer 1991, "Mesopotamia" p. 26.
14. Boyer 1991, "Mesopotamia" p. 27.
15. Aaboe, Asger (1998). Episodes from the Early History of Mathematics. New York: Random House. pp. 30-31.
16. Boyer 1991, "Mesopotamia" p. 33.
17. Boyer 1991, "Mesopotamia" p. 39.
18. Imhausen, Annette (2006). "Ancient Egyptian Mathematics: New Perspectives on Old Sources". The Mathematical Intelligencer. 28 (1): 19-27. doi:10.1007/bf02986998. S2CID 122060653.
19. Burton, David (2005). The History of Mathematics: An Introduction. McGraw-Hill. ISBN 978-0-07-305189-5.
20. Eglash, Ron (1999). African fractals : modern computing and indigenous design. New Brunswick, N.J.: Rutgers University Press. pp. 89, 141. ISBN 0813526140.
21. Eglash, R. (1995). "Fractal Geometry in African Material Culture". Symmetry: Culture and Science. 6-1: 174-177.
22. Katz V, Imhasen A, Robson E, Dauben JW, Plofker K, Berggren JL (2007). The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. ISBN 978-0-691-11485-9.
23. Panchenko, D. V. (Dmitrii Vadimovich) (1993). "Thales and the Origin of Theoretical Reasoning". Configurations. 1 (3): 387-414. doi:10.1353/con.1993.0024. ISSN 1080-6520.
24. Boyer, Carl B.; Merzbach, Uta C. (2011), A History of Mathematics (3rd ed.), John Wiley & Sons, Inc., ISBN 978-0-471-54397-8, pp. 40-89.
25. Boyer, Carl (1968). A History of Science. p. 45. ISBN 0471543977.
26. Netz, Reviel (2014), Huffman, Carl A. (ed.), "The problem of Pythagorean mathematics", A History of Pythagoreanism, Cambridge: Cambridge University Press, pp. 167-184, ISBN 978-1-107-01439-8, retrieved 2021-05-26
27. Green, P. (1990). Alexander to Actium: The Historical Evolution of the Hellenistic Age (1 ed.). University of California Press. ISBN 978-0-520-08349-3. JSTOR 10.1525/j.ctt130jt89.
28. Luce, J. V. (1988). "Greek Science in its Hellenistic Phase". Hermathena (145): 23-38. ISSN 0018-0750. JSTOR 23040930.
29. Acerbi, F. (2018). Keyser, Paul T; Scarborough, John (eds.). "Hellenistic Mathematics". Oxford Handbook of Science and Medicine in the Classical World. pp. 268-292. doi:10.1093/oxfordhb/9780199734146.013.69. ISBN 978-0-19-973414-6. Retrieved 2021-05-26.
30. Boyer 1991, "Mesopotamia" p. 43.
31. Boyer 1991, "Mesopotamia" p. 86.
32. Boyer 1991, "Mesopotamia" p. 88.
33. Calian, George F. (2014). "One, Two, Three... A Discussion on the Generation of Numbers". New Europe College.
34. Boyer 1991, "Mesopotamia" p. 87.
35. Boyer 1991, "Euclid of Alexandria" p. 119.
36. Boyer 1991, "Euclid of Alexandria" p. 100.
37. Boyer 1991, "Euclid of Alexandria" p. 104.
38. Boyer 1991, "Euclid of Alexandria" p. 102.
39. Kurt Von Fritz (1945). "The Discovery of Incommensurability by Hippasus of Metapontum". The Annals of Mathematics.
40. James R. Choike (1980). "The Pentagram and the Discovery of an Irrational Number". The Two-Year College Mathematics Journal
41. Kline, M. (1990). Mathematical Thought from Ancient to Modern Times, Vol. 1. New York: Oxford University Press (original work published 1972), p. 32.
42. John M. Henshaw (10 September 2014). An Equation for Every Occasion: Fifty-Two Formulas and Why They Matter. JHU Press. p. 68.
43. Powers, J (2020). "Did Archimedes do calculus?" (PDF).
44. O'Connor, J.J.; Robertson, E.F. (February 1996). "A history of calculus". University of St Andrews.
45. Goe, G. (1972). "Archimedes' theory of the lever and Mach's critique". Studies in History and Philosophy of Science Part A. 2 (4): 329-345.
46. Berggren, J. L. (1976). "Spurious Theorems in Archimedes' Equilibrium of Planes: Book I".
47. Boyer 1991, "Euclid of Alexandria" p. 145.
48. Boyer 1991, "Euclid of Alexandria" p. 146.
49. Boyer 1991, "Euclid of Alexandria" p. 152.
50. Boyer 1991, "Euclid of Alexandria" p. 156.
51. Boyer 1991, "Euclid of Alexandria" p. 175.
52. Boyer 1991, "Euclid of Alexandria" p. 162.
53. Boyer 1991, "Euclid of Alexandria" p. 178.
54. Boyer 1991, "Euclid of Alexandria" p. 180.
55. Boyer 1991, "Euclid of Alexandria" p. 181.
56. Boyer 1991, "Euclid of Alexandria" p. 183.
57. Boyer 1991, "Revival and Decline of Greek Mathematics" p.190-94.
58. Boyer 1991, "Revival and Decline of Greek Mathematics" p. 193.
59. Boyer 1991, "Revival and Decline of Greek Mathematics" p. 194.
60. Boyer 1991, p. 215.
61. John Bowman (2000). Columbia Chronologies of Asian History and Culture. Columbia University Press. p. 596. ISBN 978-0-231-50004-3.
62. Boyer 1991, "China and India" p. 210.
63. Boyer 1991, "Greek Trigonometry and Mensuration" p. 168.
64. Boyer 1991, "China and India" p. 208.
65. Bourbaki, Nicolas Elements of the History of Mathematics (1998), p. 46.
66. Weiss, Ittay (20 September 2017). "Nothing matters: How India's invention of zero helped create modern mathematics". The Conversation.
67. Devlin, Hannah (13 September 2017). "Much ado about nothing: ancient Indian text contains earliest zero symbol". The Guardian. ISSN 0261-3077.
68. Qiu, Jane (7 January 2014). "Ancient times table hidden in Chinese bamboo strips". Nature. doi:10.1038/nature.2014.14482. S2CID 130132289. Retrieved 15 September 2014.
69. Katz, Victor J. (2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press, ISBN 978-0-691-11485-9, pp. 194-99.
70. Boyer 1991, "China and India" p. 202.
71. Boyer 1991, "China and India" p. 205.
72. Volkov, Alexei (2009), "Mathematics and Mathematics Education in Traditional Vietnam", in Robson, Eleanor; Stedall, Jacqueline (eds.), The Oxford Handbook of the History of Mathematics, Oxford: Oxford University Press, pp. 153-76, ISBN 978-0-19-921312-2, p.153-56
73. Volkov 2009, pp. 154-55
74. Volkov 2009, pp. 156-57
75. Volkov 2009, p. 155
76. Boyer 1991, "China and India" p. 198.
77. Needham, Joseph; Wang, Ling (1995) [1959], Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth, vol. 3, Cambridge: Cambridge University Press, ISBN 978-0-521-05801-8, pp. 91-92
78. Needham & Wang 1995, p. 94
79. Boyer 1991, "China and India" p. 198.
80. Straffin, Philip D. (1998), "Liu Hui and the First Golden Age of Chinese Mathematics", Mathematics Magazine, 71 (3): 163-81, doi:10.1080/0025570X.1998.11996627, p. 164.
81. Needham & Wang 1995, p. 22
82. Needham & Wang 1995, p. 99-100
83. Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B. (2004), Pi: A Source Book, New York: Springer, ISBN 978-0-387-20571-7, p. 27
84. Boyer 1991, "China and India" p. 202
85. Zill, Dennis G.; Wright, Scott; Wright, Warren S. (2009). Calculus: Early Transcendentals (3 ed.). Jones & Bartlett Learning. p. xxvii. ISBN 978-0-7637-5995-7. Extract of p. 27
86. O'Connor, J.J. & Robertson, E.F. (February 1996). "A history of calculus". University of St Andrews. Retrieved 2007-08-07.
87. Boyer 1991, "The Arabic Hegemony" p. 230
88. Gandz and Saloman (1936), The sources of Khwarizmi's algebra, Osiris i, pp. 263-77
89. Boyer 1991, "The Arabic Hegemony" p. 229
90. Rashed, R.; Armstrong, Angela (1994). The Development of Arabic Mathematics. Springer. pp. 11-12. ISBN 978-0-7923-2565-9. OCLC 29181926.
91. Sesiano, Jacques (2000). "Islamic mathematics". In Selin, Helaine; D'Ambrosio, Ubiratàn (eds.). Mathematics Across Cultures: The History of Non-Western Mathematics. Springer. p. 148. ISBN 1-4020-0260-2.
92. O'Connor, John J.; Robertson, Edmund F., "Abu Kamil", MacTutor History of Mathematics archive, University of St Andrews
93. Knuth, D. E. (1997). The Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd ed.). Addison-Wesley. ISBN 0-201-89684-2, p. 318.
94. Stillwell, J. (1997). Numbers and Geometry. New York: Springer-Verlag. ISBN 0-387-98289-2, p. 31.
95. Marie-Therese d'Alverny, "Translations and Translators", pp. 421-62 in Robert L. Benson and Giles Constable, Renaissance and Renewal in the Twelfth Century, (Cambridge: Harvard University Press, 1982).
96. Singh, Parmanand (1985), "The So-called Fibonacci numbers in ancient and medieval India", Historia Mathematica, 12 (3): 229-44, doi:10.1016/0315-0860(85)90021-7
97. DeBaggis, Henry F.; Miller, Kenneth S. (1966). Foundations of the Calculus. Philadelphia: Saunders. OCLC 527896.
98. Boyer, Carl B. (1959). The History of the Calculus and its Conceptual Development. New York: Dover. OCLC 643872
99. Mazur, Joseph (2014). Enlightening Symbols / A Short History of Mathematical Notation and Its Hidden Powers. Princeton University Press. p. 166. ISBN 978-0-691-17337-5.
100. Frautschi, Steven C.; Olenick, Richard P.; Apostol, Tom M.; Goodstein, David L. (2007). The Mechanical Universe: Mechanics and Heat (Advanced ed.). Cambridge [Cambridgeshire]: Cambridge University Press. ISBN 978-0-521-71590-4. OCLC 227002144.
101. Duhem, Pierre (1891). Lecons sur l'electricite et le magnetisme (in French). Paris Gauthier-Villars. vol. 1, ch. 4, p. 22-23. shows that Lagrange has priority over Gauss. Others after Gauss discovered "Gauss' Law", too.
102. Lagrange, Joseph-Louis (1773). "Sur l'attraction des spheroides elliptiques". Memoires de l'Academie de Berlin (in French): 125.
103. Gauss, Carl Friedrich (1877). Theoria attractionis corporum sphaeroidicorum ellipticorum homogeneorum methodo nova tractata (in Latin). (Gauss, Werke, vol. V, p. 1). Gauss mentions Newton's Principia proposition XCI regarding finding the force exerted by a sphere on a point anywhere along an axis passing through the sphere.
104. Halliday, David; Resnick, Robert (1970). Fundamentals of Physics. John Wiley & Sons. pp. 452-453.
105. LIGHTNER, JAMES E. (1991). "A Brief Look at the History of Probability and Statistics". The Mathematics Teacher. 84 (8): 623-630. doi:10.5951/MT.84.8.0623. ISSN 0025-5769. JSTOR 27967334.
106. Grinstead, Charles Miller; James Laurie Snell. "Introduction". Introduction to Probability. pp. vii.
107. Daston, Lorraine J. (1980). "Probabilistic Expectation and Rationality in Classical Probability Theory". Historia Mathematica. 7 (3): 234-260. doi:10.1016/0315-0860(80)90025-7.
108. ""The origins and legacy of Kolmogorov's Grundbegriffe", by Glenn Shafer and Vladimir Vovk" (PDF). Retrieved 2012-02-12.
109. Bix, Robert A.; D'Souza, Harry J. "Analytic geometry". Encyclopedia Britannica. Retrieved 6 August 2017.
110. Kent, Alexander J.; Vujakovic, Peter (4 October 2017). The Routledge Handbook of Mapping and Cartography. Routledge. ISBN 9781317568216.
111. Burton, David M. (2011), The History of Mathematics/An Introduction (7th ed.), New York: McGraw-Hill, ISBN 978-0-07-338315-6, p. 374.
112. Berlinski, David. A Tour of the Calculus.
113. Axler, Sheldon (2015). Linear Algebra Done Right - Springer. Undergraduate Texts in Mathematics. p. 1. doi:10.1007/978-3-319-11080-6. ISBN 978-3-319-11079-0.
114. Biggs, N.; Lloyd, E.; Wilson, R. (1986), Graph Theory, 1736-1936, Oxford University Press
115. Cauchy, A. L. (1813), "Recherche sur les polyedres - premier memoire", Journal de l'ecole Polytechnique, 9 (Cahier 16): 66-86.
116. L'Huillier, S.-A.-J. (1812-1813), "Memoire sur la polyedrometrie", Annales de Mathematiques, 3: 169-189.
117. Myerson, Roger B. (1991). Game Theory: Analysis of Conflict. Harvard University Press.ISBN 9780674341166.
118. Shapley, Lloyd S.; Shubik, Martin (1 January 1971). "Game Theory in Economics: Chapter1, Introduction, The Use of Models". Archived from the original on 23 April 2023.Retrieved 23 April 2023.
119. von Neumann, John (1928). "Zur Theorie der Gesellschaftsspiele" [On the Theory of Gamesof Strategy]. Mathematische Annalen [Mathematical Annals] (in German). 100 (1): 295-320.doi:10.1007/BF01448847. S2CID 122961988.
120. Mirowski, Philip (1992). "What Were von Neumann and Morgenstern Trying to Accomplish?".In Weintraub, E. Roy (ed.). Toward a History of Game Theory. Durham: Duke UniversityPress. pp. 113-147. ISBN 978-0-8223-1253-6.
121. Leonard, Robert (2010), Von Neumann, Morgenstern, and the Creation of Game Theory, New York: Cambridge University Press, doi:10.1017/CBO9780511778278, ISBN 978-0-521-56266-9
122. Joyce, James (2003), "Bayes' Theorem", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2019 ed.), Metaphysics Research Lab, Stanford University, retrieved 2020-01-17.
123. Normal Distribution, Gale Encyclopedia of Psychology
124. Lyon, A. (2014). Why are Normal Distributions Normal?, The British
125. Journal for the Philosophy of Science.
126. Johnson, Norman L.; Kotz, Samuel; Balakrishnan, Narayanaswamy (1994). Continuous Univariate Distributions, Volume 1. Wiley. ISBN 978-0-471-58495-7.(1994, p. 85)
127. Boyer, Carl B.; Merzbach, Uta C. (1991). A History of Mathematics (2nd ed.). JohnWiley & Sons, Inc. ISBN 978-0-471-54397-8, pp. 252-253.
128. Ifrah, Georges (2001). The Universal History of Computing: From the Abacus to theQuantum Computer. New York, NY: John Wiley & Sons, Inc. ISBN 978-0-471-39671-0., p. 11