Computing: Birth, Growth, Exaflops Computation and Beyond

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Decision Making in Social Sciences: Between Traditions and Innovations

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 247))

Abstract

Computing is a generic term implying activities such as design, development, and construction of hardware, firmware, and software systems using a computer or benefitting from it or creating it. Besides, structuring, processing, and managing different types of information, performing scientific/engineering work/research on and with the systems, making the systems behave intelligently, and creating and using communications and entertainment media are some of the applied aspects of computing. Computing comprises the subject areas such as computer science, computer/computational mathematics, and artificial intelligence. Mathematics—traditional/usual, computer/computational, and natural—did exist for millennia. These mathematics are connected intimately with computing explicitly or implicitly. We attempt to record a brief history of birth, growth, exponentially increasing computational power of over quintillion flops related to computing, specifically related to the computer mathematics/science, and beyond. In the process we stress the real-world importance and gigantic differences of computer mathematics over the usual mathematics as well as natural mathematics.

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References

  • Abramowitz, M., Stegun, I.A. (ed.): Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Dover Books on Mathematics (1965)

    Google Scholar 

  • Agarwal, R.P., Sen, S.K.: Creators of Mathematical and Computational Sciences. Springer, New York (2014)

    MATH  Google Scholar 

  • Agarwal, R.P., Agarwal, H., Sen, S.K.: Birth, growth and computation of Pi to ten trillion digits. Adv. Differ. Equ. 2013(2013), 100 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Aitken, A.C.: Studies in practical mathematics, Part II: the evaluation of the latent roots and latent vectors of a matrix. Pro. Roy. Soc. (Edinburgh) 57, 269 (1937)

    Google Scholar 

  • Al-Daffa, A.A.: The Muslim Contribution to Mathematics. Humanities Press, Atlantic Highlands (1977)

    Google Scholar 

  • Al-Daffa, A.A., Stroyls, J.J.: Studies in the Exact Sciences in Medieval Islam. Wiley, New York (1984)

    Google Scholar 

  • Allen, R.E.: Greek Philosophy: Thales to Aristotle. The Free Press, New York (1966)

    Google Scholar 

  • Allman, G.J.: Greek Geometry from Thales to Euclid. Arno Press, New York (1976)

    MATH  Google Scholar 

  • Andrade, E.N.C.: Sir Issac Newton, His Life and Work. Doubleday & Co., New York (1954)

    Google Scholar 

  • Anglin, W.S.: Mathematics: A Concise History and Philosophy. Springer, New York (1994)

    Book  MATH  Google Scholar 

  • Anglin, W.S.: The Queen of Mathematics. Kluwer, Dordrecht (1995)

    Book  MATH  Google Scholar 

  • Anthony, H.D.: Sir Isaac Newton. Abelard-Schuman, New York (1960)

    Google Scholar 

  • Apostle, H.G.: Aristotle’s Philosophy of Mathematics. The University of Chicago Press, Chicago (1952)

    MATH  Google Scholar 

  • Archibald, R.C.: Outline of the history of mathematics. Amer. Math. Monthly 56 (1949)

    Google Scholar 

  • Artmann, B.: Euclid—The Creation of Mathematics. Springer, New York (1999)

    Chapter  MATH  Google Scholar 

  • Bag, A.K.: Mathematics in Ancient and Medieval India. Chaukhambha Orientalia, Varanasi (1979)

    MATH  Google Scholar 

  • Ball, W.W.R.: A short Account of the History of Mathematics. Dover, New York (1960)

    MATH  Google Scholar 

  • Barker, S.F.: Philosophy of Mathematics. Prentice-Hall, Englewood Cliffs (1964)

    MATH  Google Scholar 

  • Baron, M.E.: The Origin of Infinitesimal Calculus. Dover, New York (1993)

    Google Scholar 

  • Barrow, J.D.: Pi in the Sky: Counting, Thinking, and Being. The Clarendon Press, New York (1992)

    MATH  Google Scholar 

  • Baumgardt, C.: Johannes Kepler: Life and Letters. Victor Gollancz, London (1952)

    MATH  Google Scholar 

  • Beckman, P.: A History of π. St. Martin’s Griffn, New York (1976)

    Google Scholar 

  • Beiler, A.: Recreations in the Theory of Numbers. Dover, New York (1964)

    MATH  Google Scholar 

  • Belhoste, B.: Augustin–Louis Cauchy: A Biography (trans. by F. Ragland). Springer, New York (1990)

    Google Scholar 

  • Bell, E.T.: Men of Mathematics. Touchstone Books, New York (1986)

    MATH  Google Scholar 

  • Bell, E.T.: The Development of Mathematics, 2nd edn. Dover, New York (1992)

    MATH  Google Scholar 

  • Benson, D.C.: The Moment of Proof: Mathematical Epiphanies. Oxford University Press, New York (1999)

    MATH  Google Scholar 

  • Berggren, J.L.: Episodes in the Mathematics of Medieval Islam. Springer, New York (1986)

    MATH  Google Scholar 

  • Berlinski, D.: A Tour of Calculus. Vintage, New York (1995)

    Google Scholar 

  • Berndt, B.E.: Notebooks of S. Ramanujan. Springer, New York (1985)

    Book  Google Scholar 

  • Berndt, B.C., Rankin, R.A.: Ramanujan Letters and Commentary. Affiliated East West Press, New Delhi (1997)

    MATH  Google Scholar 

  • Beth, E.W.: The Foundations of Mathematics. North-Holland, Amsterdam (1959)

    MATH  Google Scholar 

  • Beth, E.W.: Mathematical Thought: An Introduction to the Philosophy of Mathematics. D. Reidel, Dordrecht (1965)

    Book  MATH  Google Scholar 

  • Bhaskar, T.G., Kovach, D., Lakshmikantham, V.: The hybrid set theory. Nonlinear Anal. Hybrid Syst. 1, 414–416 (2007)

    Article  MATH  Google Scholar 

  • Bishop, M.G.: Pascal, The Life of Genius. Reynal & Hitchcock, New York (1936)

    MATH  Google Scholar 

  • Black, M.: The Nature of Mathematics: A Critical Survey. Routledge & Kegan Paul, London (1965)

    MATH  Google Scholar 

  • Blatner, D.: The Joy of Pi. Walker Publishing Co., New York (1997)

    Google Scholar 

  • Bose, D.M., Sen, S.N., Subbarayappa, B.V.: A Concise History of Science in India. Indian National Science Academy, New Delhi (1971)

    Google Scholar 

  • Boyer, C.: The History of the Calculus and its Conceptual Development. Dover, New York (1959)

    MATH  Google Scholar 

  • Boyer, C.: A History of Mathematics, 2nd edn. Wiley, New York (1991)

    Google Scholar 

  • Brewer, J.W., Smith, M.: Emmy Noether, A Tribute to Her Life and Work. Marcel Dekker, Inc., New York (1981)

    Google Scholar 

  • Brody, D.E., Brody, A.R.: The Science Class You Wish You Had: The Seven Greatest Scientific Discoveries in History and the People Who Made Them. Berkeley Publishing Group, New York (1997)

    Google Scholar 

  • Brumbaugh, R.S.: Plato’s Mathematical Imagination. Indiana University Press, Bloomington (1954)

    Google Scholar 

  • Bunt, L.N.H., Jones, P.S., Bedient, J.D.: The Historical Roots of Elementary Mathematics. Prentice-Hall, Englewood Cliffs (1976)

    Google Scholar 

  • Burton, D.M.: The History of Mathematics: An Introduction, 4th ed. McGraw-Hill, New York (1999)

    Google Scholar 

  • Cajori, F.: The history of the notations of calculus. Ann. Math. 25, 1–46 (1923)

    Article  MathSciNet  MATH  Google Scholar 

  • Cajori, F.: Leibniz, the master builder of notations. Isis 7, 412–429 (1925)

    Article  MATH  Google Scholar 

  • Cajori, F.: A History of Mathematics, 4th edn. Chelsea Publishing, New York (1985)

    MATH  Google Scholar 

  • Calinger, R.: Gottfried Wilhelm Leibniz. Rensselaer Polytechnic Institute, Troy, N.Y. (1976)

    Google Scholar 

  • Calinger, R. (ed.): Classics of Mathematics. Prentice-Hall, Englewood Cliffs (1995)

    Google Scholar 

  • Calinger, R.: A Contextual History of Mathematics: To Euler. Prentice Hall, Upper Saddle River (1999)

    MATH  Google Scholar 

  • Cantor, G.: Contributions to the Founding of the Theory of Transfinite Numbers (trans. by P.E.B. Jourdain). Dover, New York (1952)

    Google Scholar 

  • Cantor, M.: Vorlesungen uber¨ Geschichte der Mathematik, Leipzig (1907)

    Google Scholar 

  • Cardano, G.: The Book of My Life (trans. by J. Stoner). Dover, New York (1962)

    Google Scholar 

  • Cardano, G.: The Great Art (trans. by T.R. Witmer). MIT Press, Cambridge (1968)

    Google Scholar 

  • Chandrasekhar, S.: Newton’s Principia for the Common Reader. Oxford University Press, Oxford (1995)

    MATH  Google Scholar 

  • Chattopadhyaya, D.: History of Science and Technology in Ancient India: The Beginnings. Firma KLM PVT., Calcutta (1986)

    Google Scholar 

  • Clagett, M.: Greek Science in Antiquity. Collier, New York (1963)

    MATH  Google Scholar 

  • Clark, W.E. (ed.): The Aryabhatia of Aryabhata. The University of Chicago Press, Chicago (1930)

    Google Scholar 

  • Clawson, C.C.: Mathematical Mysteries: The Beauty and Magic of Numbers. Plenum Press, New York (2000)

    MATH  Google Scholar 

  • Closs, M.P. (ed.): Native American Mathematics. University of Texas Press, Austin (1986)

    MATH  Google Scholar 

  • Cohen, I.B.: Sir Issac Newton’s Papers and Letters on Natural Philosophy. Harvard University Press, Cambridge (1958)

    Google Scholar 

  • Cole, J.R.: Pascal: The Man and His Two Loves. New York University Press, New York (1995)

    Google Scholar 

  • Conant, L.: The Number Concept. Its origin and Development. Macmillan, New York (1923)

    MATH  Google Scholar 

  • Cooke, R.: The Mathematics of Sonya Kovalevskaya. Springer, New York (1984)

    Book  MATH  Google Scholar 

  • Coolidge, J.L.: The Mathematics of Great Amateurs. Dover, New York (1963)

    MATH  Google Scholar 

  • Copernicus, N.: On the Revolutions of Heavenly Spheres, Great Mind Series. Prometheus Books, New York (1995)

    MATH  Google Scholar 

  • Courant, R., Robbin, H., Stewart, I.: What is Mathematics?. Oxford University Press, New York (1996)

    Google Scholar 

  • Crowther, J.G.: Six Great Scientists. Barnes & Noble, New York (1995)

    Google Scholar 

  • Cullen, C.: Astronomy and Mathematics in Ancient China: The Zhou Bi Suan**g. Cambridge University Press, Cambridge (1996)

    Book  MATH  Google Scholar 

  • Dennis, J.B., Fosseen, J.P., Linderman, J.P.: Data flow schemes. In: Symposium on Theoretical Programming, Novosibirsk, pp. 187–216 (1972)

    Google Scholar 

  • Dunham, W.: Euler: The Master of Us All. Mathematical Association of America (1999)

    Google Scholar 

  • Dunham, W.: The genius of Euler: reflections on his life and work. Mathematical Association of America (2007)

    Google Scholar 

  • Egervary, E.: On combinatorial properties of matrices (trans. by H.W. Kuhn). Office of Maval Research Logistic Project Report, Department of Mathematics, Princeton University, Princeton (1931)

    Google Scholar 

  • Farkas, J.: Uber die theorie der einfachen ungleichungen. Jr.und angew. Math. 124(1–24), 1901–1902

    Google Scholar 

  • Feynman, R.P.: Simulating physics with computers (PDF). Int. J. Theor. Phys. 21(6), 467–488 (1982)

    Article  Google Scholar 

  • Filon, L.N.G.: On a quadrature formula for trigonometric integrals. Proc. Roy. Soc. (Edinburgh) 49, 38–47 (1928)

    Article  MATH  Google Scholar 

  • Finilla, A.B., Gomez, M.A., Sebenik, C., Doll, J.D.: Quantum annealing: a new method for minimizing multidimensional functions. Chem. Phys. Lett. 219, 343 (1994)

    Article  Google Scholar 

  • Forsythe, G.E.: Escalator method for latent roots. Q. J. Mech. 5, 178–190 (1952)

    Article  MathSciNet  Google Scholar 

  • Halmos, P.R.: Measure Theory. D. Van Nostrand, New York (1950)

    Book  MATH  Google Scholar 

  • Hildebrand, R.B.: Introduction to Numerical Analysis. McGraw-Hill, New York (1956)

    MATH  Google Scholar 

  • Hildebrand, F.B.: Methods of Applied Mathematics. Dover Books on Mathematics (1965)

    Google Scholar 

  • Hirvensalo, M.: Quantum Computing. Springer, Berlin (2004)

    Book  MATH  Google Scholar 

  • Hitchcock, F.L.: An improvement on the G.C.D. method for complex roots. J. Math. Phys. 23, 69–74 (1944)

    Article  MathSciNet  MATH  Google Scholar 

  • Holmes, P.: History of Dynamical System. Princeton University, Princeton (2007)

    Book  Google Scholar 

  • James, D.: Recent advances in memory technology. In: Advanced Semiconductor Manufacturing Conference (ASMC) (2013). http://dx.doi.org/10.1109/ASMC20136552766

  • Kitaev, A.Y., Shen, A.H., Vyalyi, M.N.: Classical and Quantum Computation. AMS (2002)

    Google Scholar 

  • Krishnamurthy, E.V., Sen, S.K.: Numerical Algorithms: Computations in Science and Engineering. Affiliated East West Press, New Delhi (2009)

    Google Scholar 

  • Kuhn, H.W.: Variants of the Hungarian method for assignment problems. Nav. Res. Logist. Q. 3, 253–258 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  • Kung, H.T., Leiserson, C.E.: Algorithms for VLSI processor arrays. In: Mead, C., Conway, L. (eds.) Introduction to VLSI Systems. Addison-Wesley, New York (1979)

    Google Scholar 

  • Kung, S.Y.: VLSI Array Processors; Prentice-Hall, Inc., Upper Saddle River (1988)

    Google Scholar 

  • Lakshmikantham, V., Sen, S.K.: Computational Error and Complexity in Science and Engineering. Elsevier, Amsterdam (2005)

    MATH  Google Scholar 

  • Manchester Dataflow Research Project: Research Reports: Abstracts, Sept 1997

    Google Scholar 

  • Mermin, N.D.: Quantum Computer Science. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  • Moore, E.H.: On the reciprocal of the general algebraic matrix (abs.). Bull. Amer. Math. Soc. 26, 394–95 (1920)

    Google Scholar 

  • National Bureau of Standards, Tables of Lagrangian Interpolation Coefficients, Washington (1944)

    Google Scholar 

  • Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  • Petkov, N.: Systolic Parallel Processing. North Holland Publishing Co., Amsterdam (1992)

    Google Scholar 

  • Prall, K., Parat, K.: 25 nm 64 Gb MLC NAND technology and scaling challenges. Trans. IEDM 102–105 (2010)

    Google Scholar 

  • Ralston, A., Wilf, H.S.: Mathematical Methods for Digital Computers, vol. 2. Wiley, New York (1967)

    Google Scholar 

  • Ranga Charya, M. (ed.and trans.): Mahavira (author), Ganita Sara Sangraha, Madras (1912)

    Google Scholar 

  • Richtmyer, R.D.: Difference Methods for Initial-Value Problems. Wiley-Interscience, New York (1957)

    MATH  Google Scholar 

  • Sen, S.K.: Natural mathematics, computer mathematics, and mathematics: scope in engineering computation. Nonlinear Stud. 21(2), 309–318 (2014)

    Google Scholar 

  • Sen, S.K., Agarwal, R.P.: Zero: A Landmark Discovery, The Dreadful Void, and the Ultimate Mind. Academic Press, New York (2016)

    Chapter  Google Scholar 

  • Sokolnikoff, I.S., Redheffer, R.M.: Mathematics of Physics and Modern Engineering. McGraw-Hill, New York (1958)

    Article  Google Scholar 

  • Srinivasa Ayyangar, C.N.: The History of Ancient Indian Mathematics. World Press Private Ltd., Calcutta (1967)

    Google Scholar 

  • Wilkinson, J.H.: The Algebraic Eigenvalue Problem. Clarendon Press, Oxford (1965)

    MATH  Google Scholar 

  • World’s most powerful supercomputer unveiled in US, p. 9. Deccan Herald Daily News Paper, Tuesday, 19 June 2018

    Google Scholar 

  • Young, D.: Iterative methods for solving partial difference equations of elliptic type. Trans. Amer. Math. Soc. 76, 92–111 (1954)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Certainly an article of this type cannot be written without deriving many valuable ideas from several sources. We express our indebtedness to all authors, too numerous to acknowledge individually, from whose specialized knowledge we have been benefitted. We have also been immensely benefitted from several websites such as Wikipedia.org.

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Correspondence to Ravi P. Agarwal .

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Sen, S.K., Agarwal, R.P. (2020). Computing: Birth, Growth, Exaflops Computation and Beyond. In: Flaut, D., Hošková-Mayerová, Š., Ispas, C., Maturo, F., Flaut, C. (eds) Decision Making in Social Sciences: Between Traditions and Innovations. Studies in Systems, Decision and Control, vol 247. Springer, Cham. https://doi.org/10.1007/978-3-030-30659-5_1

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