Abstract

The mankind is now entering a new era of information age or computer age characterized in particular by the presence of the powerful tool of computers. Before we consider how the mankind should deal with and act in this coming era, let us first give a brief reflection of what the mankind had thought about and had act in the past era of industrial revolutions accompanied by technological revolutions. Being a mathematician, the present author would like to present some of such reflections from a mathematical point of view. In fact, the novel creations of coordinate geometry by R.Descartes (1596-1650) and P.Fermat (1601-1665) as well as the infinitesimal calculus by I.Newton (1642-1665) and G.W.Leibniz (1646-1716) in 17th century made possible the study of movements and variations in a quantitave way. It provided thus powerful tools to nourish and impede the coming revolutions in industry and technology. The past era of industrial revolutions may be roughly subdivided into 3 stages. The first stage, from 60th and 70th of 18th century onwards, was accompanied by the invention of Watt’s vapor machine, the sewing machine, etc. in industry. Mathematicians, being intoxicated by the wonderful powerfulness and wide applicability of the newly invented method of calculus, were delighted to indulge themselves to such applications like improving of manufacturies, building of ships and even constructions of frigates, etc. Mathematics was itself benefitted in that calculus had grown up to become a giant discipline of mathematical analysis. Among the mathematicians involved in this movement we may cite particularly: D’Alembert (1717-1783), G.Monge (1746-1810), L.Euler (1707-1783), J.L.Lagrange (17361813), P.S..Laplace (1749-1827), etc. The second stage may be considered to be roughly from 60th of 19th century onwards. In technology it was characterized by the invention of electric machine, electric motor, electric telegraphy, etc. Among mathematicians-physicists we may cite e.g.: G.Green (1793-1841) and S.D.Poisson (1791-1840) for the creation of potential theory, C.F.Gauss (1777-1855) for the study of magnetism and invention of telegraphy, and J.C.Maxwell (1831-1879) for the establishment of electro-magnetism theory and equations. The third stage was roughly from 40th of 20th century onwards. It was accompanied by exciting achievements in the revolution of technologies: The discoveries and inventions of computers, atomic energies, satellites, production automation, genetic engineering, superconductivity, lasers, etc. In mathematics and related fields there appeared a lot of entirely

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