On the shoulders of genius

Look at almost anything we do, and however modern andexciting the innovation may seem, there's almost alwaysa mathematician, fifty, a hundred, sometimes two hundred ago whothought about the issues raised and contributed something to the solutions

George Boole was born in Lincoln, England in 1815 and published The Calculus of Logic in 1848 - almost exactly 100 years after Euler's Introductio in analysin infinitorum

Nothing in modern, science based, computing originated in either publication, but the two set in stone the roots of the research behind almost everything we do in the field today.

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Boole actually took the first real steps along the road to today's systems in his own 1854 publication Investigation of the Laws of Thought; in which he enunciates much of what we now know as boolean logic. Euler's methods dominate the development of better numerical solutions - from 19th century methods of using series to find roots and sums right down to the interval arithmetic Sun is about to release as the foundation paradigm for the first generation of predictable precision computing.

Some of Boole's ideas became computing reality in 1937 when John Atanasoff and Clifford Berry, at Iowa State, built the first electronic digital computer. Rebuilt by volunteers at Ames in the late nineties the machine looks nothing like today's computers but everything in the Sun workstation I'm typing this on has an analog or ancestor in that 1937 design.

Meanwhile, of course, other people with more theoretical interests were doing other things. Thus the work Jan von Neumann and Oskar Morgenstern did on economic game theory during the late 1920s and "regularized" for publication in their 1944 The Theory of Games and Economic Behaviour, set in place the theoretical foundations for today's ERP/SCM applications - because they were the first to model the effect of overall process optimisation on an economic entity with competitors.

Hardware helped make that work real, but software, particularly for linear programming and related optimisation techniques was equally critical. Thus hidden deep inside the proprietary guts of Oracle's enterprise suite today you'll find the descendents of original work on algorithms by George Dantzig, Leonid Vital'evich Kantorovich and von Neumann himself.

Interior point solutions have advanced on their work by about four orders of magnitude since, but it was Dantzig's 1947 simplex algorithm, along with Alston Householder's 1951 work on sparse arrays, that ultimately made possible the realization in today's large scale ERP/SCM applications of the global optimisation ideas developed by von Neumann and Morgenstern in the late 1920s - and the whole field is like that. Look at almost anything we do, and however modern and exciting the innovation may seem, there's almost always a mathematician, fifty, a hundred, sometimes two hundred ago who thought about the issues raised and contributed something to the solutions we're finally getting to now.

All of which raises a question: what are today's mathematicians thinking about and how long will it take us to make their dreams real?

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