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Pafnuty L. Chebyshev

BIOGRAPHY 7.1 Pafnuty L. Chebyshev (1821 -1894)

Pafnuty Lvovich Chebyshev was born in Okatovo, Russia. His parents, who belonged to the gentry, had him privately tutored. He quickly became fascinated by mathematics and eventually studied mathematics and physics at Moscow University. Even as a student, he won a silver medal for a now-famous paper on calculating the roots of equations. It was only the first of many brilliant papers that he wrote while teaching mathematics at St. Petersburg University and pursuing a keen interest in mechanical engineering. (Among other things, he contributed significantly to ballistics, which gave rise to various innovations in artillery, and he invented a calculating machine.) Always, he stressed the unity of theory and practice, saying:

Mathematical sciences have attracted especial attention since the greatest antiquity; they are attracting still more interest at present because of their influence on industry and arts. The agreement of theory and practice brings most beneficial results; and it is not exclusively the practical side that gains; the sciences are advancing under its influence as it discovers new objects of study for them, new aspects to exploit in subjects long familiar.

Chebyshev typically worked toward the effective solution of problems by establishing algorithms (methods of computation) that gave either an exact numerical answer or an approximation that was correct within precisely defined limits. A most important example of this approach in the field of statistics is his formulation of what is now called Chebyshev's theorem, discussed in Chapter 7. For practical purposes, many a frequency distribution that is only slightly skewed (with a coefficient of skewness between -0.5 and +0.5, for example) can be treated as a perfectly symmetrical one, and the higher percentages applicable to a normal curve (discussed in Application 7.1, Standard Scores) can be applied to estimate the proportions of observations falling within specified distances from the mean. Chebyshev's theorem, however, demonstrates a radical change: He was the first mathematician to insist on absolute accuracy in limit theorems. In the words of A. N. Kolmogorov, another eminent Russian mathematician, "he always aspired to estimate exactly in the form of inequalities absolutely valid under any number of tests the possible deviations from limit regularities."

Source: Dictionary of Scientific Biography, vol.3 (New York: Charles Scribner's, 1971), pp. 226 and 231.

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