Born: 21 Aug 1789 in Paris, France
Died: 23 May 1857 in Sceaux (near Paris), France
Biography
Augustin Cauchy (1789-1857) was a prolific mathematician whose 200th birthday is commemorated on this French stamp. Besides his portrait, we see the Cauchy integral formula at right: the Cauchy integral of a regular analytic function f(z) of a complex variable is evaluated along a closed, smooth curve L in a domain D. Several paths are indicated, all enclosing the pole a. The value of these contour integrals is f(a) while contour integrals of a function not enclosing a pole are all equal to zero. On the left side of the stamp is another type of Cauchy integral, this time of a real variable, x. The function is a parabola, y=x2, and the definite integral is over the span -1=< x =<+1. It can be written as a limit as the increments along the x axis approach 0.
Born: 29 June 1893 in Stracov, Bohemia (now Czech Republic)
Died: 15 March 1960 in Prague, Czechoslovakia (now Czech Republic)
Biography
Biography
Biography
Chebyshev was a Russian mathematician working in number theory, particularly with prime numbers, probability theory, and function approximation using orthogonal polynomials. Chebyshev is considered the founder of the St. Petersberg school of mathematics, and his mathematical descendants include Markov, Lyapunov, and Kolmogorov. His work was well-known in europe since he published in european journals and made several extended trips to european mathematical centers; he was eventually elected to many foreign memberships including the Royal Society and France's Academy of Sciences. His mathematical legacy includes Chebyshev polynomials in approximation theory, the law of large numbers in probability theory, and almost a proof of the prime number theorem. Work on prime numbers included the determination of the number of primes not exceeding a given number, wrote an important book on the theory of congruences, proved that there was always at least one prime between n and 2n for n > 3.
The most convincing proof for the Goldbach conjecture so far was provided by the Chinese mathematician Chen Jing-run (1933-1996) in 1965 and is expressed by the inequality at the top of the stamp at left. This stamp was issued in 1999 by China as part of a set of four science and technology motifs and shows the late Chen in profile.
Born: 430 in Fan-yang (now Hopeh), China
Died: 501 in China
Biography
Ch'ung was a mathematician and astronomer. His approximation of pi was 355/113, which is correct to six decimal places. In astronomy, he arrived at the precise time of the solstice by measuring the sun's shadow at noon on days around the solstice
Cusa, in De docta ignorantia, said that the Truth can neither be increased nor diminished and that Intellect, or Reason, can never completely comprehend Truth. But "the more deeply we are instructed in this ignorance, the closer we approach the truth" (Cusa 1440:53). This is at the same time NeoPlatonist mysticism and post-Scholastic Humanism. Instead of the opposition between physics and astronomy, he set up an opposition "between the absolute physics of real essences and genuine causes and the relative and developing physics of abstract essences and fictive causes" (Duhem 1908:58). Reviving Platonic arithmology, Cusa "again associated the entities of mathematics with ontological reality and restored the cosmological status which Pythagoras had bestowed upon it" (Boyer 1949:90). In other words, he viewed mathematics as independent of the evidence of the senses. This encouraged the conceptual possibility of the infinite and the infinitesimal, which had been inimical to the Aristotelianism of the Middle Ages. Cusa held that "a finite intelligence can approach the truth only asymptomatically[; i.e., the infinite was] the unattainable goal of all knowledge" (ibid.:91). He compared man's search for the truth to the squaring of the circle, which, indeed, he attempted by treating the circle as a polygon with an infinite number of sides. This was later named the 'exhaustion method.'
