Waclaw Sirpenski

Waclaw Sierpinski

Waclaw Franciszek Sierpinski was born March 14, 1882 in the capital city of Warsaw, Poland. He attended school in Warsaw where his talent for mathematics was quickly spotted by his first mathematics teacher. This was the phase of Russian occupation of Poland and it was a complicated time for the talented Sierpinski to be educated in Poland. The Russians had enforced their language and culture on the people in Poland in sweeping changes to all secondary schools implemented between 1869 and 1874. (websource)The Russian aim was to keep illiteracy in Poland as high as possible, so they discouraged learning and the number of students fell. Then despite all of the hardships Sierpinski was able to finish up his pre college education with out any problems.

Sierpinski then would enter the Department of Mathematics and Physics of the University of Warsaw in 1899. (websource) While at the University of Warsaw, the Department of Mathematics and Physics offered a prize for the best essay from a student on Voronoy's contribution to number theory. Sierpinski was awarded a gold medal for his essay, thus laying the foundation for his first major mathematical contribution. Because he didn’t want his work to be published in Russia he waited until 1907 to get his materials published by a mathematics magazine. Once he graduated, he then taught math and physics in Warsaw. Once the school he was working in closed; he then started to pursue a doctorates degree from the Jagiellonian University in Krakow. He then studied astronomy and philosophy and received his doctorates in 1908. From 1908 to 1914 Sierpinski lectured at the University of Lvov, followed by three years at the University of Moscow. After the end of World War I he returned to the University of Warsaw and spent the rest of his career there. By all accounts he was an excellent teacher.

Two well-known fractals are named after him the Sierpinski triangle and the Sierpinski carpet, as are Sierpinski numbers and the associated Sierpinski problem. The Sierpinski triangle, also called the Sierpinski gasket, is a fractal, named after Sierpinski who described it in1915.Originally constructed as a curve; this is one of the basic examples of self-similar sets. The Sierpinski triangle has Hausdorff dimension log (3)/log (2) ≈ 1.585, which follows from the fact that it is a union of three copies of itself, each scaled by a factor of Ѕ.If one takes Pascal's triangle with 2n rows and colors the even numbers white, and the odd numbers black, the result is an approximation to the Sierpinski triangle. The area of a Sierpinski triangle is zero this can be seen from the infinite iteration, where we remove 25% of the area left at the previous iteration. (Paul W. K. Rothemund, Nick Papadakis, and Erik Winfree) Another one of his contributions was the Sierpinski numbers.

Another contribution he made was to the number theory. A Sierpinski number is a positive, odd integer k for which the integer’s k*2n+1 are all composite, that is, for every positive integer n. In 1960 Sierpinski shoed that there were infinitely many such numbers k but he did not explicitly give a numerical example. (Sierpinski, 1972) The congruencies provided a sufficient, but not necessary, condition for an integer to be a Sierpinski number. Of course Sierpinski also asked what the smallest such number might be--determining this number is called the Sierpinski problem. If the congruencies proposed by Sierpinski are solved, a 19-digit number k is obtained as their smallest solution. The much smaller example k = 78557, now conjectured to be the smallest Sierpinski number, was found by John Selfridge in 1962. (Sierpinski, 1972) Sierpinski's most important mathematical work was in the areas of set theory, point set topology, and number theory.

It was in 1907 that Sierpinski first became interested in set theory. It happened when he came across a theorem which stated that points in the plane could be specified with a single coordinate. He wrote to Banachiewicz, who was at Gottingen at the time, asking him how such a result was possible. Sierpinski began to study set theory and in 1909 he gave the first ever lecture course devoted entirely to set theory. Although Sierpinski was not the first to discover