# The Beginnings of Polish Mathematics

Is it possible that our country, a land of great poets, writers, and poets, can also be one of the centers of world mathematics? Of course, thanks to the great mathematician, and astronomer, Nicolas Copernicus (1473-1543).

Were there others like him? And, by the way, what else can be discovered in the history of mathematics? We start with a few names from the distant past. Some of the young Poles studying at Italian, Austrian, or French universities in the twelfth and thirteenth centuries returned to Poland; others went from court to court practicing more applied notions of mathematics. Examples, writes R. Duda, include Witelon of Śląsk (ca.1230-ca. 1280) and Marcin Bylica (ca. 1434-1493; he spent almost his entire adult life in Italy and Hungary, as a professor at universities in Bologna and in Buda, or also as court astrologer to Roman cardinals and Hungarian kings). As we know, Copernicus, after studying at Italian universities, returned to Poland and created his greatw works in Frombork.

Every American student studying differential equations (for example, future engineers) encounters the Wronskian, a certain type of determinant named for the Polish philosopher and mathematician Józef Maria Hoene-Wroński (1778-1853). The majority of this mathematician’s works are forgotten. In the period preceding the rebirth of the Polish state in 1918 two distinguished professors, Stanisław Zaremba and Kazimierz Żórawski, taught at Jagiellonian University. Józef Puzyna and Wacław Sierpiński (1882-1969), from Warsaw, were professors at the university in Lwów.

The situation was a little worse at Warsaw University, which Polish youth boycotted. The tsarist powers did not agree to the creation of a Polish university. In 1906 the „Scientific Courses” were founded and taught by, among others, L. Zarzecki and Samuel Dickstein. The courses substituted for a university. The Warsaw Scientific Society was also created by Polish youth during this period. The group worked vigorously and, in 1911, Count Józef Potocki gave to the Society a home at Śniadeckich 8, which to this day is the home of the Institute of Mathematics of the Polish Academy of Sciences. There is still no unified Polish school of mathematics. There is a lack of a common theme, a common place of work. In addition, many unusually talented Poles were educated abroad.

Mathematics in Poland began to develop in 1918. Poland became the place of birth of many fundamental theorems and even complete mathematical theories. Z. Janiszewski’s article in the first volume of „Nauka Polskiej” (1918) is very significant in this regard. The article introduces his vision suggesting the direction of development of Polish mathematics. He writes: „To be sure, mathematics does not need any laboratories for its work; it does need, however, a suitable mathematical atmosphere and contact with cooperative colleagues.” He suggested Polish mathematicians occupy themselves only with newly developing disciplines such as set theory and topology (also known as „rubber geometry”) and the grammar of „pure” mathematics, which had as its task to define very abstract space for use in the incredibly dynamically developing physics at that time.

Dr. Janiszewski suggested that a journal devoted only to these themes be founded in Poland. His dreams were fulfilled. In spite of the friendly warnings of H. Lebesgua, Fundamenta Mathematicae was founded, until this day a mathematics journal at the highest world level. Janiszewski, the godfather of the Polish School of Mathematics, died at the age of 32 of complications of the Spanish flu. In order that the achievements of Polish mathematics would never be wasted, he suggested the publication of mathematical works only in English, French, and German. This practice is still maintained.

The interwar period saw an explosion of Polish mathematics. In addition to the Warsaw School of Mathematics, which included W. Sierpiński, K. Kuratowski, czy S. Mazurkiewicz, there arose the famous Lwów School of Mathematics. One can say without exaggeration that Lwów in the interwar period was one of the greatest mathematics centers in the entire world. Working in Lwów were Stefan Banach (1892-1945), one of the greatest geniuses of the twentieth century, the creator of functional analysis, a new branch of mathematics; Hugo Steinhaus, Stefan Mazur, and Stanisław Ulam. Every student of mathematics or physics worldwide learns about Banach’s method of spaces. The Department of Mathematics at Kent State University is universally regarded as one of the strongest centers in research on Banach’s spaces.

I mentioned cooperation among mathematicians. In Lwów, they met in that city’s cafes. The Scottish Cafe, a place of inspiration for mathematical thought, was particularly known as a site of long discussions, often lasting for several hours. Results, even conclusions, were simply written…on the table. These were new, still unknown mathematical theorems. new, still unknown conclusion of mathematics. Many are still not able to recreate the results today. It was easy to think that the theorems would just be wiped away by the staff of the cafe. So an idea arose to write everything into a special notebook, known later as the Scottish Book. Prizes, sometimes completely humorous ones, were offered for the solving of the problems. For example in 1936, Professor Stanisław Mazur wrote down a problem relating to the existence of a certain type of base in Banach’s spaces. The prize for solving the problem was supposed to be…a live goose. After 36 years, in 1972, a twenty-eight-year old Swede, Dr. Per Enflo solved this problem, and at the S. Banach Center in Warsaw, Professor S. Mazur offered him the promised prize.

As it happens, Professor Enflo teaches at Kent State University. The original copy of the Scottish Book can be found in the Stefan Banach International Center for Mathematics; in the 1990s, an American press published the Scottish book, under the direction of a well-known professor in Texas, D. Mauldin. In this book are presented all the problems and solutions known to this time.

Zbigniew Piotrowski

Forum, 1/2007