# Polish Mathematics in World Science

In the last issue of the Forum, we published the first part of this history of mathematics in Poland. The article below continues the topic with a description of the influence of Polish mathematics on world science.

In any discussion of mathematics in Poland, one has to mention Professor J. Łukasiewicz, who created multi-valued logic. For example, if someone says that when visiting Warsaw, she always goes to the theater, and out of ten visits to Warsaw, she went to the theater seven times, we would say that the „degree of participation” is 0.7. There have long been computers built for „fuzzy” logic” and not only binary logic (there is current „1” – there is no current „0”); they run, for example, the metros in many cities in Japan.

Stanisław Ulam, a mathematician from Lwów, left for the United States before the outbreak of the Second World War. He was soon invited to join the elite group of the world’s best scientists working on the atom bomb by Professor John von Neumann, probably the greatest mathematician of the twentieth century. Together with his wife, who was from France, Ulam lived in a closely guarded area in New Mexico, where with Teller (a physicist from Hungary) and other renowned scientists, he worked on the atom bomb. Teller himself visited Cleveland a couple of times at the invitation of Hungarian emigre organizations. Using newly discovered mathematical-statistical methods, they studied whether or not dropping the atomic bomb could lead to the burning of oxygen in the earth’s atmosphere. Ulam also took part in the program planned for the use of nuclear energy as fuel for spaceships. Later he was the chair of the Department of Mathematics at the University of Colorado in Boulder. Professor Ulam died in 1984. The next head of the Department of Mathematics in Boulder was another excellent mathematician from Poland, Professor Jan Mycielski, from Wrocław.

One should not omit the Polish mathematicians who worked on breaking Red Army codes, such as Jan Kowalewski. It’s difficult to overrate their participation in the victory of the Polish army near Warsaw in 1920, the so-called „Miracle on the Vistula”. One should also add the achievements of a group of mathematicians less connected with academia, such as Marian Rejewski, Jerzy Różycki and Henryk Zegalski, who broke the „Enigma” code. I had the honor to meet Rejewski in person at a conference of the Polish Mathematical Society in Łodz.

The Wrocław School of Mathematics was the continuation of the Lwów School of Mathematics after World War II. For many years the Wrocław School concentrated on applied mathematics. For example, Professor H. Steinhaus published almost exclusively on the effective method of establishing paternity. Professor C. Ryll-Nardzewski, probably the greatest living mathematician, is a world famous mathematician working in Wrocław. Think about the applications of mathematics: You know a computer, right? Who came up with this idea? Many of you have heard of a cocktail of medicines taken by individuals with multi-symptom illnesses, such as AIDS? We have a number of medicines which treat the symptoms of such diseases with good results. Methods taken from Operations Research coupled with the information from the FDA guarantee proper proportions of medications in the mixture. This is part of mathematics, Decision Theory and linear programming. I discussed such an example, the cocktail of medicines, for doctors in my lectures at St. Elizabeth’s Hospital in Youngstown.

In other applications of mathematics, Professor Kenneth Kunen, a well-known topologist working at the University of Kansas, not long ago proved that if in a model of four-dimensional space-time continuum, we assume the topology of a separate continuity, as suggested by Professor Zeeman, then it follows from a theorem authored by Professor E. Wingler from Youngstown State University and me, that in this model the outer space in which we live need not be regular, which means that it may happen that will not be able to separate a point from a closed set using disjoint open sets containing the point and the closed set, respectively. (If you didn’t understand this, please don’t worry. The editor didn’t understand it either. – Ed.) But with each new theorem are born…new questions! Is the converse theorem also correct? Is it possible to weaken the assumptions? Each new scientific work in mathematics includes completely new theorems with proofs still unknown to humanity. In proofs there are no numbers. A real mathematician-scientist even feels an aversion to numbers (!); letters are used instead in proofs.

In 1870 approximately 840 mathematical works were published. By the 1990s, more than 50,000 mathematical works were published yearly(!).There are tens of thousands of unsolved problems in mathematics! But let’s return to the influence of Polish mathematics – our scientists have served the United States well. Many of them are members of the American Academy of Sciences. Some of the greatest Polish mathematicians working in the United States have already died: A. Tarski, A. Zygmund, and J. Spława-Neyman. A fact mentioned by Professor K. Kuratowski attests to the strength of Polish mathematics. A majority of sessions at a national conference of the American Mathematical Society were led by Poles. At a lecture given by Professor W. Sierpiński at the University of California at Berkeley, most of the audience raised their hands when asked who was his student or the student of one of his students. One of the objects studied in Mathematics is „Polish space”; as Professor Z. Opial explains the term, „Polish space” was coined by a group of American and French professors (N. Bourbaki) to honor the role of Polish mathematics in world science. We also have several Polish mathematicians in Ohio. Alphabetically, they include Professor Krystyna Fabrykowska, a professor of mathematics working at John Carroll University. Her husband, Professor Jacek Fabrykowski (a student of Professor Schinzl, who was a student of Professor W. Sierpiński) is a numbers theorist lecturing at Youngstown State University; Professor W. A. Woyczyński (a student of Professor Urbanik), is a probabilist from Wrocław University lecturing at Case Western Reserve University; and, not alphabetically, the author of this article.

Zbigniew Piotrowski

Forum, 2/2007