What is mathematics for Krzysztof Ciesielski

By on 01/02/2016

This is a very difficult question, and there is probably no one answer to which all mathematicians would subscribe. We have collected a number of partial answers. There is great variation in the ambitions of the authors and the demands placed by them on the reader

by Krzysztof Ciesielski

For me, the most important feature of mathematics is, that it is the science of logical thinking and absolute truth. Here, all results follow from others in a clear and precise way on the base of a precise reasoning. Any mistake caused by a bad experiment is impossible, the individual opinion of the author as well as the present political situation do not matter at all. If the theorem is true, it is true forever. The Pythagorean Theorem was true 20 centuries ago and is true now. Mathematics is the only discipline (scientific discipline) with this property. Even in physics and chemistry some experiments could change a lot and show the mistakes in the theory that was earlier regarded as fully true… However, this would not be a full picture of mathematics, if I didn’t write something more. One could say: ”well, formulate any abstract assumptions and deduce from them something”. This also would be mathematics, but rather not too interesting and not worth too much. Mathematical results have their ”reasons”. New results are either taken from the existing (and valuable) results and research, or they pretend to be the models of real life or facts from other sciences. Probably people who work in mathematics generally do not see it as a collection of abstract symbols. I, personally, for sure do not think about mathematics this way. I look at mathematics from the point of view: ”what is hidden behind the symbols” and look for it in the way suitable for me, with the use of my imagination. Thanks to it I see the beauty of several theorems, theories, mathematical objects. One could compare that to the poetry and particular poems in different languages. If you hear the poem said in a foreign language, you hear nice sounds, rhythm, but you can understand the poem only when you know the language. You may said ”ah, that sounds beautiful” but without understanding the meaning you do not know what’s going on. Speaking about elementary mathematics, we mean simple addition or multiplication, simple properties of geometrical figures or logical puzzles. Yes, this is mathematics. This is the beginning. Higher mathematics investigates mainly some general structures which have simple models we meet during our school education. Well known natural numbers are models of some general structures, we may look for geometric objects as for models of some abstract objects. During the research, the definition of new objects naturally come to our mind, new problems appear – some of them still wait for solutions… Mathematics is present everywhere, in all our life. Many of us do not realise that without mathematics we would not manage to do almost anything. We would have diffi- culties in such simple task as moving from one point to another (we need a map, on the other hand, if we go by bus, then buses are usually numbered). More advanced, how would computers work without mathematics? I think that mathematics would interest anyone, however, of course, not anyone is obliged to be expert in higher mathematics. In my opinion, everyone can find in mathematics something nice for himself or herself. After that, he will discover a special beauty of mathematics and very probably will be interested in something more…

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