Koło Naukowe Matematyków U¦ PL SMS

XXX SMS' Session
Pathologies and paradoxes in mathematics

Szczyrk, 29th Apr - 3rd May 2011


This year's May weekend at last suited our needs to organize a longer session. We managed to book the resort, assemble a team of participants and prepare a bunch of talks. It only remained to get there and show Szczyrk, how mathematicians spend the beginnings of spring!

Aside from its length, the May session was exceptional in that only five Society's members were in the train at the same time. The rest of the participants either joined us on the way, or arrived in another train, or - mainly - got there by cars. Well, we are becoming quite a motorized group. Those who went by train were at their destination earlier than some of the car riders anyway - sadly, that group was the most important one because they carried food! Well, we endured this trial, survived till the evening and planned the rest of the session, including planting the Murderer among us.

One of the advantages of longer sessions is the fact that the talks do not take a hundred percent of available time - so, using the great weather we had, we decided to spend Saturday on hiking (at least the majority of us decided so). Relax on Klimczok and oranges on high altitude gave us strength and energy to be the freshest on Szymon Draga's (a little roasted by the sun) evening talk „Patological theorem about the sets of distances", which opened the mathematical part of XXX session. Of course, there also was the parallel talk „I slept in the woods”, but it was less mathematical, so I do not include it in this report - sorry to the talker.

This session was also the debut of Wiochmen Rejser, which can truly be named a Bang alternative. We have two games now, with eleven people able to play at the same time - two more and all of us will be able to spend every evening of every session playing. Our first evening therefore consisted mainly of BANG gunshots, Wiochmen's bottles (and many joy from discovering the game's settings, rules and descriptions on cards) and delicious cakes provided by Daria Morys.

However, in the morning we had to resign from our Sunday mountain trip because of the rain - however, plenty of games in the resort kept us busy enough ;) The evening was the time for more talks - Marek Biedrzycki told us about paradoxes in logic, and Weronika Siwek told us the tale of the known-to-all, bot with no one knowing the details, Banach-Tarski paradox. We ended the evening with doctor Rafał Kucharski unveiling the meaning of secret surveys we all filled during the session - and even though our steel mathematical logics and brilliance of every member of the Society prevented the talker from acquiring some of the paradoxical results he hoped for (HA!), we fell for some of his tricks (once, maybe twice). Doctor made sure, however, that no one goes to bed depressed that „I play stupidly on lotteries” (even though he had plenty of evidence that it is so). Before going to bed we also managed to play some Psychologist, half of which consisted of strange talks about bizarre configurations in, hmm, private situations - it is enough to say that the word „Mechanoturtle” appeared a tiny little bit too often for a normal talk of a group of mathematicians.

Hence Monday came, the official day of talks. Armed with coffee, cookies, drinks, fruits, sympathy and strength, we listened to Mateusz Jurczyński, who told the tale of big measure zero sets, very discontinuous functions with the Darboux property and generally he showed us, how we should be vary of the word „almost” in mathematics. After him, Daria Morys described the Appert space, so that no one would anymore think, that the normality and local compactness of a topological space are linked in any way. At eleven o'clock our guests arrived - professor Tomasz Połacik from the University of Silesia and Adam Wegert, a student of AGH in Kraków. We listened to the talk of Tomek Kania about mixed Tsirelson spaces, after which our guests started their talks. Professor told us, how ancient logical problems influenced mathematics, guiding us from the liar's paradox to Goedel theorems. Adam explained how we should go about introducing a measure on infinite-dimensional space (we shouldn't, because it is impossible in a "nice" way). After a small lunch break (OK, a longer one) it was time for Piotr Idzik's referat about a thirteens function, or in other words, how to construct a patology, without the Patologies Axiom (or the so called axiom of choice). After him our tutor, doctor Tomasz Kochanek, described the Schroeder-Bernstein problem, creating a theory of left isomorphisms (not too interesting for me because of the lack of empty functions) and swiftly destroying, bending or chaning all of our intuitions concerning the matter of „a small part resembling the entirety". The mathematical part was ended by Jolanta Marzec, who constructed the Bernstein set on the plane and told us about its amazing qualities.

To end the officialities, we needed to vote for the best talk and to decide about the next session's topic. The winners were - doctor Tomasz Kochanek and the topic „Motivations, intuitions and constructions in mathematics”. When it was done, we could gladly indulge in other entertainments - Tomek Kania finished murdering, some of us hurled bottles at each other and the rest shot at each other from behind the barrels. Normal evening in Szczyrk.

And even though we learned about ourselves that we eat and drink to much, even though we had plenty of trips to the shop for food and drinks, even though it was the first time on our Szczyrk sessions that a theorem was proved using a computer, even though we had many talks on many topics, even though we shouldn't play on lotteries, even though pizza arrived to the resort twice, even though we were completely flooded for the second half of the session, even though Basia had to leave earlier, even though Weronika and Marek had to leave us for one whole day, even though there is much left to tell about - it is time to end the resort with the words: it was great! We are waiting for November :)

Innocent Wolverine
last update: 19.03.2013


Students' Mathematical Society of the University of Silesia
(Koło Naukowe Matematyków Uniwersytetu ¦l±skiego)
40-007 Katowice, ul. Bankowa 14 (room 524)
tel. (032) 359-20-96, email: knm@knm.katowice.pl