On May 15, as part of the scientific marathon organized by the Faculty of Computer Science, Physics and Mathematics at Kherson State University, an open lecture was held to mark the 100th anniversary of the Banach–Tarski paradox—one of the most astonishing phenomena in mathematics.
The speaker was Professor Oleksandr Savchenko, Doctor of Physical and Mathematical Sciences and a faculty member of the Department of Algebra, Geometry, and Mathematical Analysis.
He guided the audience through the mysterious realms of set theory, probability theory, and mathematical logic.
During the lecture, attendees learned:
• Whether it is possible to divide a three-dimensional ball into parts and reassemble them into two identical copies (!) — the Banach–Tarski paradox not only astonishes but also prompts deeper reflection on the nature of infinity;
• What Markov chains are and what role they play in modeling random processes, particularly in gaming systems;
• Whether Alfred Tarski’s problem of squaring the circle has been solved;
• What the seemingly paradoxical Sharkovsky order means when applied to the familiar set of natural numbers, and why it is considered natural in modern dynamical systems theory and chaotic dynamics;
• Why mathematics is always a bit like magic, where logic intertwines with imagination.
The organizers expressed their gratitude to everyone who took part in the event and shared in this intellectual thrill!
A recording of the lecture is available on the faculty’s YouTube channel.
Thank you to everyone who joined us on Zoom! See you again in the world of science!
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