Infiro Recommends – The Labyrinths of Mathematics
The lecture series “The Labyrinths of Mathematics” by Prof. Tomasz Szarek is an extraordinary journey through the ideas that have shaped science — from philosophical debates on the nature of mathematics, through paradoxes of infinity, to models describing life and disease. These lectures reveal how mathematics both explains the world and continues to surprise us.
Mathematics and Philosophy
“The history of mathematics is a history of expansion” - this is how Prof. Tomasz Szarek opens his lecture, guiding the audience from antiquity, where mathematics was primarily a tool for exploring nature, constructing buildings, and designing war machines, to the modern era, in which mathematics has become the language that allows us to describe even the most complex realities.
The professor juxtaposes two major perspectives on the nature of mathematics.
For Plato , mathematics exists independently of human beings — it is something we discover, not something we create. In this spirit, Professor Kazimierz Kuratowski would later remark that "mathematics is wiser than mathematicians.".
Aristotle , by contrast, viewed mathematics differently: as rooted in the world of the senses, imbued with harmony and beauty. From this perspective arise questions that continue to fascinate scholars to this day: Is mathematics beautiful? And what, in fact, constitutes its beauty?
During the lecture, the Professor also addresses a number of other fundamental questions:
- what distinguishes a priori reasoning from a posteriori reasoning,
- how infinity should be defined and why it takes two distinct forms,
- whether everything that is true can be proven,
- and which twentieth-century discovery — in the Professor’s view — shook the foundations of mathematics and transformed our understanding of what mathematical thinking truly is.
This lecture is an intellectual journey through the history of ideas, beauty, infinity, and truth. It invites us to look at mathematics not as a collection of definitions, but as a profound reflection on the world and on human knowledge.
Mathematics in Biology
Today, mathematics offers an extraordinarily rich set of tools that make it possible to describe even the most complex phenomena — including the phenomenon of life. The first applications of mathematics in the natural sciences emerged with the development of statistics, which began to be used, among other fields, in genetic research. Over time, probability theory, differential equations, and the theory of dynamical systems were added to this toolkit.
The Professor raises an important question: do practical applications drive the development of new areas of mathematics, or does mathematics evolve independently and only later prove to be an ideal tool for describing the world?
The lecture also addresses topics such as:
- what a dynamical system is and what it allows us to study,
- what makes the Fibonacci sequence so remarkable,
- why modeling reality is so difficult,
- what the predator–prey population model looks like and what insights it provides.
Although biology may seem unpredictable, its processes often lend themselves to mathematical description. The Professor presents models of how dynamical systems function, methods for analyzing population growth, and tools that help investigate changes occurring in living organisms. This lecture demonstrates that mathematics can explain life, not merely measure it.
Paradoxes in Mathematics
Mathematics adopted the concept of infinity from philosophy — and with it came paradoxes that have fascinated scholars since antiquity. Paradoxes have accompanied mathematicians since the time of Anaximander and continue to raise fundamental questions about the limits of intuition and the nature of reasoning.
During the lecture, the Professor explains paradoxes such as:
- Achilles and the Tortoise paradox — will Achilles ever catch up with the tortoise if he runs twice as fast?
- Hilbert’s Hotel paradox — is it possible to find a room in a hotel where all rooms are already occupied?
The concept of infinity has become key to understanding many paradoxes that have intrigued thinkers since ancient times. This lecture teaches humility toward intuition and reveals the beauty of logical thinking.
Mathematics Saving Lives
One of the defining features of mathematics — particularly emphasized today — is its remarkable ability to describe phenomena rooted in the real world. Recent decades have brought fascinating advances in the application of mathematical methods in biology and medicine. With the development of technology, mathematics has begun to play a crucial role in analyzing the course of diseases and supporting therapeutic decision-making.
Professor Tomasz Szarek discusses discoveries that connect seemingly simple differential equations with the mechanisms governing how the human body functions. A particularly important place is given to the groundbreaking results of Prof. Andrzej Lasota, obtained in collaboration with hematologist Dr. Ważewska-Czyżewska. The lives of many patients suffering from leukemia depended on understanding a single partial differential equation — it turned out that bone marrow follows specific, mathematically describable rules.
This is a moving example of how abstract ideas can have a deeply practical — and profoundly human — dimension.
Certificate of Participation
After watching all the lectures, participants may download an official certificate of participation in the educational project Labyrinths of Knowledge , organized by Gdańskie Wydawnictwo Oświatowe. We also encourage you to follow our social media profiles — contests are regularly announced there, offering free access to new educational materials.