Speaker: Alba Crespi
Abstract: Some humans dream of conquering outer space and establish colonies on Mars and the Moon. Science-fiction writers warn us of alien invasion or colonization of the Earth. However, so far microscopic life seems to dominate the entire planet, while humans have only colonized humans. The first colonizers on the Earth were microorganisms, because of their power to mutate and adapt to different environments. Not only are they found in symbiosis with animals or causing diseases, but they are also able to transform environments such as deserts. They are part of our daily lives, present in what we eat, what we drink and breathe.
Modern technologies such as sequencing have revealed a wide variety of life in so called ‘extreme conditions’ such as in thermal and sulphurous waters or even in the upper atmosphere. Will they be the first to colonize the rest of the universe? Or are they already there?
Speaker: Balazs Szigeti
Title: An incomplete talk on the incompleteness theorem(s)
Abstract: No other result in modern logic has produced near the same impact as Kurt Gödel’s 1931 study the On Formally Undecidable Propositions of Principia Mathematica and Related Systems. The paper proves the incompleteness theorems that demonstrate some inherent limitations of formal reasoning. The theorems not only brought the end of the formalist approach to mathematics, but had far reaching consequences.
In this talk I will give a sketch of the proof, explain when the theorems are applicable and briefly discuss their wider philosophical implications.