Infinite fun with infinite worlds | Science - Mirage News

The fact that there are many different types of infinities is one of the big puzzles in mathematics. One mathematician who enjoys investigating which infinities can actually occur is Saharon Shelah, the guest speaker at this year’s Paul Bernays Lectures.

Israeli mathematician Saharon Shelah is one of the top experts on infinity and how it can be understood and distinguished mathematically.
Photo: Wikipedia / ETH Zurich

One of the most astonishing findings in mathematics is the discovery that there are many different types of infinities – and for a long time, it was an unresolved problem whether some of these infinities could be of different sizes without contradiction.

One mathematical logician who has been studying this intensively for years is Saharon Shelah from the Hebrew University of Jerusalem. As the guest speaker at this year’s Paul Bernays Lectures, he will discuss the current developments in “Struggling with the size of infinity”. Shelah is an established expert on the topic of mathematical infinity. A year ago, he managed to prove with Martin Goldstern and Jakob Kellner from the TU Wien that ten – and no more – infinities can have different sizes and can be arranged according to their sizes in what is known as Cichoń’s diagram (see figure).

This was a ground-breaking proof, as history shows: the modern mathematical debate on infinity began with a series of discoveries made in the 1870s by German mathematician Georg Cantor (1845-1918)...

At the Bernays Lectures, Shelah will discuss whether such an arrangement of the infinities and the cardinal arithmetic allow new insights into the continuum hypothesis. “The proof that ten infinities can be different in Cichoń’s diagram is not just ground-breaking, but also typical for Shelah,” says Halbeisen. “He considers mathematical matters in a completely unbiased manner and is able to see astonishing connections. His instinct for possible solutions is unerring.”
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Source: Mirage News