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Thursday, September 04, 2014

A new foundation for mathematics

Photo: Florian Meyer
"Is there a revolution coming along in mathematics? A shift that will fundamentally change the way in which mathematicians work? In the near future, will computers rather than humans reliably verify whether a mathematical proof is correct?" reports Florian Meyer, ETH Zurich. 
According to Julie Rehmeyer, a blogger for the popular science magazine Scientific American, the Russian mathematician Vladimir Voevodsky (*1966) has developed an approach that could indeed revolutionize mathematics and its foundations: He has been able to show in principle that homotopy theory, which deals with the deformation of geometric objects, expresses the same ideas as the theory of programming languages and mathematical logic, only in a different language (homotopy theory plays a major role in Voevodsky’s work on the Milnor conjecture which earned him the prestigious Fields medal in 2002).

At scientific meetings, Vladimir Voevodsky inspires audiences as a visionary mathematician and an elegant speaker. In September he will present his ideas at ETH Zurich. (Image: HLFF/Kreutzer)

Voevodsky, a professor at the Institute for Advanced Study in Princeton, wants to bring together two streams of development of today’s mathematics. ETH has invited him to present his ideas in Zurich as a speaker of the 2014 Paul Bernays Lectures in September. Giovanni Felder, the director of the ETH Institute for Theoretical Studies (ITS), will introduce his research to the lecture audience at ETH. He says: “Voevodsky is developing a new theory which places mathematics on a new foundation. The questions he raises concern the foundations of mathematics as well as those of computer science and logic.” This theory is called “Homotopy Type Theory (HoTT)”, and “Univalent Foundations of Mathematics” is the computer-oriented project in which it is being investigated.

Univalent Foundations: New Foundations of Mathematics | Vladimir Voevodsky

Paul Bernays Lectures 

The Paul Bernays Lectures  are a new, annual three-part honorary lecture series dealing with topics from the philosophy of the exact sciences. The series was started in 2012 in honour of the mathematician and philosopher of mathematics Paul Bernays (1888-1977), who taught and did research at ETH Zurich from 1933 to 1959.

This year, Vladimir Voevodsky will speak about the foundations of mathematics, type theory and univalent foundations. His talks will take place in Auditorium F 5 of the ETH Zurich main building on:

9 September 2014 at 5:00 p.m. and
10 September 2014 at 2:15 p.m. and 4:30 p.m.

The lectures arepublic and will be held in English.

Source: ETH Zurich and videosfromIAS's Channel (YouTube).

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