6th December 2011, 6:30pm
Metamathematics: Strange Loops and Incompleteness, Dr Joel Haddley (University of Liverpool)
Abstract
The Goldbach Conjecture states that every even number greater than 2 can be written as the sum of two primes. Do you think this is true? Do you think this will ever be proven? More interestingly, if we could demonstrate that this conjecture could never be proven either true or false, could the conjecture still be true?
Mathematics is widely regarded as a very logical language. If you are given the mathematical statements “A implies B” and “B implies C,” you will quickly deduce using your innate logic that “A implies C.” What happens in this intermediate ‘innate logic’ stage is what we refer to as the study of metamathematics. When we attempt to understand and rationalise this step, we are faced with mathematical contradictions and paradoxes that bear strong resemblances to plot lines in science fiction, levels in Super Mario, songs from The Muppet Show and artwork from M. C. Escher.
Early mathematicians’ attempts at resolving these contradictions were essentially fruitless, until Gödel proved his Incompleteness Theorem. This theorem makes it entirely plausible for statements such as the Goldbach Conjecture to be true but impossible to prove. We will discuss and demonstrate how contradictions and paradoxes occur in both media and mathematics, describe Gödel’s theorem in an informal way, and discuss the impact this has on the study of mathematics.
Venue: Mitchell and Kenyon Cinema, Foster Building, University of Central Lancashire, Preston
No charge is made to attend meetings and non-members are welcome.
