Some exciting news, I will next month be giving a talk which, amongst other things, will resolve the Goldbach Conjecture. That is a rather famous conjecture in Number Theory that asserts that every even number can be written as the sum of two primes.

The talk will be in the Pure Mathematics Colloquium on **November 8 2016** at the University of New South Wales, Sydney (UNSW), probably at 3 pm. (Note the change in date from a previous announcement!)

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Speaker: A/Prof N J Wildberger (UNSW)

Title: Primes, Complexity and Computation: How Big Number theory resolves the Goldbach Conjecture

Abstract: The Goldbach Conjecture states that every even number greater than 2 can be written as the sum of two primes, and it is one of the most famous unsolved problems in number theory. In this lecture, we look at the problem from the novel point of view of *Big Number theory* – the investigation of large numbers exceeding the computational capacity of our computers, starting from Ackermann’s and Goodstein’s hyperoperations, to the presenter’s successor-limit hierarchy which parallels ordinal set theory.

This will involve a journey to a distant, seldom visited corner of number theory that impinges very directly on the Goldbach conjecture, and also on quite a few other open problems. Along the way we will meet some seriously big numbers, and pass by vast tracts of *dark numbers*. We will also bump into philosophical questions about the true nature of natural numbers—and the arithmetic that is possible with them.

We’ll begin with a review of prime numbers and their distribution, notably the Prime Number Theorem of Hadamard and de la Vallee Poussin. Then we look at how complexity interacts with primality and factorization, and present simple but basic results on the *compression of complexity*. These ideas allow us to slice through the Gordian knot and resolve the Goldbach Conjecture: using common sense, an Aristotelian view on the foundations of mathematics as espoused by James Franklin and his school, and back of the envelope calculations.

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This lecture will be live streamed on YouTube at

So anyone from around the world who is interested can watch if they like. Hope you all will be able to join us for this fun, invigorating, and enlightening event! If you are in Sydney on the day, and can head over the UNSW for the event, we will be delighted to see you there.

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gentzenSo I stood-up at 5 am to watch this live stream. Was it worth it? Yes and no. No, because the link to the live stream turned into a link to the recorded session now, so it was totally unnecessary for me to get up so early. I could have just watched it later at a more convenient time. Yes, because there was also a live chat, where I learned for example that googling for “fast-growing hierarchy” is the way to go for learning more about “the presenter’s successor-limit hierarchy which parallels ordinal set theory”. But I can no longer access the live chat now, which is strange. And I had to create a YouTube channel for being able to talk in the live chat, maybe I will start using that channel later. And it felt good to express support for Norman by getting up so early, after all I like his style of ultrafinitism. Many other styles of ultrafinitism are just too trivial for my taste.