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!)
**********************************
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.
*******************************
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.
Like this:
Like Loading...
njwildberger: tangential thoughts 
Looking forward to this first-time event! However, this idea that big number theory resolves, or rather disproves the Goldbach conjecture due to the fact that we can never fully grasp all the natural numbers, is a bit of a misnomer. By this “big number theory”, a great number of theoretic questions are rendered false trivially because there are natural numbers (dark numbers) that we can never understand. The Fundamental Theorem of arithmetic is false. The Green-Tao theorem is false. Fermat’s Little Theorem is false. Basically any theorem which contains the words; “for every integer/natural number” is ‘resolved’ using this big number theory (that is unless I have completely misunderstood, in which case please correct me).
However if not, I do understand why technically all of theses theorems/conjectures are technically false, but it definitely seems to me that the underlying principle behind them is very valuable to mathematics, they just need to be reworded or adjusted in some way to get rid of the trivial dilemma of dark numbers. Hence my question becomes; how can we go about tweaking these theorems so that they don’t violate big number theory, yet still keep their essential meaning for 21st century mathematics?
Very much looking forward to this!
Best o fluck
I think you will enjoy John Baez in-depth 8 part series on “Struggles with The Continuum”.
https://johncarlosbaez.wordpress.com/2016/09/08/struggles-with-the-continuum-part-1/
A most engaging survey of all the problems in mathematical physics wrought by the continuum.
https://www.researchgate.net/profile/Norman_Wildberger/publications
Le 4 oct. 2016 21:40, “njwildberger: tangential thoughts” a écrit :
> njwildberger: tangential thoughts posted: “Some exciting news, I will at > the end of the 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” >
All very interesting.
We can show that the set of even numbers is countable infinite , the probability of breaking an even number into two prime numbers increase with the magnitude of the even number, then for an even number very , very big is 1 .
For small number the computer make the work very well. We only need a nice function densite of probability for big even numbers.
Thank you, I’ll be watching. Your explanation of numeric complexity has been very thought-inspiring.
A cartoon on the Goldbach Conjectures, licensed for reuse:
https://xkcd.com/1310/
Goldbach’s conjecture should not be viewed as an ‘unsolved problem’. If it is too complicated for math, it isn’t math. You know that.
-sacred: #1-imo.
I will be getting up early to watch your talk from Amsterdam.
So 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.