Goldbach... if unprovable, then true!

 IF Goldbach's Conjecture is UNprovable, well then, it must be true! (via Peter Lynch):

https://thatsmaths.com/2021/03/04/goldbachs-conjecture-if-its-unprovable-it-must-be-true/

"... if it were false, there would be some finite even number that is not the sum of two primes. A finite search could confirm this, making the conjecture 'provably false'! In other words, falsehood of the conjecture is incompatible with unprovability. This contradiction forces us to an ineluctable conclusion: if Goldbach’s Conjecture is unprovable, it must be true!"

 

A Little Catch-up

Just a small catch-up potpourri of things from this week's world of math. Besides the Yitang Zhang news related to prime number gaps, the other big news was Harald Helfgott's proof of the "ternary" or "weak" Goldbach conjecture (every odd number above 5 is the sum of three prime numbers). Evelyn Lamb covers it well at her Scientific American "Roots of Unity" blog here:

http://blogs.scientificamerican.com/roots-of-unity/2013/05/15/goldbach-variations/

Speaking of Scientific American, I was happy to see Joselle Kehoe, who blogs at Mathematics Rising, get to do a guest blogpost for them today (math, language, biology/evolution, and reality in a single post!):

http://tinyurl.com/atg7mbx

Mark Chu-Carroll over at "Good Math, Bad Math" blog has initiated a series of posts on "discrete probability theory." Ought to be good given Mark's methodical approach to most subjects. His first introductory post is here:

http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/

And, in the event that "probability" is your thing, here's another page of links to some sources on probability theory (based largely on the work of E.T. Jaynes):

http://bayes.wustl.edu/

Finally, if you're in the mood for a puzzle, Futility Closet has put up a little algebra brain-twister (from the 2003 Moscow Mathematical Olympiad) here:

http://www.futilitycloset.com/2013/05/16/going-up/