Chinese High School Student “Proves” Goldbach Conjecture

URL: https://bbs.hupu.com/24931041.html

According to popular Chinese Social Media, a Chinese teenager from high school has purportedly proven the difficult Goldbach Conjecture, which is that every even integer greater than two is the sum of two prime numbers.

Update: He has recently realized his mistake and deleted the post. Do check out his proof if you are interested!

Union-closed sets conjecture

Just read about this conjecture: Union-closed sets conjecture.

The conjecture states that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in the family. (Wikipedia)

It is quite interesting in the sense that the statement is extremely elementary (just basic set notation knowledge is enough to understand it). But it seems that even the experts can’t prove it.

One basic example is: {{1},{2},{1,2}}. The element 2 belongs to 2/3>1/2 of the sets in the family.