Math Professor Makes Breakthrough in Ramsey Numbers

How many people would you need at a party to guarantee that at least three individuals know each other, or that at least three do not know each other? Working this out with pen and paper may take a while, but many mathematicians will readily tell you the answer is six. This party scenario, also called the "friends and strangers" theorem, is based on a concept known as Ramsey numbers, named after early 20th-century British Mathematician Frank Ramsey. Now, imagine that more people are invited to this hypothetical party. How many would be required to ensure that at least five people know each other, or, conversely, that at least five are strangers? The answer is not clear. Indeed, mathematicians only know that the number of required people would be at least 43 and no more than 48. The actual answer falls somewhere in this range but is unknown. Add even more people to the party, and the uncertainty in the problem quickly becomes enormous.