Transcript:

So, what is a Ramsey number? A Ramsey number is a number of guests, the minimum number of guests that you have to invite so that some ( n ) of them mutually know each other or some ( n ) of them are complete strangers. So, when you get to this number of the guests that satisfy this condition, that number of guests is called the Ramsey number. 

For example, if you want to find what the Ramsey number for 3 is, then you need 6, minimum number of 6 guests to ensure that there are some 3 who know each other or that there are some 3 who are complete strangers. So, the Ramsey number for 3 is 6. Ramsey number for 4 is 18. Ramsey number for 5 is not known; it's between 43 and 48, something like that. Ramsey number for 6 also is not known. 

So, it's very easy to formulate this conjecture of finding Ramsey numbers but very difficult to compute it. Pretty interesting.