3 days ago , i had a discussion with a close friend who studies physics - still a student - . and i was telling her about the biggest known numbers in maths , so i told her about numbers such googol and googolplex, then about Graham number and she asked me , what is the application of this number in maths problems ? i answered , it's a solution of a famous problem in Ramsey theory and Ramsey theory is a branch if modern mathematics .
but suddenly , the question arise ! what is Ramsey theory ? what is its importance ? has it any relation with other branches like mathematical logic or group theory ?
is it advanced topic in maths ?
so i have googled and found that it's a branch which talk about the properties of particular structures in maths when we divide this structure into new substructures .
this is all what i could understand !
so can give us more information , reference for beginners , application of it in other branches in science like physics or chemistry , the relation with other mathematical branches and resources for more readings ?