There were three major points of view in the debate about the nature of mathematics the formalists argued roughly the short summaries that follow are really caricatures that mathematics was really simply the formal manipulation of symbols based on arbitrarily chosen axioms. Virtually all philosophers treat mathematics as isolated timeless ahistorical inhuman in what is mathematics really renowned mathematician reuben hersh argues the contrary in a subversive attack on traditional philosophies of mathematics most notably platonism and formalism he shows that mathematics must be understood as a human activity a social phenomenon part of human culture . What is mathematics really january 1998 mitteilungen der deutschen mathematiker vereinigung 62 doi 101515 dmvm 1998 0205 authors reuben hersh university of new mexico download full text . Mathematics is the science that deals with the logic of shape quantity and arrangement math is all around us in everything we do it is the building block for everything in our daily lives