Philosophy of mathematics
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities.
Major themes that are dealt with in philosophy of mathematics include:
Major themes[edit]
Reality[edit]
The connection between mathematics and material reality has led to philosophical debates since at least the time of Pythagoras. The ancient philosopher Plato argued that abstractions that reflect material reality have themselves a reality that exists outside space and time. As a result, the philosophical view that mathematical objects somehow exist on their own in abstraction is often referred to as Platonism. Independently of their possible philosophical opinions, modern mathematicians may be generally considered as Platonists, since they think of and talk of their objects of study as real objects (see Mathematical object).[1]
Armand Borel summarized this view of mathematics reality as follows, and provided quotations of G. H. Hardy, Charles Hermite, Henri Poincaré and Albert Einstein that support his views.[2]
Contemporary schools of thought[edit]
Artistic[edit]
The view that claims that mathematics is the aesthetic combination of assumptions, and then also claims that mathematics is an art. A famous mathematician who claims that is the British G. H. Hardy.[32] For Hardy, in his book, A Mathematician's Apology, the definition of mathematics was more like the aesthetic combination of concepts.[33]