Philosophy of mathematics
- Does math really make sense?
- Do numbers really exist, or are they just made up?
- Can math explain everything?
- Why do people do math?
- Why do some people think math is "beautiful"?
- Is mathematics really true, or just something that we think is true?
Some ways to think about math[change | change source]
None of those questions has a clear answer, so mathematicians are free to choose which answers they like. For example:
Platonism[change | change source]
Fictionalism[change | change source]
Logicism[change | change source]
Mathematicians who believe in Logicism believe that math is true because it is based on true sentences (called axioms). It does not matter if numbers and shapes exist, or not, just that they represent true things.