What is the nature of maths?

Answer 1

Mathematics is a science that deals with quantity, structure, space and change (adapted from Wikipedia - Mathematics).

More generally, mathematics is a description of the natural world by means of symbol systems (numbers and symbols that stand for numbers), according to principles, laws and rules of mathematics. Maths uses deduction to apply its fundamental rules to real-world situations. The rule for the ratio of a circle's diameter and circumference can be applied to any circle in Euclidean space - that is, in two dimensions.

Go outside the two dimensions, and the rule may break down. Maths needs to be understood as having some definite limits in its real-world applicability.

Maths is criticised for its lack of rigor when applied to some situations:

a 95% chance of fatal injury when not wearing a seat belt in a high-speed crash does not mean: if 95 people have already been killed this way, the next five will survive. This is not a problem with maths - it's a problem of a lack of understanding of mathematical principles.