Relying upon math experts and enthusiasts to define the subject is likely to lead to a variety of conflicting and wide-ranging answers. Let’s be safe, then, and call upon dictionary solutions to this question. Most non-specialist dictionaries define mathematics by summarizing the main mathematics topics and methods.
The Oxford English Dictionary states that mathematics is an “abstract science which investigates deductively the conclusions implicit in the elementary concepts of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra”. The American Heritage Dictionary sums up the subject as the “study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols”.