Mathematics is a thinking discipline that studies the internal relations between abstract things, while science is a discipline that studies the objective world. The characteristics of science are verifiability and repetition, which are also the process of falsification. Science is always advancing in constant error correction, while mathematics needs a complete system and cannot have inherent logical errors. Therefore, mathematics does not belong to science strictly, but it is the necessary foundation of all scientific research.

Supplementary example:

1. number system only expands without denying the past; The physics society in Science denies the past-Newtonian mechanics is a relativistic approximation whose speed is much less than the speed of light, but it cannot be said that real numbers are approximations of complex numbers, because complex numbers completely contain real numbers.

2. Irrational numbers can only be established by logic in any case, and will not be verified by calculating infinite decimals, but verification is the most important feature of science;

3. Science is based on objective knowledge, while mathematics is based on assumptions, and results are deduced according to logic. They are completely different in methods, purposes and systems.