why math is the branch of science
Answers
Because we take help of mathematics for measurements, predictions and calculations.
Neither. Science uses mathematics as a means of describing relationships, but the point of science is not aesthetics or precision, as it is in mathematics. Mathematics is about truth. Science is not (contrary to popular belief). Science is about making extremely accurate estimates of reality (as accurate as can be measured, given our limited knowledge, which varies from one area of study to the next), which can be used for prediction within constraints. It also always takes into account the fallibility of scientists and the instruments they use. Mathematics tries to find abstract truths re. assertions, which can come from many sources, not all of them relating to reality. The conclusions that are drawn from it also do not have to have any relationship to real phenomena, though it's a requirement in applied mathematics.
They share some qualities. Both value concepts which explain one thing, but also have relevance to other concepts. Mathematicians conduct thought experiments, to try to find new truths, and this has a scientific quality to it. Mathematicians are also very interested in patterns, as are scientists.
The difference between them can be summed up as mathematicians understand mathematics as an art--a thing unto itself. Scientists understand it as an essential tool for analysis and modeling.