Is science a part of math?
In many ways, math is closely related to science. Mathematics is a scholarly domain, and so the mathematical community works as the scientific community does — mathematicians build on each other's work and behave in ways that push the discipline forward. This progress contributes to scientific breakthroughs.
Mathematics is certainly a science in the broad sense of "systematic and formulated knowledge", but most people use "science" to refer only to the natural sciences.
Mathematics, in the broadest sense, is just a synonym of formal science; but traditionally mathematics means more specifically the coalition of four areas: arithmetic, algebra, geometry, and analysis, which are, to some degree, the study of quantity, structure, space, and change respectively.
Science is based on observation, hypothesis, and experimentation. Math is one of the languages used by science to express hypotheses, but not all hypotheses are expressed this way. It is easy to mistakenly think that some (hard) sciences, like physics, are based on math since math is so prevalent.
Most science students know that the sciences use a lot of math. After all, all science disciplines require that students take a number of math courses. Research papers in professional journals often contain lots of what is clearly math, including in recent years many biomedical research journals.
Eminent biologist E. O. Wilson, however, has good news for science lovers who are wary of higher math: You don't have to be great at math to do great science. In fact, "Many of the most successful scientists in the world today are mathematically no more than semiliterate," he writes.
In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation.
Mathematics is an intrinsic component of science, part of its fabric, its universal language and indispensable source of intellectual tools. Reciprocally, science inspires and stimulates mathematics, posing new questions, engendering new ways of thinking, and ultimately conditioning the value system of mathematics.
Mathematics is both an art and a science, and pure mathematics lies at its heart. Pure mathematics explores the boundary of mathematics and pure reason.
The main branches of mathematics are algebra, number theory, geometry and arithmetic.
Is math the mother of science?
Mathematics is considered as the mother of all sciences because it is a tool which solves problems of every other science. Other subjects like biology, Chemistry or Physics is based on simple chemical solutions.
Mathematics is a living science, where problems and theory come from the discipline itself. As such, pure mathematics can be considered both as an art and a science. Mathematics is actually much more than just a tool and methodology!
Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.