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Mathematics (also math or maths, from Greek *mathematicos*, *learned*) is the best [science](science.md) (yes, it is a formal science), which deductively deals with [numbers](number.md) and other [abstract](abstraction.md) structures with the use of pure [logic](logic.md), in as rigorous and objective way as possible. In fact it's the only true science that can actually prove facts thanks to its tool of mathematical [proof](proof.md) (other sciences may only disprove or show something to be very [probable](probability.md)). It's an immensely important discipline for [programming](programming.md) and [computer science](compsci.md). Mathematics is possibly intellectually the most difficult field to study in depth, meant only for the smartest; the difficulty, as some mathematicians point out, comes especially from the exceptionally deep [abstraction](abstraction.md) (pure mathematics often examines subjects with no obvious connection to reality and only exist as a quirk of logic itself). It is said that mathematics is the only **universal [language](language.md)** in our [universe](universe.md) -- if we were ever to establish contact with an intelligent alien civilization, we'd likely use mathematics for communication. While most people only ever learn basic algebra and some other mechanical operations that are necessary for mathematics, true mathematics is not about blind calculation, it is a creative discipline and [art](art.md) of constructing [proofs](proof.md) from basic [axioms](axiom.md), sometimes so difficult that a solution demands many lifetimes of the brightest minds.
Some see math not as a science but rather a discipline that develops formal tools for "true sciences". The reasoning is usually that a science has to use [scientific method](scientific_method.md), but that's a limited view as scientific method is not the only way of obtaining reliable knowledge. Besides that math can and does use the principles of scientific method -- mathematicians first perform "experiments" with numbers and generalize into [conjectures](conjecture.md) and later "strong beliefs", however this is not considered [good enough](good_enough.md) in math as it actually has the superior tool of [proof](proof.md) that is considered the ultimate goal of math. I.e. math relies on [deductive](deduction.md) reasoning (proof) rather than less reliable [inductive](induction.md) reasoning (scientific method) -- in this sense mathematics is more than a science.
Some (especially the [English](english.md) speaking world) perceive math not as a science but rather a discipline that develops formal tools for "true sciences". The reasoning is usually that a science has to use [scientific method](scientific_method.md), but that's a limited view as scientific method is not the only way of obtaining reliable knowledge. Besides that math can and does use the principles of scientific method -- mathematicians first perform "experiments" with numbers and generalize into [conjectures](conjecture.md) and later "strong beliefs", however this is not considered [good enough](good_enough.md) in math as it actually has the superior tool of [proof](proof.md) that is considered the ultimate goal of math. I.e. math relies on [deductive](deduction.md) reasoning (proof) rather than less reliable [inductive](induction.md) reasoning (scientific method) -- in this sense mathematics is more than a science.
Mathematics as a whole is constructed with [logic](logic.md) from some basic system -- [historically](history.md) it was based e.g. on [geometry](geometry.md), however modern mathematics has since about 19th century been built on top of **[set theory](set_theory.md)**, i.e. all thing such as [numbers](number.md), [algebra](algebra.md) and [functions](function.md) are all derived from just the existence of [sets](set.md) and [classes](class.md) and some basic operations with them. Specifically *Zermelo–Fraenkel set theory with [axiom of choice](axiom_of_choice.md)* (ZFC, made in the beginning of 20th century) is mostly used nowadays -- it's a theory with 9 [axioms](axiom.md) that we can consider kind of ["assembly"](assembly.md) of mathematics.