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Pure Mathematics is the branch of mathematics that deals only with mathematics and how it works - it is the HOW of mathematics. It is abstracted from the real world and provides the "tool box" of mathematics; it includes things like calculus. Applied mathematics is the branch of mathematics which applies the techniques of Pure Mathematics to the real world - it is the WHERE of mathematics; it includes things like mechanics. Pure Mathematics teaches you HOW to integrate, Applied mathematics teaches you WHERE to use integration.
Euclid is best known for being the Father of geometry. He also created the oldest mathematical school teaching book called 'Euclid's Elements' which is still being used in school's world wide.
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Mr Andreas Ryve of Mälardalen University, Västerås and Eskilstuna, Sweden, is the youngest professor in mathematics didactics in the world. See the related link for more information.
he made the basics of algebra