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Why mathematics is called the queen of science?
Carl Friedrich Gauss, a famous mathematician, said that "Mathematics is the queen of the sciences and number theory is the queen of mathematics."
Who was a famous series whose mathematics occurs in nature?
The Fibonacci series.
Who are some famous mathematicians and what are some examples of their work?
This question is too general to give a short answer to. The top three names are usually considered to be Archimedes, Newton, Gauss (in historical order). Some more are Euclid, Fermat, Leibniz, the Bernoulli family, Euler, Laplace, Lagrange, Weierstrass, Hilbert, Noether, von Neumann. A very extensive website is http://www-history.mcs.st-and.ac.uk/ - look at the Biographies Index. There is an overwhelming amount of information here. A book on the history of mathematics will give an overview.
Why was Euclid famous?
He is famous for his Elements, a presentation in thirteen books of the geometry and other mathematics known in his day.He also was the first person to study geometry.
What is pure math?
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.
