## Question

• Write about one mathematical progress or one mathematician in the period after creation of Calculus up to Poincare.

• Review the history of one of the three major branches of mathematics: Algebra (quadratic equations, cubic equations, equations of several variables, modern notations, Abel-Galois theorem, the concept of vectors, complex numbers, ...)

• Review the history of one of the three major branches of mathematics: Geometry (classical geometric problems, Euclidean geometric, conic sections, non-Euclidean geometry, Rieammnian geometry, topology, ....)

• Review the history of one of the three major branches of mathematics: Analysis (Zeno’s paradoxes, Archimedes’ exhaustion theorem, Descartes and Format’s work, calculus, rigorous theory of calculus, ....)

## Solution Preview

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1) Georg Ferdinand Ludwig Philipp Cantor was a German mathematician who invented the set theory or the fundamental theory. He stated that why the importance of one to one correspondence is very necessary for member of two sets which can be like real numbers, infinite numbers, well ordered sets, natural numbers etc. Cantor proved this theory is based on existence of infinity. He states that all cardinal and ordinal numbers are arithmetic. Cantor theory of transfinite numbers was challenge to the uniqueness of the absolute infinity. Cantor’s proof was that the algebraic numbers are countable and the transcend numbers are uncountable. But this theory harsh criticism but still became an integral part of world....

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