30 Greatest Breakthroughs in Mathematics

Ancient Humanity develops the know how to reason and comprehend numbers.
Development of the standard operations of Addition, Subtraction, Multiplication and Division.
The development of Fractions.
The development of the concept of the positive and negative integer.
Euclid formalizes Geometric Knowledge.
Early Development of Algebra by the Ancient Greeks and Arabs.
The development of the number zero by the Ancient Indians.
Arab Numerals make their way into the Western World.
Rene Descartes creates the discipline of Cartesian Geometry. Birth of the Era of the Graph.
Issac Netwton and Gottfried Leibnitz independently invent the calculus.
Birth of the discipline of trigonometry.
Indians develop what will later become known as Pythagoras's Theorem.
Development of the concept of the vector and n-space: Birth of Vector Algebra and Vector Geometry.
Blaise Pascal's work gives rise to Probability Theory.
The development of logarithms as a calculating technique by John Napier.
Development of Statistics as a mathematical discipline.
Development of the discipline of Numerical iteration by messrs: Newton, Simpson, Euler and Runge-Kutte.
Development of Matrix Algebra by Messrs Gauss, Jordan.
Geometrical work on the Theory of Conic Sections.
Development of the concept of Irrational numbers.
The Development of Set Theory.
Number Theory comes to light in the 19th century.
Invention of the concept of the Imaginary Number.
Invention of the discipline of game theory.
The development of Chaos Theory in the 20th century.
Birth of the discipline of surface topography.
Development of the concept of infinity.
Development of the mathematics of Solids and Crystals.
Omar Khayyam Develops the Binomial Theorem.
Formalization of Fermat's Last Theorem (by Pierre Fermat) and its eventual proof by Andrew Wiley.