Portal:Mathematics
Mathematics is the study of numbers, quantity, space, structure, and change. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.
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There are approximately 31,444 mathematics articles in Wikipedia.
Example of a four color map Image credit: User:Inductiveload 
The four color theorem states that given any plane separated into regions, such as a political map of the counties of a state, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color. Two regions are called adjacent if they share a border segment, not just a point. "Color by Number" worksheets and exercises, which combine learning art and math for people of young ages, are a good example of the four color theorem.
It is often the case that using only three colors is inadequate. This applies already to the map with one region surrounded by three other regions (even though with an even number of surrounding countries three colors are enough) and it is not at all difficult to prove that five colors are sufficient to color a map.
The four color theorem was the first major theorem to be proven using a computer, and the proof is disputed by some mathematicians because it would be infeasible for a human to verify by hand (see computeraided proof). Ultimately, in order to believe the proof, one has to have faith in the correctness of the compiler and hardware executing the program used for the proof.
The lack of mathematical elegance was another factor, and to paraphrase comments of the time, "a good mathematical proof is like a poem — this is a telephone directory!"
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This is a handdrawn graph of the absolute value (or modulus) of the gamma function on the complex plane, as published in the 1909 book Tables of Higher Functions, by Eugene Jahnke and Fritz Emde. Such threedimensional graphs of complicated functions were rare before the advent of highresolution computer graphics (even today, tables of values are used in many contexts to look up function values instead of consulting graphs directly). Published even before applications for the complex gamma function were discovered in theoretical physics in the 1930s, Jahnke and Emde's graph "acquired an almost iconic status", according to physicist Michael Berry. See a similar computergenerated image for comparison. When restricted to positive integers, the gamma function generates the factorials through the relation Γ(n) = (n − 1)!, which is the product of all positive integers from n − 1 down to 1 (0! is defined to be equal to 1). For real and complex numbers, the function is defined by the improper integral . This integral diverges when t is a negative integer, which is causing the spikes in the left half of the graph (these are simple poles of the function, where its values increase to infinity, analogous to asymptotes in twodimensional graphs). The gamma function has applications in quantum physics, astrophysics, and fluid dynamics, as well as in number theory and probability.
 ...that Euler found 59 more amicable numbers while for 2000 years, only 3 pairs had been found before him?
 ...that you cannot knot strings in 4dimensions? You can, however, knot 2dimensional surfaces like spheres.
 ...that there are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?
 ...that there are different sizes of infinite sets in set theory? More precisely, not all infinite cardinal numbers are equal?
 ...that every natural number can be written as the sum of four squares?
 ...that the largest known prime number is over 22 million digits long?
 ...that the set of rational numbers is equal in size to the subset of integers; that is, they can be put in onetoone correspondence?
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