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black holes. So far, all tests of general relativity have been shown to be in agreement with the theory. The timedependent solutions of general relativity enable us to talk about the history of the universe and have provided the modern framework for cosmology, thus leading to the discovery of the Big Bang and cosmic microwave background radiation. Despite the introduction of a number of alternative theories, general relativity continues to be the simplest theory consistent with experimental data. (Full article...)


An actuary is a professional with advanced mathematical skills who deals with the measurement and management of risk and uncertainty. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms. The name of the corresponding academic discipline is actuarial science.
While the concept of insurance dates to antiquity, the concepts needed to scientifically measure and mitigate risks have their origins in the 17th century studies of probability and annuities. Actuaries of the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems to design programs that manage risk, by determining if the implementation of strategies proposed for mitigating potential risks, does not exceed the expected cost of those risks actualized. The steps needed to become an actuary, including education and licensing, are specific to a given country, with various additional requirements applied by regional administrative units; however, almost all processes impart universal principles of risk assessment, statistical analysis, and risk mitigation, involving rigorously structured training and examination schedules, taking many years to complete. (Full article...) 





The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as are commonlyEgyptians and Babylonians, required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians made a fivedigit approximation, both using geometrical techniques. The first computational formula for π, based on infinite series, was discovered a millennium later. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by the Welsh mathematician William Jones in 1706. (Full article...)




Inrational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of its mathematical predictions have since been proven rigorously. (Full article...)

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In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.
For example,
is a matrix with two rows and three columns. This is often referred to as a "twobythree matrix", a " matrix", or a matrix of dimension . (Full article...) 

Orestes, the Roman prefect of Alexandria, who was in the midst of a political feud with Cyril, the bishop of Alexandria. Rumors spread accusing her of preventing Orestes from reconciling with Cyril and, in March 415 AD, she was murdered by a mob of Christians led by a lector named Peter. (Full article...)



In number theory, specifically the study of Diophantine approximation, the lonely runner conjecture is a conjecture about the longterm behavior of runners on a circular track. It states that runners on a track of unit length, with constant speeds all distinct from one another, will each be lonely at some time—at least units away from all others.
The conjecture was first posed in 1967 by German mathematician Jörg M. Wills, in purely numbertheoretic terms, and independently in 1974 by T. W. Cusick; its illustrative and nowpopular formulation dates to 1998. The conjecture is known to be true for seven runners or fewer, but the general case remains unsolved. Implications of the conjecture include solutions to viewobstruction problems and bounds on properties, related tochromatic numbers, of certain graphs. (Full article...) 

The Erdős–Straus conjecture is an unproven statement in number theory. The conjecture is that, for every integer that is 2 or more, there exist positive integers , , and for which
In other words, the number can be written as a sum of three positiveconjectures by Erdős, and one of many unsolved problems in mathematics concerning Diophantine equations. (Full article...) 



Did you know (autogenerated) –
 ... that after Florida schools banned 54 mathematics books, Chaz Stevens petitioned that they also ban the Bible?
 ... that the prologue to The Polymath was written by Martin Kemp, a leading expert on Leonardo da Vinci?
 ... that in the aftermath of the American Civil War, the only Blackled organization providing teachers to formerly enslaved people was the African Civilization Society?
 ... that two members of the French parliament were killed when a delayedaction German bomb exploded in the town hall at Bapaume on 25 March 1917?
 ... that the British National Hospital Service Reserve trained volunteers to carry out first aid in the aftermath of a nuclear or chemical attack?
 ... that mathematician Mathias Metternich was one of the founders of the Jacobin club of the Republic of Mainz?
 ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
 ... that more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
More did you know –
 ...that amicable numberswhile for 2000 years, only 3 pairs had been found before him?
 ...that you cannot knot strings in 4 dimensions, but you can knot 2dimensional surfaces, such as spheres?
 ...that there are 6 unsolved mathematics problemswhose 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 milliondigits long?
 ...that the set of onetoone correspondence?
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A homotopy from a circle around a sphere down to a single point. Image credit: Richard Morris 
The
The goal of algebraic topology is to categorize or classify topological spaces. Homotopy groups were invented in the late 19th century as a tool for such classification, in effect using the set of mappings from a csphere into a space as a way to probe the structure of that space. An obvious question was how this new tool would work on nspheres themselves. No general solution to this question has been found to date, but many homotopy groups of spheres have been computed and the results are surprisingly rich and complicated. The study of the homotopy groups of spheres has led to the development of many powerful tools used in algebraic topology. (Full article...)
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 ^ Coxeter et al. (1999), p. 30–31 ; Wenninger (1971), p. 65 .