Different types of numbers are used in many cases. Numbers can be classified into sets, called number systems. (For different methods of expressing numbers with symbols, such as the Roman numerals, se ...
A number is a mathematical object used to count, label, and measure. In mathematics, the definition of number has been extended over the years to include such numbers as 0, negative numbers, rational ...
Millennium Prize Problems Of the seven Millennium Prize Problems set by the Clay Mathematics Institute, six have yet to be solved:P versus NPHodge conjectureRiemann hypothesisYang–Mills existence and ...
There are an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geograph ...
If one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefor ...
Sumerian astronomers studied angle measure, using a division of circles into 360 degrees. They, and later the Babylonians, studied the ratios of the sides of similar triangles and discovered some prop ...
Trigonometry (from Greek trigōnon, "triangle" + metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged during the 3rd ce ...
Logic, especially in the field of proof theory, considers theorems as statements (called formulas or well formed formulas) of a formal language. The statements of the language are strings of symbols a ...
It has been estimated that over a quarter of a million theorems are proved every year.The well-known aphorism, "A mathematician is a device for turning coffee into theorems", is probably due to Alfré ...
A theorem and its proof are typically laid out as follows:Theorem (name of person who proved it and year of discovery, proof or publication).Statement of theorem (sometimes called the proposition).Pro ...
A number of different terms for mathematical statements exist, these terms indicate the role statements play in a particular subject. The distinction between different terms is sometimes rather arbitr ...
Theorems in mathematics and theories in science are fundamentally different in their epistemology. A scientific theory cannot be proven; its key attribute is that it is falsifiable, that is, it makes ...
To establish a mathematical statement as a theorem, a proof is required, that is, a line of reasoning from axioms in the system (and other, already established theorems) to the given statement must be ...
Logically, many theorems are of the form of an indicative conditional: if A, then B. Such a theorem does not assert B, only that B is a necessary consequence of A. In this case A is called the hypothe ...
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms. The proof of ...
