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The exact origins of the LTE lemma are unclear; the result, with its present name and form, has only come into focus within the last 10 to 20 years. [1] However, several key ideas used in its proof were known to Gauss and referenced in his Disquisitiones Arithmeticae. [2]
Bayes' theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. Beckstrom's law, in economics, states that the value of a network equals the net value added to each user's transactions conducted through that network, summed over all users. Named for Rod Beckstrom.
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem.
Subsidiarity is a principle of social organization that holds that social and political issues should be dealt with at the most immediate or local level that is consistent with their resolution.
Stokes' theorem. It is named after Sir George Gabriel Stokes (1819–1903), although the first known statement of the theorem is by William Thomson (Lord Kelvin) and appears in a letter of his to Stokes. The theorem acquired its name from Stokes' habit of including it in the Cambridge prize examinations. In 1854 he asked his students to prove ...
With the increase in computing power in the 1960s, significant work began to be done investigating mathematical objects beyond the proof-theorem framework, [27] in experimental mathematics. Early pioneers of these methods intended the work ultimately to be resolved into a classical proof-theorem framework, e.g. the early development of fractal ...
The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus (of some formal system) to the previous well-formed formulas in the proof sequence.
The theorem implies both the Hermite–Lindemann and Gelfond–Schneider theorems. [8] The theorem deals with a number field K and meromorphic functions f 1 ,..., f N of order at most ρ , at least two of which are algebraically independent, and such that if we differentiate any of these functions then the result is a polynomial in all of the ...