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It created mathematical proof for the Pythagorean theorem, [112] and a mathematical formula for Gaussian elimination. [113] The treatise also provides values of π , [ 107 ] which Chinese mathematicians originally approximated as 3 until Liu Xin (d. 23 AD) provided a figure of 3.1457 and subsequently Zhang Heng (78–139) approximated pi as 3. ...
The development of mathematical proof is primarily the product of ancient Greek mathematics, and one of its greatest achievements. [9] Thales (624–546 BCE) and Hippocrates of Chios (c. 470–410 BCE) gave some of the first known proofs of theorems in geometry.
In other words, despite their claim of mathematics being human, established mathematical knowledge — which is what we learn in school — is assumed to be and treated as abstract, completely detached from its physical origin. It cannot account for the way learners could access to such knowledge. [7] WMCF is also criticized for its monist ...
The independence of the mathematical objects is such that they are non physical and do not exist in space or time. Neither does their existence rely on thought or language. For this reason, mathematical proofs are discovered, not invented. The proof existed before its discovery, and merely became known to the one who discovered it. [13]
Bertrand's postulate and a proof; Estimation of covariance matrices; Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational
Thus the only thing we do not have is a formal proof of consistency of whatever version of set theory we may prefer, such as ZF. In practice, most mathematicians either do not work from axiomatic systems, or if they do, do not doubt the consistency of ZFC, generally their preferred axiomatic system. In most of mathematics as it is practiced ...
[8] [9] Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. [10] Contemporaneous with but independent of these traditions were the mathematics developed by the Maya civilization of Mexico and Central America, where the concept of zero was given a standard symbol in Maya numerals.
God Created the Integers: The Mathematical Breakthroughs That Changed History is a 2005 anthology, edited by Stephen Hawking, of "excerpts from thirty-one of the most important works in the history of mathematics." [1] Each chapter of the work focuses on a different mathematician and begins with a biographical overview. Within each chapter ...