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In the later 19th century, Georg Cantor established the first foundations of set theory, which enabled the rigorous treatment of the notion of infinity and has become the common language of nearly all mathematics. Cantor's set theory, and the rise of mathematical logic in the hands of Peano, L.E.J. Brouwer, David Hilbert, Bertrand Russell, and ...
Two abstract areas of modern mathematics are category theory and model theory. Bertrand Russell [94] once said, "Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say."
The origin of language, its relationship with human evolution, and its consequences have been subjects of study for centuries.Scholars wishing to study the origins of language draw inferences from evidence such as the fossil record, archaeological evidence, contemporary language diversity, studies of language acquisition, and comparisons between human language and systems of animal ...
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 ...
The highly diverse Nilo-Saharan languages, first proposed as a family by Joseph Greenberg in 1963 might have originated in the Upper Paleolithic. [1] Given the presence of a tripartite number system in modern Nilo-Saharan languages, linguist N.A. Blench inferred a noun classifier in the proto-language, distributed based on water courses in the Sahara during the "wet period" of the Neolithic ...
This is a timeline of pure and applied mathematics history.It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic ...
The history of logic deals with the study of the development of the science of valid inference ().Formal logics developed in ancient times in India, China, and Greece.Greek methods, particularly Aristotelian logic (or term logic) as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. [1]
The scope of the history of knowledge encompass all the discovered and created fields of human-derived knowledge such as logic, philosophy, mathematics, science, sociology, psychology and data mining. [3] The history of knowledge is an academic discipline that studies forms of knowledge in the recorded past. [4]