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Greek mathematics refers to the mathematics written in the Greek language from the time of Thales of Miletus (~600 BC) to the closure of the Academy of Athens in 529 AD. [39] Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language.
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]
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 ...
For example, in mathematics, "or" means "one, the other or both", while, in common language, it is either ambiguous or means "one or the other but not both" (in mathematics, the latter is called "exclusive or"). Finally, many mathematical terms are common words that are used with a completely different meaning. [100]
Greek mathematics constitutes an important period in the history of mathematics: fundamental in respect of geometry and for the idea of formal proof. [44] Greek mathematicians also contributed to number theory , mathematical astronomy , combinatorics , mathematical physics , and, at times, approached ideas close to the integral calculus .
[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.
If mathematics is a language, it is a different type of language from natural languages. Indeed, because of the need for clarity and specificity, the language of mathematics is far more constrained than natural languages studied by linguists.
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."