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The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc.) with concision, precision and unambiguity.
Euler's identity is a special case of Euler's formula, which the physicist Richard Feynman called "our jewel" and "the most remarkable formula in mathematics". [7] Modern examples include the modularity theorem, which establishes an important connection between elliptic curves and modular forms (work on which led to the awarding of the Wolf ...
Biological secondary abilities are attained through personal experiences and cultural customs, such as reading or high level mathematics learned through schooling. [35] Literacy and numeracy are similar in the sense that they are both important skills used in life. However, they differ in the sorts of mental demands each makes.
Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. [127]
Considerations about mathematics being the language of nature can be found in the ideas of the Pythagoreans: the convictions that "Numbers rule the world" and "All is number", [7] [8] and two millennia later were also expressed by Galileo Galilei: "The book of nature is written in the language of mathematics". [9] [10]
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts. Mathematics and art have a long historical ...
For example, the tools of linguistics are not generally applied to the symbol systems of mathematics, that is, mathematics is studied in a markedly different way from other languages. If mathematics is a language, it is a different type of language from natural languages .
Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice , quasi-empiricism in mathematics , and so-called folk mathematics , oral traditions ...