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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.
Paulus Gerdes' writings about how mathematics can be used in the school systems of Mozambique and South Africa, and D'Ambrosio's 1990 discussion of the role mathematics plays in building a democratic and just society are examples of the impact mathematics can have on developing the identity of a society. In 1990, Bishop also writes about the ...
For example, mathematical beauty arises in a Math Circle activity on symmetry designed for 2nd and 3rd graders, where students create their own snowflakes by folding a square piece of paper and cutting out designs of their choice along the edges of the folded paper. When the paper is unfolded, a symmetrical design reveals itself.
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]
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 .
German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
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 ...
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]