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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.
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.
It is clear that numbers held a particular importance for the Pythagorean school, although it was the later work of Plato that attracts the label of mathematicism from modern philosophers. Furthermore it is René Descartes who provides the first mathematical epistemology which he describes as a mathesis universalis , and which is also referred ...
The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning ' something learned, knowledge, mathematics ', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning ' mathematical science '. It entered the English language during the Late Middle English period through French and ...
Thus Hilbert is insisting that mathematics is not an arbitrary game with arbitrary rules; rather it must agree with how our thinking, and then our speaking and writing, proceeds. [11] We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules.
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 addresses only a part of human experience. Much of human experience does not fall under science or mathematics but under the philosophy of value, including ethics, aesthetics, and political philosophy. To assert that the world can be explained via mathematics amounts to an act of faith. 4. Evolution has primed humans to think ...
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. [41] Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language.