Editing Language of mathematics (section)

==Understanding mathematical text==
The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "''a [[free module]] is a [[module (mathematics)|module]] that has a [[basis (linear algebra)|basis]]''" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of ''basis'', ''module'', and ''free module''.

[[Horatio Burt Williams|H. B. Williams]], an [[electrophysiologist]], wrote in 1927:
{{blockquote |Now mathematics is both a body of truth and a special language, a language more carefully defined and more highly abstracted than our ordinary medium of thought and expression. Also it differs from ordinary languages in this important particular: it is subject to rules of manipulation. Once a statement is cast into mathematical form it may be manipulated in accordance with these rules and every configuration of the symbols will represent facts in harmony with and dependent on those contained in the original statement. Now this comes very close to what we conceive the action of the brain structures to be in performing intellectual acts with the symbols of ordinary language. In a sense, therefore, the mathematician has been able to perfect a device through which a part of the labor of logical thought is carried on outside the [[central nervous system]] with only that supervision which is requisite to manipulate the symbols in accordance with the rules.<ref name=HBW>[[Horatio Burt Williams]] (1927) [https://projecteuclid.org/euclid.bams/1183492099 Mathematics and the Biological Sciences], [[Bulletin of the American Mathematical Society]] 33(3): 273–94 via [[Project Euclid]]</ref>{{rp| 291}}}}