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Some people think that mathematics can also be seen as a language. I use this categorization quite frequently nowadays and it really simplifies my work a lot. B

Some people think that mathematics can also be seen as a language. I use this categorization quite frequently nowadays and it really simplifies my work a lot. By not using a more elaborate mathematical notation, you basically are able explain mathematical concepts to people who are not "speaking math" like you would explain the work of Montesquieu to anyone not speaking french: It takes more time and effort, and francophone readers of Montesquieu will hate you for doing it. ;)

Koshkin 9y ago
On the other hand, some things can get lost in translation. This, of course, depends on the language (and culture), and mathematics is probably the strongest example of such language (with, say, physics being the "culture").
eftychis 9y ago
Skipping the notation sure is nice and fine as long as you don't end up losing any of its benefits. The whole idea of notation/language is: 1.to have a common reference for each definition that is explicit 2. forces you to define and handle proofs from a proper angle of detail (think of it like trying to write the specification of a data structure and an algorithm in prose instead of Haskell, C, some assembly dialect. This is actually interesting because what people call "math language" comprises a wide variety of different styles, like programming languages do. 2. concise -- again and again using notation and prior well-defined notions saves a lot of time and space; you don't tangle on the properties of registers for everything you do. I would say that mathematics has a variety of languages that were, and are introduced per area, to go along. If you have a programming languages background you are familiar with the setting (and joke) that each new work defines a new (somewhat) programming language. In general, there is a reason computer science is regarded to be that close to math.

Koshkin 9y ago

On the other hand, some things can get lost in translation. This, of course, depends on the language (and culture), and mathematics is probably the strongest example of such language (with, say, physics being the "culture").

eftychis 9y ago

Skipping the notation sure is nice and fine as long as you don't end up losing any of its benefits. The whole idea of notation/language is: 1.to have a common reference for each definition that is explicit 2. forces you to define and handle proofs from a proper angle of detail (think of it like trying to write the specification of a data structure and an algorithm in prose instead of Haskell, C, some assembly dialect. This is actually interesting because what people call "math language" comprises a wide variety of different styles, like programming languages do. 2. concise -- again and again using notation and prior well-defined notions saves a lot of time and space; you don't tangle on the properties of registers for everything you do. I would say that mathematics has a variety of languages that were, and are introduced per area, to go along. If you have a programming languages background you are familiar with the setting (and joke) that each new work defines a new (somewhat) programming language. In general, there is a reason computer science is regarded to be that close to math.