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Mathematics is not a language. Your question is like asking if database-backed web applications are typed. Mathematics is often expressed in language, That lan

by gertef 9y ago

Mathematics is not a language. Your question is like asking if database-backed web applications are typed. Mathematics is often expressed in language, That language us usually a mix of a human natural language English/French/German/etc plus symbolic extensions, and that is very poorly typed. In the recent failed proof of P!=NP, the flaw was a type error: https://cstheory.stackexchange.com/questions/38803/is-norbert-blums-2017-proof-that-p-ne-np-correct/38823 https://cstheory.stackexchange.com/questions/38803/is-norber... Type errors are rather common in math proofs that end up retracted. But it's hard to call them type errors, because it's not like a computer program where the typechecker detected the collision or failed in some way: the proofs make very little mention of types at all, and it's up to the readers to apply a type-system from their own heads.

kruhft 9y ago
The conveyance of mathematics from one mind to another must be done with some form of language.
- adrianratnapala 9y ago
  This is trivially true, but only because you can keep stretching the definition of language. For example suppose a geometer explains something to another geometer just by drawing diagrams with no verbal or textual annotation. You can plausibly claim that "geometry diagrams" are a language, but now you are defining language so broadly that the term is almost useless.
  - kruhft 9y ago
    Why would you say that "geometry diagrams" are not a language? Google, define language: lan·guage ˈlaNGɡwij/Submit noun 1. the method of human communication, either spoken or written, consisting of the use of words in a structured and conventional way. "a study of the way children learn language" 2. the system of communication used by a particular community or country. "the book was translated into twenty-five languages" synonyms: tongue, mother tongue, native tongue; More I would say "geometry diagrams" are a language, by the second definition.
- guelo 9y ago
  There are loose conventions. For example, in some contexts θ and α usually designate angles. But even then the only way to know if the angle is in degrees or radians is by tracing the proof from the start. It's easy to make errors.
tom_mellior 9y ago
> In the recent failed proof of P!=NP, the flaw was a type error: The link you gave does not support this statement.

by gertef 9y ago

kruhft 9y ago

The conveyance of mathematics from one mind to another must be done with some form of language.

adrianratnapala 9y ago
This is trivially true, but only because you can keep stretching the definition of language. For example suppose a geometer explains something to another geometer just by drawing diagrams with no verbal or textual annotation. You can plausibly claim that "geometry diagrams" are a language, but now you are defining language so broadly that the term is almost useless.
- kruhft 9y ago
  Why would you say that "geometry diagrams" are not a language? Google, define language: lan·guage ˈlaNGɡwij/Submit noun 1. the method of human communication, either spoken or written, consisting of the use of words in a structured and conventional way. "a study of the way children learn language" 2. the system of communication used by a particular community or country. "the book was translated into twenty-five languages" synonyms: tongue, mother tongue, native tongue; More I would say "geometry diagrams" are a language, by the second definition.
guelo 9y ago
There are loose conventions. For example, in some contexts θ and α usually designate angles. But even then the only way to know if the angle is in degrees or radians is by tracing the proof from the start. It's easy to make errors.

tom_mellior 9y ago

> In the recent failed proof of P!=NP, the flaw was a type error: The link you gave does not support this statement.