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The Hilbertian position differs because it depends on a distinction within mathematical language between a finitary sector, whose sentences express contentful propositions, and an ideal, or infinitary sector.
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The division of mathematical theory into "definitions" and "theorems" may be considered as a distinction between mathematical language and content, respectively.
The abc conjecture describes this connection in precise mathematical language, highlighting how the underlying "tension" between the operations of addition and multiplication produce such lopsided equations: many small primes on one side, a few relatively large primes on the other.
More research is needed on this, for example about the relation between the amount of topics covered and student learning of formal mathematical language such as algebraic symbolic expressions in school mathematics.
As a matter of practice, we use a language to state the properties, and in informal mathematics, this is a mixture of natural language and special mathematical language.
"English, to me, is a more mathematical language, it is the language of precision.
Strip away the mathematical language of economists, and conventional theories of economic growth are rather crude.
Decoding the mathematical language of science and translating it to an interesting story is far from trivial.
He made a special mathematical language for the machine one that he and Minsky thought children might like called the LOGO language.
While the T/NT dichotomy in a way distinguishes between content and pure language, the F/NF dichotomy measures to what extent the mathematical language involved is "formal".
into a coherent mathematical language [11].
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com