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'mathematical reasoning' is a correct and usable phrase in written English.
It is typically used to refer to one's ability to use logical and analytical thinking to solve a mathematical problem. For example, "He is an excellent student, with a strong aptitude for mathematical reasoning."
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The National Council of Teachers of Mathematics has pressed for more mathematical reasoning and less memorizing of facts and formulas.
Such loose mathematical reasoning would have riled a punctilious logician like Dodgson.
He is also the author of books that include "How the Other Half Thinks: Adventures in Mathematical Reasoning".
In The Theory of Political Coalitions (1962), Riker demonstrated by mathematical reasoning why and how politicians form alliances.
It combines experiment with mathematical reasoning, even if it is generally used for validation rather than discovery.
Much of what earlier philosophers said of mathematical reasoning must, thus, be understood as applying to relational (first-order) reasoning.
One of these, called Alice Heim 4-I, is a series of 65 verbal and mathematical reasoning problems which get progressively more difficult.
Mathematics was developed once and collectively — your culture cannot be complete if you don't have at least a glimpse of what is mathematical reasoning".
Primarily a mathematician, Frege's interest in language developed as a result of his attempt to devise a logical notation adequate for the formalization of mathematical reasoning.
Some children are especially proficient with verbal problems and less proficient at problems involving spatial relations or mathematical reasoning, for example.
Such descriptions are commonly used in formal mathematical reasoning, as in a proof by reductio ad absurdum that there is no greatest prime number.
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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