Sentence examples for mathematics is not from inspiring English sources

This seems to contradict mathematical methodology; mathematics is not empirical (at least not usually), and most mathematical truths (e.g., "2 + 3 = 5") cannot be empirically falsified by discoveries about the nature of the physical world.

I would say it is difficult to acquire deep mathematical skills if mathematics is not the first area of study, although I have met biologists who are quite good in certain areas of mathematics related to their work.

The involvement of mathematical theory in TIMSS Advanced mathematics is, not surprisingly, found to be much larger than in all the other studies.

The weak counterexamples, introduced by Brouwer in 1908, are the first examples that Brouwer used to show that the shift from a classical to an intuitionistic conception of mathematics is not without consequence for the mathematical truths that can be established according to these philosophies.

In philosophy of mathematics, he and his mentor W. V. Quine developed the "Quine Putnam indispensability thesis", an argument for the reality of mathematical entities, later espousing the view that mathematics is not purely logical, but "quasi-empirical".

Steps are mathematical equations, so anyone who doesn't understand mathematics is not going to understand how to remember steps… The steps in themselves have no meaning.

However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models.

Mathematics is not a spectator sport.

"Science is discovering the laws of the natural world, and mathematics isn't that, it's logical, deductive truth, and its experiments don't have error bars," he said.

The Bush Administration is pushing to prove Albert Einstein's maxim that mathematics isn't necessarily reality.

But mathematics isn't reality, while consciousness is.