Math is fundamentally different from science. Math is about constructs of the mind, such as "numbers" and "primes" and "equalateral triangles" and their relationships. It may or may not apply to physical reality, but there need not be such a reality for the concepts to have strict logical consistancy.
Science, OTOH, is about nature and the way things work. Light moves at a certain speed, bends through water and gravitational fields, and can dislodge electrons from certain metals. When you mix certain chemicals, they change color or explode. Electric current causes compass needles to move. Etc. Scientific "facts" are less strongly known than mathematical facts - there could be some level of external gravitational field, or velocity, at which what is believed to be true turns out to be measurably not so. But the fact that 2+2 = 2x2 = 2^2 does not depend on gravity, the speed of light, or anything else.
there are an infinite number of primes is untestable. This truth is easy to prove but impossible to test.
I disagree: the proof is not only simple, but it certainly generates what must be an infinite list of primes. The proof is, take all the primes you know of, multiply them together, and add 1. The new number can't possibly be wholly divided by any of its divisors - it therefore must be prime or be a composite number containing prime factors not in the original list. No matter how many primes you multiply, there is always at least one more. Hence, the number of primes must be, quite simply, infinite.
But I’m not a mathematician and perhaps a rigorous proof is equivalent to a test. I differentiate the two myself.
A proof is different from a test: A proof is a demonstration of certainty, while a test is merely a demonstration of likelihood. To my knowledge there are no proofs in science: It might yet be shown that everything presently understood is wrong within some domain, that we haven't explored yet and might not even be aware exists.
Not sure I'm following you here. E.g., suppose you only "knew about" the primes 3 and 5. Multiplying them and adding 1 gives you 16, which is certainly dividable. (3x5x7)+1 is 106, etc.
Excellent response, and my only, not very important, objection is to the above.
There are many, "proofs," in both science and technology (think computer science) as well. Many proofs are actually applications of the abstract, "sciences," to the real world. In topology, for example, how various real physical configurations can or cannot behave can be proved (consider the Mobius band), not by observation, but by the application of topological principles.
Chemistry involves myraid proofs of both composition and behavior. (The double helix of DNA is not a hypothesis but a proven theory.) (The entire periodic table is a huge proof of many different hypotheses.) The laser is "proof" of certain quantum mechanics principles applied to nature of light.
Hank
1 X 1 = 1. 1+1=2, not a prime number. :)
hehe......I'm just playin'