You ask what mathematics represent to me. Let me say that I like the idea that mathematics is the music of reason. To my understanding, mathematics is the queen of sciences, that is, mathematics is the door and the key to sciences. Therefore, I think that the more a science is mathematized, the more advanced it is.To an extent, numbers -- which lies at the very nature of mathematics -- are intellectual witnesses that belong to mankind. Mathematics also reminds me of an infinite universe. Note that, for example, the sequence of cardinal positive numbers (i.e, 1, 2, 4, 5, 6, and so forth) never ends. In other words, such as there is always something to be found and known when we look for the unknown hidden in the physical universe, there is always, for example, a prime number to be discovered when we look, for instance, for a not yet known prime number. Mathematics also represents to me not only what is true, but mainly what is necessary. Note, for example, that there would be no logical contradiction if bodies did not become hot when they are heated. This means that physical truths are only contingent truths. However, it would contradictory to affirm that, in the case of an "if p, then q" statement, q has not to be case when p is the case. Accordingly, mathematics and logic reminds me of necessary knowledge -- what is the case and has to be the case because it cannot be otherwise. And physics reminds me of true knowledge -- what is the case, but could not be the case.
In fact , I read beautiful saying about mathematics that attracts me .." God used the beauty of mathematics in creating the world "..Physicist Paul Dirac
"Pure mathematics is, in its way, the poetry of logical ideas" Albert Einstein
My husband is a mathematician and he used to tell me that mathematics may not teach us how to add love or minus hate but it gives us every reason to hope that every problem has a solution.