Mathematics is necessarily true, but only to the extent it deals with mathematical objects, which are conceptual. There is potentially a difficulty in mapping the real world to mathematical objects.

So here I have "three apples", and I map that to the mathematical object 3.
And there I have "four apples", and I map that to the mathematical object 4.

It is objectively and necessarily true in the mathematical world that 3 + 4 = 7.

I map that 7 back to the real world and deduce that I have "seven apples".

Are we allowed to do that? Now it may seem utterly obvious that to the extent that 3+4=7 (and while that looks fairly simple, many other mathematical truths, while much harder to prove, like Fermat's last theorem, are just as utterly true), then 3 apples + 4 apples = 7 apples.

But 3ml of water + 4 ml of pure alcohol doesn't give 7ml of diluted alcohol. The "3" in 3ml doesn't map so well to the 3 in 3+4=7 as it did with apples, nor did the + work so well when we mixed the liquids. Even if did it as 3g + 4g and weighed the result with sufficient sensitivity, I would actually find a very small mass change (teh very fact that I call it a mass change implicitly assumes that addition works for adding masses of substances).

We do an awful lot of mathematics, geometry and more, in Euclidean space. This admits unlimited division, which doesn't match very well to what quantum mechanics tells us. It is sort of assumed that if actual space is "flat", then it is Euclidean. What about those volumeless points, lines and surfaces that geometry deals with? So there are quite tricky issues of the extent to which we can match the geometry we do in that theoretical construct to the actual physical space we have.

Even if I am confident of the mapping, like I might be with money and arithmetic operations (but I think that is begging the question, I think the way we use money we actually take it as the mathematical object, especially once it gets into banks as virtual money rather than being in our hands as notes and coins), I think it is an open philosophical question whether mathematical truths can be mapped back to the real world.