Most of the posts above follow the conventional common sense view of the issue. (4 objects are 4 objects, period)
This view neglects issues dealth with by Bertrand Russel and others about actual inconsistencies in math. In a long proof, he finally came up with 1=0. “Obviously” this is not true, even tho he proved it. What is wrong, either the idea that 1=0 OR one of the steps in his proof, all of which were sound mathematically. (I can try to find this and print it, although it is several hundred pages long - it is well known to those in the field).
An article in Scientific American last year challenged the idea that numbers can be infinite.
I think math is MORE objective, but from a philosophical standpoint, may not be ultimately objective - for the simple reason that it is a man made system (I am taking a position that no communication medium can be 100% objective, as all such systems are integrally tied to their creators and users).
Even if it describes qualities that are “out there”, some of the characterizations and how they are re-applied may be man made.
Positive and negative numbers are a good example. We could have created neutral numbers as well, and created a rule for them as such - 2 positives = a neutral, 2 negatives = a neutral, and 2 neutrals = a neutral.
An organism with tri-lateral symetery might do the same. Human math is very concerned with dualist divisions - thus the binary computer. Three states could be used to encode information.
We also confuse zero, the place holder with an actual number, having qualities (such as: it is even). The ancients did not think this way, thus 1BC is followed by 1AD. Zero used as an actual number yields non-unique counter-intuitive results, results I often felt were glossed over. (0 x anything = 0, this only occurs with zero. Dividing by zero seems more appropriate to Buddhism than mathematics).
While most of the posts have followed the common sense approach that it is objective - this is by no means universal in philosophy these days.