There are two erroneous extremes one might fall into in regard to the philosophy of mathematics. In the one, which we could call naive objectivism, mathematical objects, such as the triangle, the regular solids, the various numbers, a proof, or abelian groups, are taken as simply existent apart from the work of mathematicians. They exist whether we discover them or not. In the other, which we could call naive subjectivism or psychologism, mathematical items are taken to be mental constructs of mathematicians, with no more objectivity than the feelings someone might have had when he thought about a rectangle or worked out a proof. The truth, as usual, lies in the middle.
Mathematical items are indeed objective.
There are mathematical objects, facts, and valid proofs that transcend the thinking of any individual. However, if we, as philosophers, wish to discuss the objectivity of such items, we must also examine the thinkers, the mathematicians, for whom they are objective, for whom they are facts. The philosophy of mathematics carries out its work by focusing on the correlation between mathematical things and mathematicians. He draws especially but not exclusively on the phenomenological tradition. Rather, the mind finds its fulfillment in the presentation of things, and things are enhanced by the truth they display to us.