All mathematical "truths" are defined into existence as you call it. All mathematical proofs are essentially of the form If A Then B. B is only a "truth" since

All mathematical "truths" are defined into existence as you call it. All mathematical proofs are essentially of the form If A Then B. B is only a "truth" since we defined A a certain way and accept it as True. Due to its very nature, there are no empirical facts in mathematics. You can argue that the is no Truth is mathematics, which is a perfectly reasonable position to take.