What is a mathematical proof? Is formal logic capable of shedding light on its nature or essence? The author maintains that the answer is negative. Mathematical proof requires a more intrinsic investigation and explanation due to its specific structure. The crucial element is usually situated on the top level of the proof structure, so that an axiomatic basis is as a rule useless in mathematical thinking. The final conclusion is that the formal-logical foundations of mathematics should be complemented with a phenomenology of mathematical thinking. The latter should be developed in a manner that is understandable for ordinary mathematicians. Philosophy would thus show its applicability and usefulness beyond its own purely theoretical and speculative domain. The general should be embodied in the concrete. The author believes that this type of interdisciplinary, philosophico-mathematical research will attract mathematicians to philosophy with profit for their own domain.