In an empirical science nothing is ever proven. Observations yield evidence that may support or refute a theory, but no matter how well supported by data, no scientific theory is ever proven in the mathematical sense. In mathematics we start with clearly identified assumptions and proceed carefully, logically, in a reproducible way to a result. The result is absolutely certain, predicated only on the initial assumptions made and a universe where the rules of logic used in the process are valid. But this is so only because mathematics does not attempt to draw absolute conclusions .
All mathematical truths are relative, conditional .
Thus though mathematics is useful in the physical world, mathematics is independent of physical reality. Created out of pure intelligence. Yet, mathematics is not without applications, and mathematical models often suggest interactions in the real world. Neptune, for example, was discovered by mathematics. History and Background Man first began to use tools about 35,000 years ago.