Why? Why Why? Is there an answer? ON MATHEMATICAL IMPLICATIONS IN PHYSICS It is a topic that has been well discussed and thought over by many well learned individuals. Scientific endeavors are not always necessarily pursued using the mathematical method that we have come to assume in this day and age. In fact, the mathematical method appears to me to have matured only after the introduction of Newton’s mechanical vision of the universe as well as the introduction of calculus to the available tools. In Aristotle’s day, misguided if well meaning scholars rarely make use of mathematical tools at all, nor in fact do they make use of any experimental basis for their conclusions, firm in their belief of the infallibility of their logic and intuition. These days, the importance of mathematics in the study of science is well documented and taken for granted. Regardless of the fact that some eminent scientists (such as the late Richard Feynman, who had once claimed that physics would have progressed even without mathematics) still remain doubtful of the mathematical methods and their overarching meaning in the overall picture, they remain far in the minority. Most people involved in the study of the physical sciences now freely admit that without mathematical methods, they see no way of gaining any further understanding of the mechanics of the universe. Indeed, there are many examples of physical theories appearing only after certain mathematical methods have matured or have been discovered. One notable example is the geometry of non-Euclidean space, studied in great detail by eminent mathematician Herbert Minkowski, which precedes the appearance of the General Theory of Relativity by his student, Albert Einstein. Of course, the great usefulness of mathematics in physics does not give any clear indication of why mathematics has any implications in the real world at all. In what has been called the ‘ridiculous effectiveness of mathematics’, mathematicians and physicist alike cannot supply convincing explanations for the inextricable link between the two fields. Why is it in fact that the Universe follows mathematical laws at all? Perhaps this has something to do with why we have developed mathematical reasoning in the first place, and mathematical reasoning exists only because the physical universe behaves mathematically. But of course, this answer is not the least bit satisfying since it employs circular reasoning. In this way, it is similar to saying the Universe has the properties it possesses only because we exist to observe it. That is in no way close to the rigorous explanation that physicists seek and expect. Of course, given the axiomatic nature of physics (as well as mathematics, and indeed, any precise science in general) could mean that the mathematical nature of the Universe could be a fundamental axiom, one which forms the basis for all of physics, and need not, or could not, be explained in any manner. Unfortunately, there is no way for us to prove that the mathematical nature of physics is a fundamental axiom, nor is there a way for us to show that there is no way to explain this mathematical nature, similar to Gödel’s proof that in any axiomatic mathematical system undecidable propositions exists (see ON FORMALLY UNDECIDABLE PROPOSITIONS OF PRINCIPIA MATHEMATICA AND RELATED SYSTEMS by Kurt Gödel). Therefore it appears for now that we remain stuck in a conundrum, looking for a proof when no proof can be found, even if the proposition is correct. This in some ways parallels the search for the proof of Fermat’s Last Theorem, long suspect to be one of the undecidable propositions in Gödel’s Theorem, resisting nearly 300 years of mathematical research, including contributions by giants such as Euler. However, this theorem was finally cracked recently by the number theorist Andrew Wiles, after a new mathematical technique was developed. Perhaps in this case, what we need is just another mathematical revolution.