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" "...the entire physical world is depicted as being governed according to mathematical laws. We shall be seeing in later chapters that there is powerful (but incomplete) evidence in support of this contention. On this view, everything in the physical universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations, such as those we shall be learning about in chapters to follow, or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’. If this is right, then even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles.
Sir Roger Penrose (born 8 August 1931) is an English mathematical physicist and Professor of Mathematics at the Mathematical Institute, University of Oxford, famous for his work in mathematical physics, cosmology, general relativity, and his musings on the nature of consciousness.
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Gödel's theorem shows that this point of view is not really a tenable one in a fundamental philosophy of mathematics. The notion of mathematical truth goes beyond the whole concept of formalism. There is something absolute and 'God-given' about mathematical truth. This is what , as discussed at the end of the last chapter, is about. Any particular formal system has a provisional and 'man-made' quality about it. Such systems indeed have very valuable roles to play in mathematical discussions, but they can supply only a partial (or approximate) guide to truth. Real mathematical truth goes beyond mere man-made constructions.
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One is left with the uneasy feeling that even if supersymmetry is actually false, as a feature of nature, and that accordingly no supersymmetry partners are ever found by the LHC or by any later more powerful accelerator, then the conclusion that some supersymmetry proponents might come to would not be that supersymmetry is false for the actual particles of nature, but merely that the level of supersymmetry breaking must be greater even that the level reached at that moment, and that a new even more powerful machine would be required to observe it!