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If we had enough axioms about reality could mathematics replace physic

  1. Jul 3, 2013 #1
    Math is able to prove and disprove things while science can only disprove. The reason we can't prove much about the actual world is because unlike in mathematics we don't have enough starting axioms. If the math world isn't real and is just an object of the mind it would make sense that us humans can definitely prove things in it because it's a product of our mind. However the actual world isn't a product of our mind so maybe we are just not smart enough to prove much about our reality. Do you think all of the laws of physics and more can be proved using mathematics if we had enough axioms for our world?
  2. jcsd
  3. Jul 3, 2013 #2
    I think it's true in principle. This was one of Hilbert's main problems by the way: http://en.wikipedia.org/wiki/Hilbert's_sixth_problem

    However, let's say that we can completely axiomatize the world, then it might still be far too difficult or even impossible to make many good mathematically precise statements. For example, even if you just assume CM, then the three body problem becomes impossible to solve analytically. So it already is difficult to describe the motion of three bodies. Let alone describe the motion of all particles in the universe. So even though we can find the basic differential equation that underlies motion, it might not be possible to solve it. So it might turn out we find the basic axioms, but they involve equations we can't solve.

    Of course, it's possible to give numerical answers by approximations. This is a very useful tool. But I don't count it as a mathematical derivation from the axioms in the same way that group theory or analysis is.
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