# Mathematical approximation to physics

Why is it often said that any mathematical theory is just an approximate theory of the universe? Wouldn't there be accurate mathematical structures repressing the physical entities of the universe precisely?

• This is a Philosophy question rather than a Physics one. And is still open, since the Ancient Greece philosophers first wondered. – rmhleo Sep 20 '14 at 16:20
• I'd argue this is more a discussion of word usage and is quite appropriate on this SE site. – DanielSank Sep 20 '14 at 17:05
• This is very much a physics question: how would we even know that a given (mathematical) theory is absolutely exact in its description of nature? Suppose that your model predicts some answer, say 2 m/s as the speed of something. You test this by doing the experiment and measuring the 'real' value. You get 2 m/s... but with some uncertainty, e.g. plus or minus 0.0000001 m/s. You can NEVER have zero uncertainty, so you can NEVER be sure that your model is absolutely precise. – User 17670 Sep 20 '14 at 19:24

2. Mathematics itself cannot ever self-explain what does it describe. How is the symbol $v(t)$ connected to reality? I don't see any symbol "t" or "v" floating in space to tell me how to use it. In the end, language and it's common sense provide a bridge between mathematics and actual physics. The link between mathematics and physics is provided by labels created by people. But there is an inherent approximateness and fuzziness to things created by people (however small and negligible in many physical examples).