Math is fascinating to me, though I struggled with math in high school and only took the minimum I needed. (Age changes things, man.) I’m reading a book on Wiles’ proof for Fermat’s Last Theorem and got curious about proofs.
At what point does something move from an assumption with examples (well yeah. Look at this) to a full proof?
Simple example that came to mind:
For any number n, where n is a prime >2, the sum of the factors of n cannot be odd.
In: Mathematics
Let me start by saying that I get downvoted every time I say this, but I keep saying it anyways. Math is a language based on pure logic. It is the universe’s operating system. When you try to prove something mathematically it is basically the same as trying to prove something verbally – just in this different language.
One of the issues though is that its amazingly difficult to prove something even verbally. Consider “Does God exist?” philosophers haven’t been able to answer that even after thousands of years or trying. If we stepped back and asked “Do you BELIEVE that God exists?” you might say yes, but you could be lying. However we could look into your life, see you going to church, praying when you thought you were alone, etc. and gather up enough evidence that you did believe in god to satisfy ourselves. Math generally lets us close that tiny gap of uncertainty that verbal languages and the real world so often leave us with.
Every proof is going to look different though but all you are trying to do is construct a logical argument that covers off every base.
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