Notes to myself
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If you see any proof in fundamental maths, you'll see a portion of it is argued and the remaining gap is supposed to flow out without ambiguity from fundamental truths or axioms (mathematicians use the terms trivial or obvious for these steps).
Now most mathematicians have undergone similar training, so what flows from axioms and what needs to be proved is fairly uniformly understood in the tribe. But it is a result of their traning...because remember, there is no way of proving/disproving axioms.
Many of these same theorems are proved in other areas like physics or finance or computer science and people in those areas often prove what is taken to be axioms in maths (and take as axioms what mathematicians prove)!
So what I assume to be true and what I argue to create higher truths is often just dependent on how I have been indoctrinated!
Sorry, there must be a better way of proving things.
As of this stage, I find the physical way of proving stuff (like in physics or finance) much more appealing because what these physical scientists take as axioms can atleast be verified experimentally. But it is very haphazard and area dependent... (what physicists take as axioms is often different from what people in finance take as axioms even if they are referring to the same basic phenomenon like stochasticity).
But there must be some way of regularizing this physical approach to mathematics..
If you see any proof in fundamental maths, you'll see a portion of it is argued and the remaining gap is supposed to flow out without ambiguity from fundamental truths or axioms (mathematicians use the terms trivial or obvious for these steps).
Now most mathematicians have undergone similar training, so what flows from axioms and what needs to be proved is fairly uniformly understood in the tribe. But it is a result of their traning...because remember, there is no way of proving/disproving axioms.
Many of these same theorems are proved in other areas like physics or finance or computer science and people in those areas often prove what is taken to be axioms in maths (and take as axioms what mathematicians prove)!
So what I assume to be true and what I argue to create higher truths is often just dependent on how I have been indoctrinated!
Sorry, there must be a better way of proving things.
As of this stage, I find the physical way of proving stuff (like in physics or finance) much more appealing because what these physical scientists take as axioms can atleast be verified experimentally. But it is very haphazard and area dependent... (what physicists take as axioms is often different from what people in finance take as axioms even if they are referring to the same basic phenomenon like stochasticity).
But there must be some way of regularizing this physical approach to mathematics..
posted by Ayan Bhattacharya @ 03:52
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