Hi Realapaladi,
Both Doron and myself live in Israel. We are Jews !
You can Forgot OM. Do you believe that Mathematics have to possibility of paradigm shift like what happen in physic in 1905 ?
Moshe
Moshe, yep paradigm shifts can always happen, but just as in physics, it will be hotly debated and proofs are needed.
The whole process of science is:
- Someone sets up a theory, and he (or someone who finds the theory intuitively acceptable) goes and figures out the proof.
- Some other people retest the theory and try to corroborate the proof or find new proofs.
- The theory is accepted, until something comes along that explains the observed phenomena (in the broadest sense of the word) better.
So, it is an 'inbuilt' mechanism in science to overthrow itself, if necessary.
But you will never effect a paradigm shift because you want a paradigm shift.
A paradigm shift happens, sometimes even against the grain of it's discoverer, because it explains more and has more or better proofs or evidence.
A good example in physics is String Theory... while I do not know the finer details, I do know that the maths are more elegant, but it does not explain more or better than what we already can with current other theories.
That is why String Theory is not the prevalent theory at the moment.
That is also what I tried to explain to Doron:
Even if you can defend away any criticism, it does you no good if you can not convince anyone that your theory is better.
If nobody is convinced, then the paradigm shift will not happen.