2010/12/17 13:51
1. Survey
'Surf' the references of references
Read Tutorial
Read 'Survey' paper that has done the homework on behalf of you
2. New field. New solution concept. New formulation
It provides a 'recipe' how to formulate, what to assume, and what to show.
Academia stimulus
3. Mathematical techniques.
4. Imagination
Just imagine what would be great if you discover about nature, human mind, or complex system.
Imagine what would be surprising when achieved or showed.
Science is a process to augment evidence for hypothesis that does not have enought evidence yet.
Hypothesis only comes from imaginative power, but not the deductive reasoning.
5. Proof
By inspection:
This is the most primitive way of proving something. This purile technique is sometimes, but not widely, used in practice.
By example:
By Logic system
By
Existence ( Presence )
This proof technique is the most surprise to me in my life time. I recall I encountered this technique in the freshman's Calculus class when one studies Augustin Louis Cauchy's epsilon-delta definition of limit. Before this I was never taught about 'existence' of 'presence', and therefore it sounded very weird.
In fact, all people can define what a natural number is, but nobody properly defined its existence. We always implicitly assume the existence of natural number 11, and no one doubts about it. Further, one could define a negative number, but no one knows the existence of that negative number. What is -11? More fundamentally, what is 0? Is it nil? Is it non-existence? What is it?
Further,
