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Research

Advice to a Young Mathematician

by Sir Michael Atiyah


... "However, it is a mistake to identify research in mathematics with the process of producing proofs. In fact, one could say that all the really creative aspects of mathematical research precede the proof stage. To take the metaphor of the 'stage' further, you have to start with the idea, develop the plot, write the dialogue, and provide the theatrical instructions. The actual production can be viewed as the 'proof': the implementation of an idea."

... "Proof is the end product of a long interaction between creative imagination and critical reasoning. Without proof the program remains incomplete, but without the imaginative input it never gets started. One can see here an analogy with the work of the creative artist in other fields: writer, painter, composer, or architect. The vision comes first, it develops into an idea that gets tentatively sketched out, and finally comes the long technical process of erecting the work of art."

Random Thoughts on Mathematics

* Notation

Our mission is to advance personal and popular understanding of the nature and more importantly the mathematics. If notations are introduced such that they add confusion over facts, they should be abandoned. 

* Motifs 

My interest is led by the truth, not fame or wealth. Personal career-advancing driven research and social activities are selfish and unkind, it is an absolute shame.

* Research

"Publish or perish" should be abolished and all intellectuals be admonished. One does not live as an author of list of publications; one lives in life as a rounded person. Isn't it a great irony that most of the time the so called publications can only advance the authors themselves' careers and the general public cannot access the publications without paying (a large amount of) fees for using digital libraries. Shame.

* Mathematics is about using a minimal set of rules to generalise as many things as possible.


Theses
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Yün Han,
Jul 23, 2014, 3:38 PM