How to think like Henri Poincaré

[NOTE] The following material is from Wikipedia’s entry on Poincaré.

Summary: His method of thinking is well summarized as:
He neglected details and jumped from idea to idea, the facts gathered from each idea would then come together and solve the problem.) (Belliver, 1956)

Jules Henri Poincaré (April 29, 1854 – July 17, 1912) was one of France’s greatest mathematicians and theoretical physicists, and a philosopher of science.

Poincaré’s work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.

The mathematician Darboux claimed he was un intuitif (intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation.

[I am wondering what he used? maps, diagrams? tables? sketches?]

He did not care about being rigorous and disliked logic.
He believed that logic was not a way to invent but a way to structure ideas and [believed] that logic limits ideas.

[This is a very important point. Structuring ideas, organizing information in (linear) logical ways is a something we seem to do before and after a different type of thinking process in order to "rationalize" or explain our process of thinking. The cognitive process in between (or weaving in and out) may be non-linear and complex and would probably not be very easy to understand if written down step by step - (it wouldn't fit neatly into "logical" steps).

[Thinking purely through linear logic about specific variables is something any computer can do. I would like to think that Poincaré may have contributed a lot more to the cognitive process than linear thought.]

[He] Solved problems in his head, then commit the completed problem to paper. [lots of visualization and visual memory of internal processes]
He was ambidextrous and nearsighted. [whole brain thinker?]
He had an ability to visualise what he heard…
He never spent a long time on a problem since he believed that the subconscious would continue working on the problem while he consciously worked on another problem.

[A belief that may have triggered that part of his brain to work in the way he described]

In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré was the type that started from basic principle each time. (O’Connor et al., 2002)

[Thi is one of my favorite types of thinking. For lack of a better name I call it "reinventing the wheel" (relative of "synectics"?). While it sounds like a waste of time I think it provides the ability to use "fresh eyes" to think about a problem. It's something that can be hard to do when you're educated and informed about the "principles" and "laws" of a discipline. In a way, those who "know less" may be at an advantage on this type of thinking.]

Link
Wikipedia: “Henri Poincaré” >>

Related in this blog
“How to think like Einstein”>>

“Types of thinking”>>

Related on Wikipedia
Portal on thinking>>
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