Insight is born when Intuition meets and mates with Logic

Henri Poincare

Poincare is considered as one of the great geniuses of all time and there are two very significant sources which study his thought processes. One is a lecture which Poincaré gave to l'Institute Général Psychologique in Paris in 1908 entitled Mathematical invention in which he looked at his own thought processes which led to his major mathematical discoveries. The other is the book by Toulouse who was the director of the Psychology Laboratory of l'École des Hautes Études in Paris. Although published in 1910 the book recounts conversations with Poincaré and tests on him which Toulouse carried out in 1897.

Poincaré read widely, beginning with popular science writings and progressing to more advanced texts. His memory was remarkable and he retained much from all the texts he read but not in the manner of learning by rote, rather by linking the ideas he was assimilating particularly in a visual way. His ability to visualise what he heard proved particularly useful when he attended lectures since his eyesight was so poor that he could not see the symbols properly that his lecturers were writing on the blackboard.

Further Reading - http://www-history.mcs.st-and.ac.uk/Biographies/Poincare.html

What interested me most was that Poincare recognized the important role played by Intuition in inventive thinking

It is through science that we prove, but through intuition that we discover.

Logic, therefore, remains barren unless fertilised by intuition

Henri Poincare

Poincare's example of intuition-driven research

Professor Klein is studying one of the most abstract questions of the theory of functions to determine whether on a given Riemann surface there always exists a function admitting of given singularities. What does the celebrated German geometer do? He replaces his Riemann surface by a metallic surface whose electric conductivity varies according to certain laws. He connects two of its points with the two poles of a battery. The current, says he, must pass, and the distribution of this current on the surface will define a function whose singularities will be precisely those called for by the enunciation.

Riemann himself always called geometry to his aid; each of his conceptions is an image that no one can forget, once he has caught its meaning.

Source : http://www-groups.dcs.st-and.ac.uk/history/Extras/Poincare_Intuition.html

My Key Takeaways

• Trust your Intuition - allow it to talk to you - listen to it attentively.

• Follow up that conversation with logical thinking

• It is only when logic meets and mates with Intuition that Insight is born