Madam, - Prof William Reville is to be congratulated for his interesting article on Jules-Henri Poincaré (September 18th). It gave a fascinating insight into the mind of a great mathematician.
Poincaré's dictum, quoted by Dr Reville, that "logic remains barren unless fertilised by intuition" highlights the significant position held by imaginative insight as an integral part of effective mathematical thinking.
Jules-Henri's cousin, the politician Raymond Poincaré, is credited with coining a somewhat similar dictum: "An accumulation of facts is no more science than a pile of bricks is a house." Both dicta point to the importance of the formal, structural "big idea", compared with the mere accumulation of facts, if we are to successfully elaborate a truly comprehensive scientific theory.
Perhaps, from an examination of the life of a person such as Jules-Henri Poincaré, one might be able to deduce a profile of the ideal mathematical or scientific mind. First, as a necessary attribute, such a mind would exhibit great technical adroitness with complicated formulae - thus showing its logical or intellectual skill.
Then, more pre-eminently, such a mind might exhibit an almost unerring "instinct" for the right answer, thus manifesting the inherent beauty of the ultimately correct solution, and the mind's aesthetic appreciation of such a solution.
Finally, perhaps we should ask that such a mind would exhibit a prodigious memory. Memory is an attribute we are constantly in danger of underrating. As an example of a mathematician with an astounding memory we may mention Leonhard Culer. This Swiss mathematician, when old and blind, could yet recite in Latin the whole of Vergil's Aeneid by heart. - Yours, etc.,
THOMAS P WALSH, Faussagh Road, Cabra, Dublin 7.