Geometric Quotes (5 quotes)
If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society (1906), 286.
In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.
In 'Mathematical Games', Scientific American (Oct 1973), 229, 114.
Physics is geometric proof on steroids.
— SA Sachs
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Population, when unchecked, goes on doubling itself every twenty-five years, or increases in a geometrical ratio. … The means of subsistence, under circumstances the most favorable to human industry, could not possibly be made to increase faster than in an arithmetical ratio.
In An Essay on the Principle of Population: (new ed. 1803), Vol. 1, 5 and 7.
Sophus Lie, great comparative anatomist of geometric theories.
In Lectures on Science, Philosophy and Art (1908), 31.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
