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 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.
Physics is geometric proof on steroids.
— SA Sachs
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.
Sophus Lie, great comparative anatomist of geometric theories.