| Our greatest debt to Lefschetz lies in the fact that he showed us that a study of topology was essential for all algebraic geometers. |
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| Ancient Greek geometers knew that the number of solids that can be constructed from regular geometric figures is limited to five. |
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| Pappus of Alexandria is the last of the great Greek geometers and one of his theorems is cited as the basis of modern projective geometry. |
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| That is, the pre-Euclidean, Classical Greek geometers, typified by the Pythagoreans, and the School of Plato. |
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| Ever since Plato, philosophers have envied geometers their certitudes. |
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| When he produced his first few results on 4-manifolds, the ideas were so new and foreign to geometers and topologists that they merely gazed in bewildered admiration. |
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| Halley suggested to him that he might devote his considerable talents to the restoration of the work of the early Greek geometers, such as Euclid and Apollonius of Perga. |
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| Ancient geometers maintained some distinction between axioms and postulates. |
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| However, Tangencies was lost, and a simple and an elegant solution has escaped the grasp of some of the greatest geometers since. |
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