Ideas of Henri Poincaré, by Theme

[French, 1854 - 1912, Professor of Mathematics at the Sorbonne.]

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6. Mathematics / A. Nature of Mathematics / 4. The Infinite / d. Actual infinite
Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects
6. Mathematics / A. Nature of Mathematics / 5. Geometry
One geometry cannot be more true than another
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / a. Structuralism
Mathematicians do not study objects, but relations between objects
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Convention, yes! Arbitrary, no!
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Avoid non-predicative classifications and definitions
26. Natural Theory / D. Laws of Nature / 12. Against Laws of Nature
The aim of science is just to create a comprehensive, elegant language to describe brute facts