By N. J. A. Sloane

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CHRONOLOGY 31 And so on. If the cube is made of iron or copper, with three adjacent faces at temperature 100 degrees, and three opposite faces at temperature zero, then the temperature at the center is 50. The cube is an elementary mathematical entity easy to visualize. Its equilib¬ rium temperature distribution, not quite so elementary. We could go on to the octahedron, which has three internal diagonals, and then the other Platonic solids, and then regular polytopes in four dimensions, and on and on.

They yield reproducible results, independent of particular investigators. Such kinds of ideas are important enough to have a name. ’ A world of ideas exists, created by human beings, existing in their shared consciousness. These ideas have objective properties, in the same sense that material objects have objective properties. The construction of proof and counter-example is one method of verify¬ ing the properties of these ideas. " ( What is mathematics, really Page 19) ... A mathematical entity is a concept, a shared thought.

And a mathematical statement can be “true,” meaning simply that a mathematical problem may have a “correct” solution. These two statements arc not at all radical or surprising, of course! They can hardly be denied. But they are incompatible with either Platonism or formalism. ” Today I regret the w’ord “imaginary,” “mental” would have been better. I wras greatly helped by another piece of reading — an essay by the anthropologist Leslie White. I read it in the four-volume anthology by James Newman called The World of Mathematics.

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