Word: non-euclidean
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Mathematics had been partially unshackled from the physical world by the discovery of non-Euclidean geometrics in the nineteenth century, but the publication of Principia Mathematica in 1908 burst the chains. This three-volume monument by Bertrand Russell and Alfred North Whitehead expressed the fundamental concepts of mathematics in terms of still simpler concepts of logic, and showed that mathematics may be viewed as a game of manipulating symbols according to rules. Since mathematicians can adopt any rules they want, the truths proved in mathematics can have no necessary connection with the world outside of mathematics...
...nowhere else. Clifford emerges as a superb mathematician even in the company of the nineteenth-century geniuses. He was one of the last to work with equal success on several mathematical fronts, Poincare being perhaps the last who managed it. Clifford spun out the consequences of the new non-Euclidean geometries and of Abelian function theory; he also gripped the prickly legacy of Kantian skepticism and took to the lecture stand with clear thinking on different epistemological questions...
...Mathematician. The Liebers, who teach mathematics at New York's Long Island University, have a fine time explaining elementary things about Boolian algebra, non-Euclidean geometry and the fourth dimension. The reader is likely to share their gusto, even if he can not agree that "science and mathematics . . . can be a veritable defense against ALL evil...
...place, Mass. Ave. swerves through the northern arm of the Avenue, forming a dangerous and traditional bumping point, while Brattle surges through to the eastern arm to create another awkward rendezvous. The climax to this engineer's nightmare is the subway entrance brooding in the middle. With these non-Euclidean facilities, the Square tries to serve two purposes--a shopping center for students and a transfer station for in-town travellers. Twelve thousand outsiders shift El cars every day. Six hundred busses carry thirty thousand passengers in, out, and through the dilemma. A paltry nine thousand scholars wander and mill...
...Lazare wrote a commentary on Spinoza's Ethics, translated Descartes' Meditations from Latin into Russian. He was still in his teens when he studied abstruse mathematical logic and published attacks on non-Euclidean geometers. Meantime he was playing music on the side, making up little songs and waltzes for his cousins...