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Across 5. worked on the theory of waves, discovered the gas Argon (2 words) 8. gave three fandamental laws of planetary motion, worked in optics and geometry 9. founder of symboli logic 11. worked extensively in Fractal Geometry 12. inventor of pulleys and a screw pumping device 16. introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe 17. famous for work on prime numbers and for measuring the diameter of the earth 18. first to proof a famous right triangle theorem 20. initiated the study of quantum mechanics 22. established the science of hydrodynamics 24. theory of relativity 26. formulated the basic laws of falling bodies 31. German mathematician who developed the present day notation for the differential and integral calculus 33. published a paper which considered both the motion of the source and the motion of the observer on the apparent pitch of sound 34. pioneered the theory of permutation groups 35. father of differential geometry 37. first to provide a rigorous proof that pi is irrational 39. French mathematician who introduced the first systematic algebraic notation 40. world chess champion who introduced the notion of a primary ideal

Down 1. French lawy who worked in the foundations of calculus 2. Scottish scholar who invented logarithms 3. Polish astronomer and mathematician who proposed the earth's yearly motion around a stationary sun 4. born in Italy, took part in the Los Alamos project to build the atomic bomb 6. first account on non-Euclidian geometry to appear in print 7. constructed the theory of complex functions by means of power series 10. investigated number theory, famous for orthogonal polynomials 13. pseudonym for Charles Dodgson 14. produced a method of determining when a general equation could be solved by radicals 15. "I think, therefore I am." 19. developed a general calculus for vectors 21. originator of algebraic topology 23. investigated "integration in infinitely many dimensions" 25. between 1820 and 1823 prepared a treatise on a complete system of non-Euclidean geometry 27. proved the stability of the solar system, put the theory of mathematical probability on a sound footing 28. work in geometry had the greatest influence in that area after Euclid 29. Greek mathematician who wrote "The Elements" 30. Contributed to the theory of elliptical functional 32. approached logic by reducing it to simple algebra 36. founded set theory 38. recent mathematician who worked in probability, analysis, number theory, geometry, combinatorics, and mathematical physics