Rudi Mathematici x3 – 6’135x2 + 12’545’291 x – 8’550’637’845 = 0 www.rudimathematici.com 1 S (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 1 2 M (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 W (1643) Isaac Newton RM071 5 T (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2002, A1 (1871) Federigo Enriques RM084 Let k be a fixed positive integer. The n-th derivative of (1871) Gino Fano k k n+1 1/( x −1) has the form P n(x)/(x −1) where P n(x) is a 6 F (1807) Jozeph Mitza Petzval polynomial. Find P n(1). (1841) Rudolf Sturm 7 S (1871) Felix Edouard Justin Emile Borel A college football coach walked into the locker room (1907) Raymond Edward Alan Christopher Paley before a big game, looked at his star quarterback, and 8 S (1888) Richard Courant RM156 said, “You’re academically ineligible because you failed (1924) Paul Moritz Cohn your math mid-term. But we really need you today. I (1942) Stephen William Hawking talked to your math professor, and he said that if you 2 9 M (1864) Vladimir Adreievich Steklov can answer just one question correctly, then you can (1915) Mollie Orshansky play today. So, pay attention. I really need you to 10 T (1875) Issai Schur concentrate on the question I’m about to ask you.” (1905) Ruth Moufang “Okay, coach,” the player agreed. “I’ll do my best.” 11 W (1545) Guidobaldo del Monte RM120 “Good,” said the coach. Then he asked, “Okay, now (1707) Vincenzo Riccati really focus. What is 2+2?” All of his teammates (1734) Achille Pierre Dionis du Sejour watched quietly while the quarterback thought about 12 T (1906) Kurt August Hirsch the question. (1915) Herbert Ellis Robbins RM156 The quarterback thought for a moment. Sheepishly, he 13 F (1864) Wilhelm Karl Werner Otto Fritz Franz Wien answered, “Um, 4?” (1876) Luther Pfahler Eisenhart “Really?” said the coach. “Did you really just say 4?” (1876) Erhard Schmidt To which his teammates shouted, “Oh, c’mon, coach! (1902) Karl Menger Give him another chance!” 14 S (1902) Alfred Tarski RM096 15 S (1704) Johann Castillon 1. How many eggs can you put in an empty basket? (1717) Mattew Stewart 12. They pay out the award as follows: 1 dollar the first (1850) Sofia Vasilievna Kovalevskaja RM144 week, 1/2 dollar the second week, 1/3 dollar the third 3 16 M (1801) Thomas Klausen week, and so on. 17 T (1647) Catherina Elisabetha Koopman Hevelius (1847) Nikolay Egorovich Zukowsky And as for Mixed Mathematics, I may only make this (1858) Gabriel Koenigs prediction, that there cannot fail to be more kinds of 18 W (1856) Luigi Bianchi them, as nature grows further disclosed. (1880) Paul Ehrenfest RM204 Francis Bacon 19 T (1813) Rudolf Friedrich Alfred Clebsch “When I use a word, “Humpty Dumpty said, in a rather (1879) Guido Fubini scornful tone, “it means just what I choose it to mean – (1908) Aleksandr Gennadievich Kurosh neither more nor less.” 20 F (1775) André Marie Ampère “The question is,” said Alice, “whether you can make (1895) Gabor Szegő words mean so many different things.” (1904) Renato Caccioppoli RM072 “The question is,” said Humpty Dumpty, “which is to be 21 S (1846) Pieter Hendrik Schoute master – that’s all.” (1915) Yuri Vladimirovich Linnik Charles Lutwidge Dodgson 22 S (1592) Pierre Gassendi (1886) John William Navin Sullivan An expert problem solver must be endowed with two (1908) Lev Davidovich Landau RM063 incompatible qualities, a restless imagination and a 4 23 M (1840) Ernst Abbe patient pertinacity. (1862) David Hilbert RM060 Howard W. Eves 24 T (1891) Abram Samoilovitch Besicovitch (1914) Vladimir Petrovich Potapov Someone told me that each equation that I included in 25 W (1627) Robert Boyle the book would halve the sales. (1736) Joseph-Louis Lagrange RM048 Stephen William Hawking (1843) Karl Hermann Amandus Schwarz 26 T (1799) Benoît Paul Émile Clapeyron Mathematics knows no races or geographic boundaries; (1862) Eliakim Hastings Moore for mathematics, the cultural world is one country. 27 F (1832) Charles Lutwidge Dodgson RM108 David Hilbert 28 S (1701) Charles Marie de La Condamine (1888) Louis Joel Mordell Amusement is one of the fields of applied mathematics. (1892) Carlo Emilio Bonferroni William F. White 29 S (1817) William Ferrel (1888) Sidney Chapman 5 30 M (1619) Michelangelo Ricci 31 T (1715) Giovanni Francesco Fagnano dei Toschi (1841) Samuel Loyd RM192 (1896) Sofia Alexandrovna Janowskaja (1945) Persi Warren Diaconis RM180 www.rudimathematici.com 1 W (1900) John Charles Burkill 2 T (1522) Lodovico Ferrari Rudi Mathematici (1893) Cornelius Lanczos (1897) Gertrude Blanch 3 F (1893) Gaston Maurice Julia RM073 4 S (1905) Eric Cristopher Zeeman 5 S (1757) Jean Marie Constant Duhamel 6 6 M (1465) Scipione del Ferro RM064 February (1612) Antoine Arnauld (1695) Nicolaus (II) Bernoulli RM093 7 T (1877) Godfried Harold Hardy RM049 Putnam 2002, A2 (1883) Eric Temple Bell Prove that among any n+3 points on an n-sphere, some 8 W (1700) Daniel Bernoulli RM093 n+2 of them lie on a closed hemisphere. (1875) Francis Ysidro Edgeworth (1928) Ennio de Giorgi RM133 About a year ago, a small fire started in one of the 9 T (1775) Farkas Wolfgang Bolyai hallways. An engineer, a scientist, and a statistician (1907) Harold Scott Macdonald Coxeter RM097 began debating the best way to extinguish the blaze. 10 F (1747) Aida Yasuaki RM121 “Dump some water on it!” the engineer suggested. (1932) Vivienne Malone-Mayes “No! Remove the oxygen!” said the scientist. 11 S (1657) Bernard Le Bovier de Fontenelle The statistician, however, started running around the (1800) William Henry Fox Talbot RM205 building, starting fires in other locations. “What the (1839) Josiah Willard Gibbs heck are you doing?” the other two asked. (1915) Richard Wesley Hamming “Trying to create a decent sample size,” he said. 12 S (1914) Hanna Caemmerer Neumann (1921) Kathleen Rita Mcnulty Mauchly Antonelli 2. How is the moon like a dollar? 7 13 M (1805) Johann Peter Gustav Lejeune Dirichlet RM145 1. Just one. Then it’s no longer empty. 14 T (1468) Johann Werner (1849) Hermann Hankel Each generation has its few great mathematicians, and (1877) Edmund Georg Hermann Landau RM063 mathematics would not even notice the absence of the (1896) Edward Artur Milne others. They are useful as teachers, and their research (1932) Maurice Audin RM194 harms no one, but it is of no importance at all. A 15 W (1564) Galileo Galilei RM085 mathematician is great or he is nothing. (1850) Sophie Willock Bryant Alfred W. Adler (1861) Alfred North Whitehead (1946) Douglas Hofstadter Life is a school of probability. 16 T (1822) Francis Galton Walter Bagehot (1853) Gregorio Ricci-Curbastro (1903) Beniamino Segre If “Number rules the universe” as Pythagoras asserted, 17 F (1890) Sir Ronald Aylmer Fisher Number is merely our delegate to the throne, for we rule (1891) Adolf Abraham Halevi Fraenkel Number. (1905) Rózsa Péter Eric Temple Bell 18 S (1404) Leon Battista Alberti RM157 (1919) Clifford Truesdell Leibniz never married; he had considered it at the age of fifty; but the person he had in mind asked for time to 19 S (1473) Nicolaus Copernicus RM181 reflect. This gave Leibniz time to reflect, too, and so he 8 20 M (1844) Ludwig Boltzmann RM061 never married. 21 T (1591) Girard Desargues Bernard Le Bovier De Fontenelle (1915) Evgeny Michailovich Lifshitz 22 W (1857) Heinrich Rudolf Hertz If men didn’t know mathematics, they wouldn’t rise a (1903) Frank Plumpton Ramsey single palm from the ground. 23 T (1583) Jean-Baptiste Morin Galileo Galilei (1905) Derrick Henry Lehmer RM215 (1922) Anneli Cahn Lax Pure mathematics is on the whole distinctly more useful (1951) Shigefumi Mori than applied For what is useful above all is technique, (1561) Henry Briggs RM169 and mathematical technique is taught mainly through 24 F (1871) Felix Bernstein pure mathematics. 25 S (1827) Henry Watson Godfried Harold Hardy 26 S (1786) Dominique Francois Jean Arago RM193 9 27 M (1881) Luitzen Egbertus Jan Brouwer Let us grant that the pursuit of mathematics is a divine 28 T (1735) Alexandre Theophile Vandermonde madness of the human spirit, a refuge from the goading 29 (1860) Herman Hollerith RM109 urgency of contingent happenings. Alfred North Whitehead www.rudimathematici.com 1 W (1611) John Pell (1879) Robert Daniel Carmichael Rudi Mathematici 2 T (1836) Julius Weingarten 3 F (1838) George William Hill (1845) Georg Cantor RM062 (1916) Paul Richard Halmos 4 S (1822) Jules Antoine Lissajous 5 S (1512) Gerardus Mercator March (1759) Benjamin Gompertz (1817) Angelo Genocchi (1885) Pauline Sperry Putnam 2002, A3 (1915) Laurent Schwartz RM194 Let n 2 be an integer and Tn be the number of nonempty (1931) Vera Pless subsets≥ S of {1, 2, 3, …, n} with the property that the 10 6 M (1866) Ettore Bortolotti average of the elements of S is an integer. Prove that Tn 7 T (1792) William Herschel RM146 − n is always even. (1824) Delfino Codazzi (1922) Olga Alexandrovna Ladyzhenskaya (…continues from February) The fires were extinguished 8 W (1851) George Chrystal one by one, but when they finished, there was an unused 9 T (1818) Ferdinand Joachimsthal bucket of water. The statistician said to the (1900) Howard Hathaway Aiken mathematician, “Can you please get rid of that water?” 10 F (1864) William Fogg Osgood The mathematician proceeded to start another fire, and (1872) Mary Ann Elizabeth Stephansen then he dumped the bucket of water on it.