Rudi Mathematici x4-8184x 3+25144736x 2-34251153024x+17515362723840=0 Rudi Mathematici Gennaio 1 1 G (1803) Guglielmo LIBRI Carucci dalla Sommaja USAMO 1994 [1] (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE Siano k1<k 2<k 3<… interi positivi non (1912) Boris GNEDENKO consecutivi, e sia sm= k 1+k 2+…+k m per 2 V (1822) Rudolf Julius Emmanuel CLAUSIUS m=1 ;2;…;m. Provate che per ogni intero (1905) Lev Genr ichovich SHNIRELMAN positivo n, l’inter vallo [s n;s n+1 ) contiene (1938) Anatoly SAMOILENKO almeno un quadrato perfetto. 3 S (1917) Yuri Alexeievich MITROPOLSHY Perché un Regolo Calcolatore, Carta e 4 D (1643) Isaac NEWTON Matita sono meglio di qualsiasi computer 2 5 L (1838) Marie Ennemond Camille JORDAN (1871) Federigo ENRIQUES Un Regolo Calcolatore non si spegne (1871) Gino FANO improvvisamente quando fa troppo caldo. (1807) Jozeph Mitza PETZVAL 6 M Il Meraviglioso Mondo della Statistica (1841) Rudolf STURM 7 M (1871) Felix Edouard Justin Emile BOREL 1. Il 10% dei ladri d’auto sono mancini. (1907) Raymond Edward Alan Christopher PALEY 2. Tutti gli orsi polari sono mancini 8 G (1888) Richard COURANT Se vi hanno rubato la macchina, ci sono il (1924) Paul Moritz COHN 10% di probabilità che ve l'abbia soffiata (1942) Stephen William HAWKING un orso polare. 9 V (1864) Vladimir Adreievich STELKOV Someone told me that each equation I 10 S (1875) Issai SCHUR (1905) Ruth MOU FANG included in the book would halve its 11 D (1545) Guidobaldo DEL MONTE sales. (1707) Vincenzo RICCATI Step hen William HAWKING (1734) Achille Pierre Dionis DU SEJOUR 3 12 L (1906) Kurt August HIRSCH Physics is becoming too difficult for the 13 M (1864) Wilhelm Karl Werner Otto Fritz Franz WIEN physicists. (1876) Luther Pfahler EISENHART David HILBERT (1876) Erhard SCHMIDT 14 M (1 902) Alfred TARSKI The proof of the Hilbert Basis Theorem is 15 G (1704) Johann CASTILLON not mathematics; it is theology. (1717) Mattew STEWART Camille JORDAN (1850) Sofia Vasilievna KOVALEVSKAJA 16 V (1801) Thomas KLAUSEN Say what you know, do what you must, come what may. 17 S (1847) Nikolay Egorovich ZUKOWSKY (1858) Gabriel KOENIGS Sofia Vasilievna KOVALEVSK AJA 18 D (1856) Luigi BIANCHI (1880) Paul EHRENFEST When we ask advice, we are usually 4 19 L (1813) Rudolf Friedrich Alfred CLEBSCH looking for an accomplice. (1879) Guido FUBINI (1908) Aleksandr Gennadievich KUROS Joseph -Louis LAGRANGE 20 M (1775) Andrè Marie AMPERE It gives me the same pleasure when (1895) Gabor SZEGO (1904) Renato CACCIOPPOLI someone else proves a good theorem as 21 M (1846) Pieter Hendrik SCHOUTE when I do it myself. (1915) Yuri Vladimirovich LINNIK Lev Davidovich LANDAU 22 G (1 592) Pierre GASSENDI (1908) Lev Davidovich LANDAU I have no certainties, at most probabilities. (1840) Ernst ABBE 23 V Renato CACCIOPPOLI (1862) David HILBERT 24 S (1891) Abram Samoilovitch BESICOVITCH "When I use a word," Humpty Dumpty (1914) Vladimir Petrovich POTAPOV said, in a rather scornful tone, "it means 25 D (1627) Robert BOYLE (1736) Joseph -Louis LAGRANGE just what I choose it to mean - neither (1843) Karl Herman Amandu s SCHWARTZ more nor less." 5 26 L (1799) Benoit Paul Emile CLAPEYRON "The question is," said Alice, "whether 27 M (1832) Charles Lutwidge DODGSON you can make words mean so many 28 M (1701) Charles Marie de LA CONDAMINE different things." (1892) Carlo Emilio BONFERRONI "The question is," said Humpty Dumpty, 29 G (1817) William FERREL (1888) Sidney CHAPMAN "which is to be master - that's all." 30 V (1619) Michelangelo RICCI Charles DODGSON 31 S (1715) Giovanni Francesco FAGNANO dei Toschi (1841) Samuel LOYD (1896) Sofia Alexandrovna JANOWSKAJA www.rudimathematici.com Rudi Mathematici Febbraio 5 1 D (1900) John Charles BURKILL USAMO 1994 [2] 6 2 L (1522) Lodovico FERRARI I lati di un 99 -agono sono inizialmente colorati 3 M (1893) Gaston Maurice JULIA in modo tale che i lati consecutivi siano rosso, blu, rosso, blu, …, rosso, blu, giallo. Generiamo 4 M (1905) Eric Cristopher ZEEMAN una sequenza di modifiche nella colorazione 5 G (1757) Jean Marie Constant D UHAMEL cambiando colore ad un lato per volta e 6 V (1612) Antoine ARNAULD scegliendo tra i tre colori dati, sotto la (1695) Nicolaus (II) BERNOULLI restrizione che due lati adiace nti non siano mai 7 S (1877) Godfried Harold HARDY dello stesso colore. È possibile generare una (1883) Eric Temple BELL sequenza tale che la successione dei colori sia 8 D (1700) Daniel BERNOULLI (1875) Francis Ysidro EDGEWORTH rosso, blu, rosso, blu, rosso, blu, …, rosso, giallo, blu? 7 9 L (1775) Farkas Wolfgang BOLYAI (1907) Harod Scott MacDonald COXETER Perché un Regolo Calcolatore, Carta e 10 M (1747) A ida YASUAKI Matita sono meglio di qualsiasi computer (1800) William Henry Fox TALBOT 11 M Cent o persone che stiano usando Regoli (1839) Josiah Willard GIBBS (1915) Richard Wesley HAMMING Calcolatori, Carta e Matita non si mettono a strillare per un errore in virgola mobile. 12 G (1914) Hanna CAEMMERER NEUMANN If you have a cross-CAP on your sphere, 13 V (1805) Johann Peter Gustav Lejeune DIRICHLET And you give it a circle -shaped tear, (1468) Johann WERNER 14 S Then just shake it about (1849) Hermann HANKEL (1896) Edward Artur M ILNE And untangle it out 15 D (1564) Galileo GALILEI And a Moe bius strip will appear! (1861) Alfred North WHITEHEAD Measure what is measurable, and make (1946) Douglas HOFSTADTER measurable what is not so. 8 16 L (1822) Francis GALTON (1853) Georgorio RICCI -CURBASTRO Galileo GALILEI (1903) Beniamino SEGRE Whenever you can, count. 17 M (1890) Sir Ronald Aymler FISHER (1891) Adolf Abraham Halevi FRAENKEL Francis GALTON 18 M (1404) Leon Batti sta ALBERTI Mathematics is a language 19 G (1473) Nicolaus COPERNICUS Josiah Willard GIBBS 20 V (1844) Ludwig BOLTZMANN Mathematics is an interesting intellectual 21 S (1591) Girard DESARGUES (1915) Evgenni Michailovitch LIFSHITZ sport but it should n ot be allowed to stand 22 D (1903) Frank Plumpton RAMSEY in the way of obtaining sensible information about physical processes. 9 23 L (1583) Jean -Baptiste MORIN (1951) Shigefumi MORI Richard Wesley HAMMING 24 M (1871) Felix BERNSTEIN In most sciences one generation tears down 25 M (1827) Henry WATSON what another has built, and what one has 26 G (1786) Dominique Francois Jean ARAGO established, another undoes. In 27 V (1881) Luitzen Egbertus Jan BROUWER mathematics alone each generation adds a 28 S (1735) Alexandre Theophile VANDERMONDE new storey to the old structure. 29 D (1860) Herman HOLLERITH Hermann HANKEL I am interested in mathematics only as a creative art. Godfried Harold HARDY www.rudimathematici.com Rudi Mathematici arzo 10 1 L (1611) John PELL USAMO 1994 [3] 2 M (1836) Julius WEINGARTEN Un esagono convesso ABCDEF è iscritto in 3 M (1838) George William HILL una circonferenza in modo tale che (1845) Georg CANTOR AB=CD=EF e le diagonali AD , BE e CF sono 4 G (1822) Jules Antoine LISSAJUS concorrenti. Sia P l’intersezione di AD con CE . 5 V (1512) Gerardus MERCATOR Provate che CP/PE=(AC/CE) 2. (1759) Benjamin GOMPERTZ (1817) Angelo GENOCCHI Perché un Regolo Calcolatore, Carta e 6 S (1866) Ettore BORTOLOTTI Matita sono meglio di qualsiasi computer 7 D (1792) William HERSCHEL Un Regolo Calcolatore non comincia a fumare (1824) Delfino CODAZZI quando l’alimentazione ha il singhiozzo. E non 11 8 L (1851) George CHRYSTAL si preoccupa se cominciate a fumare o avete il 9 M (1818) Ferdinand JOACHIMSTHAL singhiozzo. (1900) Howard Hathaway AIKEN When I set k equal to 0, 10 M (1864) William Fogg OSGOOD I can be a mathema tical hero: 11 G (1811) Urbain Jean Joseph LE VERRIER If I should decide (1853) Salvatore PINCHERLE By k to divide, 12 V (1685) George BERKELEY Then it's clear that 1 = 0. (1824) Gustav Robert KIRKHHOFF (1859) Ernesto CESARO We [he and Halmos] share a philosophy 13 S (1861) Jules Joseph DRACH about linear algebra: we think basis -free, (1957) Rudy D'ALEMBERT we write basis -free, but when the chips are 14 D (1864) Jozef KURSCHAK down we close the office door and (1879) Albert EINSTEIN compute with matrices like fury. 12 15 L (1860) Walter Frank Raphael WELDON (1868) Grace CHISOLM YOUNG Irving KAPLANSKY 16 M (1750) Caroline HERSCHEL (1789) Georg Simon OHM Nature laughs at the difficulties of (1846) Magnus Gosta MITTAG -LEFFLER integration. 17 M (1876) Ernest Benja min ESCLANGON (1897) Charles FOX Pierre -Simon de LAPLACE 18 G (1640) Philippe de LA HIRE The mathematician's best work is art, a (1690) Christian GOLDBACH (1796) Jacob STEINER high perfect art, as daring as the most 19 V (1862) Adolf KNESER secret dreams of imagination, clear and (1910) Jacob WOLFOWITZ limpid. Mathematical genius and a rtistic 20 S (1840) Franz MERTENS (1884) Philip FRANCK genius touch one another. (1938) Sergi Petrovich NOVIKOV Magnus Gosta MITTAG- LEFFLER 21 D (1768 ) Jean Baptiste Joseph FOURIER (1884) George David BIRKHOFF A mathematician is a person who can find 13 22 L (1917) Irving KAPLANSKY analogies between theorems; a better mathematician is one who can see 23 M (1754) Georg Freiherr von VEGA (1882) Emmy Amalie NOETHER analogies between proofs and the best (1897) John Lighton SYNGE mathematician can notice analogies 24 M (1809) Joseph LIOUVILLE (1948) Sun -Yung (Alice) CHANG between th eories. One can imagine that the 25 G (153 8) Christopher CLAUSIUS ultimate mathematician is one who can see 26 V (1848) Konstantin ADREEV analogies between analogies. (1913) Paul ERDOS Stefan BANACH 27 S (1857) Karl PEARSON The essence of mathematics lies in its 28 D (1749) Pierre Simon de LAPLACE freedom.