Rudi Mathematici x4-8180x3+25090190x2-34200948100x+17481136677369=0 Rudi Mathematici Gennaio 1 1 M (1803) Guglielmo LIBRI Carucci dalla Somaja APMO 1989 [1] (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE K (1912) Boris GNEDENKO Siano x1 , x2 , , xn numeri reali 2 G (1822) Rudolf Julius Emmanuel CLAUSIUS n (1905) Lev Genrichovich SHNIRELMAN positivi e sia S = x . (1938) Anatoly SAMOILENKO å i i=1 3 V (1917) Yuri Alexeievich MITROPOLSHY 4 S (1643) Isaac NEWTON Provare che e`: 5 D (1838) Marie Ennemond Camille JORDAN n n S i (1871) Federigo ENRIQUES (1+ x ) £ (1871) Gino FANO Õ i å i! 2 6 L (1807) Jozeph Mitza PETZVAL i=1 i=0 (1841) Rudolf STURM 7 M (1871) Felix Edouard Justin Emile BOREL Dizionario di Matematica (1907) Raymond Edward Alan Christopher PALEY 8 M (1888) Richard COURANT Chiaramente: Non ho nessuna voglia (1924) Paul Moritz COHN di scrivere tutti i passaggi. (1942) Stephen William HAWKING 9 G (1864) Vladimir Adreievich STELKOV Prima Legge della Matematica 10 V (1875) Issai SCHUR Applicata: tutte le serie infinite (1905) Ruth MOUFANG convergono al loro primo termine. 11 S (1545) Guidobaldo DEL MONTE (1707) Vincenzo RICCATI (1734) Achille Pierre Dionis DU SEJOUR A mathematician's reputation rests 12 D (1906) Kurt August HIRSCH on the number of bad proofs he has 3 13 L (1864) Wilhelm Karl Werner Otto Fritz Franz WIEN given. (1876) Luther Pfahler EISENHART (1876) Erhard SCHMIDT Abram BESICOVITCH 14 M (1902) Alfred TARSKI Probabilities must be regarded as 15 M (1704) Johann CASTILLON analogous to the measurements of (1717) Mattew STEWART (1850) Sofia Vasilievna KOVALEVSKAJA physical magnitudes; that is to say, 16 G (1801) Thomas KLAUSEN they can never be known exactly, but 17 V (1847) Nikolay Egorovich ZUKOWSKY only within certain approximation. (1858) Gabriel KOENIGS 18 S (1856) Luigi BIANCHI Emile BOREL (1880) Paul EHRENFEST I have no certainties, at most 19 D (1813) Rudolf Friedrich Alfred CLEBSCH (1879) Guido FUBINI probabilities. (1908) Aleksandr Gennadievich KUROS Renato CACCIOPPOLI 4 20 L (1775) Andre` Marie AMPERE (1895) Gabor SZEGO What I tell you three times is true. (1904) Renato CACCIOPPOLI 21 M (1846) Pieter Hendrik SCHOUTE Charles DODGSON (1915) Yuri Vladimirovich LINNIK 22 M (1592) Pierre GASSENDI The proof of the Hilbert Basis (1908) Lev Davidovich LANDAU Theorem is not mathematics: it is 23 G (1840) Ernst ABBE (1862) David HILBERT theology. 24 V (1891) Abram Samoilovitch BESICOVITCH Camille JORDAN (1914) Vladimir Petrovich POTAPOV 25 S (1627) Robert BOYLE Probabilities must be regarded as (1736) Joseph-Louis LAGRANGE analogous to the measurement of (1843) Karl Herman Amandus SCHWARTZ physical magnitudes: they can never 26 D (1799) Benoit Paul Emile CLAPEYRON be known exactly, but only within 5 27 L (1832) Charles Lutwidge DODGSON certain approximation. 28 M (1701) Charles Marie de LA CONDAMINE (1892) Carlo Emilio BONFERRONI Emile BOREL 29 M (1817) William FERREL (1888) Sidney CHAPMAN God not only plays dice. He also 30 G (1619) Michelangelo RICCI sometimes throws the dice where they 31 V (1715) Giovanni Francesco FAGNANO dei Toschi cannot be seen. (1841) Samuel LOYD (1896) Sofia Alexandrovna JANOWSKAJA Stephen HAWKING www.rudimathematici.com Rudi Mathematici Febbraio 5 1 S (1900) John Charles BURKILL APMO 1989 [2] 2 D (1522) Lodovico FERRARI Provare che l'equazione 6 3 L (1893) Gaston Maurice JULIA 2 2 2 2 4 M (1905) Eric Cristopher ZEEMAN 6 * (6a + 3b + c ) = 5n 5 M (1757) Jean Marie Constant DUHAMEL non ha soluzioni intere tranne 6 G (1612) Antoine ARNAULD (1695) Nicolaus (II) BERNOULLI a = b = c = n = 0 7 V (1877) Godfried Harold HARDY (1883) Eric Temple BELL Dizionario di Matematica 8 S (1700) Daniel BERNOULLI (1875) Francis Ysidro EDGEWORTH Banale: Se devo spiegarvi come si fa 9 D (1775) Farkas Wolfgang BOLYAI questo, avete sbagliato aula. (1907) Harod Scott MacDonald COXETER 7 10 L (1747) Aida YASUAKI Ci sono due gruppi di persone al 11 M (1800) William Henry Fox TALBOT (1839) Josiah Willard GIBBS mondo: quelli che credono il mondo (1915) Richard Wesley HAMMING possa essere diviso in due gruppi di 12 M (1914) Hanna CAEMMERER NEUMANN persone e gli altri. 13 G (1805) Johann Peter Gustav Lejeune DIRICHLET Connaitre, decouvrir, communiquer. 14 V (1468) Johann WERNER (1849) Hermann HANKEL Telle est la destinée d'un savant (1896) Edward Artur MILNE François ARAGO 15 S (1564) Galileo GALILEI (1861) Alfred North WHITEHEAD Common sense is not really so (1946) Douglas HOFSTADTER common 16 D (1822) Francis GALTON (1853) Georgorio RICCI-CURBASTRO Antoine ARNAULD (1903) Beniamino SEGRE 8 17 L (1890) Sir Ronald Aymler FISHER "Obvious" is the most dangerous word (1891) Adolf Abraham Halevi FRAENKEL in mathematics. 18 M (1404) Leon Battista ALBERTI Eric Temple BELL 19 M (1473) Nicolaus COPERNICUS 20 G (1844) Ludwig BOLTZMANN ...it would be better for the true 21 V (1591) Girard DESARGUES physics if there were no (1915) Evgenni Michailovitch LIFSHITZ mathematicians on hearth. 22 S (1903) Frank Plumpton RAMSEY Daniel BERNOULLI 23 D (1583) Jean-Baptiste MORIN (1951) Shigefumi MORI ...an incorrect theory, even if it cannot 9 24 L (1871) Felix BERNSTEIN be inhibited bay any contradiction 25 M (1827) Henry WATSON that would refute it, is none the less 26 M (1786) Dominique Francois Jean ARAGO incorrect, just as a criminal policy is 27 G (1881) Luitzen Egbertus Jan BROUWER none the less criminal even if it 28 V (1735) Alexandre Theophile VANDERMONDE cannot be inhibited by any court that (1860) Herman HOLLERITH would curb it. Jan BROUWER Mathemata mathematici scribuntur Nicolaus COPERNICUS www.rudimathematici.com Rudi Mathematici Marzo 9 1 S (1611) John PELL APMO 1989 [3] 2 D (1836) Julius WEINGARTEN Siano A1, A2, A3 tre punti sul piano e 10 3 L (1838) George William HILL (1845) Georg CANTOR sia, per notazione, A4=A1, A5=A2. Per 4 M (1822) Jules Antoine LISSAJUS n=1, 2, e 3 supponiamo che Bn sia il 5 M (1512) Gerardus MERCATOR punto medio di AnAn+1, e che Cn sia il (1759) Benjamin GOMPERTZ (1817) Angelo GENOCCHI punto medio di AnBn. Supponiamo 6 G (1866) Ettore BORTOLOTTI che AnCn+1 e BnCn+2 si incontrino in 7 V (1792) William HERSCHEL Dn, e che AnBn+1 si incontrino in En. (1824) Delfino CODAZZI Calcolare il rapporto tra l'area del (1851) George CHRYSTAL 8 S triangolo D1D2D3 e l'area del 9 D (1818) Ferdinand JOACHIMSTHAL (1900) Howard Hathaway AIKEN triangolo E1E2E3. 11 10 L (1864) William Fogg OSGOOD Dizionario di Matematica 11 M (1811) Urbain Jean Joseph LE VERRIER (1853) Salvatore PINCHERLE Si puo` facilmente dimostrare che: 12 M (1685) George BERKELEY Servono non piu` di quattro ore per (1824) Gustav Robert KIRKHHOFF (1859) Ernesto CESARO dimostrarlo. 13 G (1861) Jules Joseph DRACH (1957) Rudy D'ALEMBERT Teorema: tutti i numeri sono noiosi. 14 V (1864) Jozef KURSCHAK (1879) Albert EINSTEIN Dimostrazione (per assurdo). 15 S (1860) Walter Frank Raphael WELDON Supponiamo x sia il primo numero (1868) Grace CHISOLM YOUNG non noioso. Chi se ne frega? 16 D (1750) Caroline HERSCHEL (1789) Georg Simon OHM Mathematics is the most beautiful (1846) Magnus Gosta MITTAG-LEFFLER 12 17 L (1876) Ernest Benjamin ESCLANGON and the most powerful creation of the (1897) Charles FOX human spirit. Mathematics is as old 18 M (1640) Philippe de LA HIRE (1690) Christian GOLDBACH as Man. (1796) Jacob STEINER Stefan BANACH 19 M (1862) Adolf KNESER (1910) Jacob WOLFOWITZ In mathematics the art of proposing a 20 G (1840) Franz MERTENS question must be held on higher value (1884) Philip FRANCK (1938) Sergi Petrovich NOVIKOV than solving it. 21 V (1768) Jean Baptiste Joseph FOURIER (1884) George David BIRKHOFF Georg CANTOR 22 S (1917) Irving KAPLANSKY When writing about transcendental 23 D (1754) Georg Freiherr von VEGA issues, be transcendentally clear. (1882) Emmy Amalie NOETHER (1897) John Lighton SYNGE Rene` DESCARTES 13 24 L (1809) Joseph LIOUVILLE (1948) Sun-Yung (Alice) CHANG The search for truth is more 25 M (1538) Christopher CLAUSIUS important than its possession. 26 M (1848) Konstantin ADREEV Albert EINSTEIN (1913) Paul ERDOS 27 G (1857) Karl PEARSON Property is a nuisance. 28 V (1749) Pierre Simon de LAPLACE Paul ERDOS 29 S (1825) Francesco FAA` DI BRUNO Don't worry about people stealing (1873) Tullio LEVI-CIVITA (1896) Wilhelm ACKERMAN your ideas. If your ideas are any good, 30 D (1892) Stefan BANACH you'll have to ram them down 14 31 L (1596) Rene` DESCARTES people's throat. Howard AIKEN Geometry is the noblest branch of physics. William OSGOOD www.rudimathematici.com Rudi Mathematici Aprile 14 1 M (1640) Georg MOHR (1776) Marie-Sophie GERMAIN APMO 1989 [4] (1895) Alexander Craig AITKEN Sia S un insieme formato da m 2 M (1934) Paul Joseph COHEN coppie (a,b) di interi positivi con la 3 G (1835) John Howard Van AMRINGE (1892) Hans RADEMACHER proprieta` che 1 £ a < b £ n . (1900) Albert Edward INGHAM (1909) Stanislaw Marcin ULAM Mostrare che esistono almeno (1971) Alice RIDDLE n 2 4 V (1809) Benjamin PEIRCE (1842) Francois Edouard Anatole LUCAS m - (1949) Shing-Tung YAU 4m * 4 5 S (1588) Thomas HOBBES 3n (1607) Honore` FABRI (1622) Vincenzo VIVIANI triple(a,b,c) tali che (a,b), (a,c) e (1869) Sergi Alexeievich CHAPLYGIN (b,c) appartengono a S. 6 D 15 7 L (1768) Francais Joseph FRANCAIS Dizionario di Matematica 8 M (1903) Marshall Harvey STONE Verificate per vostro conto: Questa e` 9 M (1791) George PEACOCK la parte noiosa della dimostrazione. (1816) Charles Eugene DELAUNAY (1919) John Presper HECKERT E` provato che la celebrazione dei 10 G (1857) Henry Ernest DUDENEY compleanni e` salutare. Le 11 V (1953) Andrew John WILES statistiche mostrano che chi celebra 12 S (1794) Germinal Pierre DANDELIN (1852) Carl Louis Ferdinand Von LINDEMANN piu` compleanni diventa piu` (1903) Jan TINBERGEN vecchio.