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
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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
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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. 14 29 L (1825) Francesco FAÀ DI BRUNO (1873) Tullio LEVI -CIVITA Georg CANTOR (1896) Wilhelm ACKERMAN This has been done elegantly by 30 M (1892) Stefan BANACH Minkowski; but chalk is cheaper than grey 31 M (1596) Renè DESCARTES mat ter, and we will do it as it comes. Albert EINSTEIN
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14 1 G (1640) Georg MOHR (1776) Marie -Sophie GERMAIN USAMO 1994 [4] (1895) Alexander Craig AITKEN Sia a1, a2, a3, … una sequenza di numeri 2 V (1934) Paul Joseph COHEN n (1835) John Howard Van AMRINGE 3 S reali positivi tali che a j ≥ n per (1892) Hans RADEMACHER ∑ j =1 (1900) Albert Edward INGHAM (1909) Stanislaw Marcin ULAM qualsiasi n ≥ 1. Provate che, per tutti gli (1971) Alice RIDDLE n 4 D (1809) Benjamin PEIRCE 2 1 1 1 (1842) Francois Edouard Anatole LUCAS n ≥ 1, ∑ a j > 1+ +K + (1949) Shing -Tung YAU j =1 4 2 n 15 5 L (1588) Thomas HOBBES (1607) Honorè FABRI Perché un Regolo Calcolatore, Carta e (1622) Vincenzo VIVIANI Matita sono meglio di qualsiasi computer (1869) Sergi Alexeievich CHAPLYGIN 6 M Potete versare tranquillamente caffè s u un Regolo Calcolatore; potete anche usarlo per 7 M (1768) Francais Joseph FRANCAIS girare il caffè. 8 G (1903) Marshall Harvey STONE Il Meraviglioso Mondo della Statistica 9 V (1791) George PEACOCK (1816) Charles Eugene DELAUNAY 1. Il 39% dei disoccupati porta gli occhiali (1919) John Presper HECKERT 2. l’80% degli occupati porta gli occhiali 10 S (1857) Henry Ernest DUDENEY Il lavoro rovina la vista. 11 D (1953) Andrew John WILES The total number of Dirichlet's 16 12 L (1794) Germinal Pierre DANDELIN (1852) Carl Louis Ferdinand Von LINDEMANN publicat ions is not large: jewels are not (1903) Jan TINBERGEN weighed on a grocery scale. 13 M (1728) Paolo FRISI Carl Frederich GAUSS (1813) Duncan Farquharson GREGORY (1879) Francesco SEVERI In describing the honourable mission I 14 M (1629) Christiaan HUYGENS charged him with, M. Pernety informed 15 G (1452) Leonardo da VINCI me that he made my name known to you. (1548) Pietro Antonio CATALDI (1707 ) Leonhard EULER This leads me to confess that I am not as (1809) Herman Gunther GRASSMANN completely unkno wn to you as you might 16 V (1682) John HADLEY believe, but that fearing the ridicule (1823) Ferdinand Gotthold Max EISENSTEIN attached to a female scientist, I have 17 S (1798) Etienne BOBILLIER (1853) Arthur Moritz SCHONFLIES previously taken the name of M. LeBlanc 18 D (1907) Lars Valerian AHLFORS in communicating to you those notes that, (1918) Hsien Chung WANG no doubt, do not deserve the indulgence (1949) Charles L uois FEFFERMAN with which you have responded. 17 19 L (1880) Evgeny Evgenievich SLUTSKY (1883) Richard VIN MISES So phie GERMAIN (1901) Kiyoshi OKA (1905) Charles EHRESMANN [He] gave a formal demonstration of the 20 M (1839) Francesco SIACCI inadequacy of formal demonstrations. 21 M (1652) Michel ROLLE Anonymous, about Kurt GODEL (1774) Jean Baptiste BIOT (1875) Teiji TAKAGI The presentation of mathematics in 22 G (1811) Otto Ludwig HESSE schools should be psychological and not (1887) Harald August BOHR systematic. The teacher, so to speak, 23 V (1858) Max Karl Ernst Ludwig PLANCK should be a diplomat. He must take 24 S (1863) Giovanni VAILATI account of the psychic processes in the 25 D (1849) Felix Christian KLEIN (1900) Wolfgang PAULI boy in order to grip his interest, and he (1903) Andrei Nicolayevich KOLMOGOROV will succeed only if he presents things in a 18 26 L (1889) Ludwig Josef Johan WITTENGSTEIN form intuitively comprehensible. A more 27 M (1755) Marc -Antoine PARSEVAL des Chenes abstract presentation is only possible in the upper classes. 28 M (1906) Kurt GODEL 29 G (1854) Jules Henri POINCARÈ Felix KLEIN 30 V (1777) Johann Carl Friedrich GAUSS (1916) Claude Elwood SHANNON
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18 1 S (1825) Johann Jacob BALMER USAMO 1995 [1] 2 D (1860) D`Arcy Wentworth THOMPSON (1905) Kazimierz ZARANKIEWITZ Sia p un primo dispari. La sequenza (a n), n≥≥≥ 0 è definita come: a0=0 , a1=1 , …, ap-2=p-2 e, per 19 3 L (1842) Otto STOLZ (1860) Vito VOLTERRA tutti gli n≥≥≥ p-1, an è il più piccolo numero 4 M (1845) William Kingdon CLIFFORD positivo che non forma una successione aritmetica di lunghezza p con nessuno dei 5 M (1833) Lazarus Emmanuel FUCHS (1897) Francesco Giacomo TRI COMI termini preceden ti. Provate che, per tutti gli n, an è il numero ottenuto scrivendo n in base p- 6 G (1872) Willem DE SITTER (1906) Andrè VEIL 1 e leggendolo in base p. 7 V (1926) Alexis Claude CLAIRAUT (1854) Giuseppe VERONESE Perché un Regolo Calcolatore, Carta e (1881) Ebenezer CUNNINGHAM Matita sono meglio di qualsiasi computer (1896) Pavel Sergieievich ALEXANDROV Un Regolo Calcolatore, Carta e Matita 8 S (1859) Johan Ludwig William Valdemar JENSEN lasciano in una borsa abbastanza spazio per 9 D (1746) Gaspard MONGE un panino e un ricambio di calzini. (1876) G ilbert Ames BLISS Mathematics: of sciences, queen (1788) Augustin Jean FRESNEL 20 10 L Has more rules than Íve ever seen. (1847) William Karl Joseph KILLING (1958) Piotr Rizierovich SILVERBRAHMS There are no exceptions, Just number deceptions. (1918) Richard Phillips FEYNMAN 11 M On calculators, I am quite keen. 12 M (1845) Pierre RenèJean Baptiste Henry BROCARD (1902) Frank YATES Euclid for children is barbarous . 13 G (1750) Lo renzo MASCHERONI Oliver HEAVISIDE 14 V (1832) Rudolf Otto Sigismund LIPSCHITZ (1863) John Charles FIELDS Now on e may ask, "What is mathematics 15 S (1939) Brian HARTLEY doing in a physics lecture?" We have several possible excuses: first, of course, 16 D (1718) Maria Gaetana AGNESI (1821) Pafnuti Lvovi CHEBYSHEV mathematics is an important tool, but that 21 17 L would only excuse us for giving the 18 M (1850) Oliver HEAVISIDE formula in two minutes. On the other hand, (1892) Bertrand Arthur William RUSSELL in theoretical physic s we discover that all 19 M (1919) Georgii Dimitirievich SUVOROV our laws can be written in mathematical 20 G (1861) Henry Seely WHITE form; and that this has a certain simplicity 21 V (1471) Albrecht DURER and beauty about it. So, ultimately, in order (1792) Gustave Gaspard de CORIOLIS to understand nature it may be necessary to 22 S (1865) Alfred Cardew DIXON have a deeper understanding of 23 D (1914) Lipa BERS mathematical relationships. 22 24 L But the real reason is that the subject is 25 M (1838) Karl Mikailovich PETERSON enjoyable, and although we humans cut 26 M (1667) Abraham DE MOIVRE (1896) Yuri Dimitrievich SOKOLOV nature up in different ways, and we have different courses in different departments, 27 G (1862) John Edward CAMPBELL such compartmentalization is really 28 V (1676) Jacopo Francesco RICCATI (1710) Johann (II) BERNOULLI artificial, and we should take our 29 S (1882) Harry BATEMAN intellectual plea sures where we find them. 30 D (1814) Eugene Charles CATALAN Richard FEYNMAN 23 31 L (1926) John KE MENY
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23 1 M (1796) Sadi Leonard Nicolas CARNOT (1851) Edward Bailey ELLIOTT USAMO 1995 [2] (1899) Edward Charles TITCHMARSH Un calcolatore è rotto in modo tale che i soli 2 M (1895) Tibor RADÒ tasti funzionanti sono sin ; cos ; tan ; sin -1; cos -1; e tan -1. Il video all’inizio segna 0. Dato 3 G (1659) David GREGORY un qualsias i razionale q; mostrate che 4 V (1809) John Henry PRATT premendo una sequenza finita di tasti è 5 S (1814) Pierre LAurent WANTZEL possibile ottenere q. Presumete che il (1819) John Couch ADAMS calcolatore effettui i calcoli con precisione 6 D (1436) Johann Muller REGIOMONTANUS infinita e che tutte le funzioni operino in (1857) Aleksandr Michailovitch LYAPUNOV radianti. (1906) Max ZORN 24 7 L (1863) Edward Burr VAN VLECK Perché un Regolo Calcolatore, Carta e Matita son o meglio di qualsiasi computer 8 M (1625) Giovanni Domenico CASSINI (1858) Charlotte Angas SCOTT Un Regolo Calcolatore vi permette di effettuare (1860) Alicia Boole STOTT cotemporaneamente calcoli seriali e paralleli 9 M (1885) John Edensor LITTLEWOOD (Non è facile, ma si riesce) 10 G (940) Mohammad ABÙL WAFA Al -Buzjani The method of Diophantus (1887) Vladimir Ivanovich SMIRNOV May cease to enchant us 11 V (1937) David Bryant MUMFORD After a life spent trying to gear 'em 12 S (1888) Zygmunt JANYSZEWSKI To Fermat's La st theorem. 13 D (1831) James Clerk MAXWELL In my opinion, a mathematician, in so far (1876) William Sealey GOSSET (Stu dent) as he is a mathematician, need not (1928) John Forbes NASH preoccupy himself with philosophy -- an 25 14 L (1736) Charles Augustin de COULOMB (1856) Andrei Andreyevich MARKOV opinion, moreover, which has been (1903) Alonzo CHURCH expressed by many philosophers. 15 M (1640) Bernard LAMY (1894) Nikolai Gregorievich CHEBOTARYOV Henri Jean LEBESGUE 16 M (1915) John Wilder TUKEY A good mathematical joke is better, and 17 G (1898) Maurits Corneli us ESCHER better mathematics, than a dozen mediocre 18 V (1858) Andrew Russell FORSYTH papers. (1884) Charles Ernest WEATHERBURN John Edensor LITTLEWOOD 19 S (1623) Blaise PASCAL (1902) Wallace John ECKERT My soul is an entangled knot, 20 D (1873) Alfred LOEWY Upon a liquid vortex wrought 26 21 L (1781) Simeon Denis POISSON By Intellect in the Unseen residing, (1828) Giuseppe BRUNO And thine doth like a convict sit, 22 M (1860) Mario PIERI With marlinespike untwisting it, (1864) Hermann MINKOWSKY Only to find its k nottiness abiding; (1910) Konrad ZUSE Since all the tools for its untying (1912) Alan Mathison TURING 23 M In four -dimensional space are lying, 24 G (1880) Oswald VEBLEN Wherein they fancy intersperses 25 V (1908) William Van Orman QUINE Long avenues of universes, 26 S (1824) William THOMPSON, Lord Kelvin While Klein and Clifford fill the void (1918) Yudell Leo LUKE With one finite, unbouded homaloid, 27 D (1806) Augustus DE MORGAN And think the Infinite is now at last destroyed. 27 28 L (1875) Henri Leon LEBESGUE James Klerk MAXWELLL 29 M (1888) Aleksandr Aleksandrovich FRIEDMANN 30 M (1791) Felix SAVART
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27 1 G (1643) Gottfried Wilhelm von LEIBNIZ (1788) Jean Victor PONCELET USAMO 1995 [3] 2 V (1820) William John Racquorn RANKINE Dato un triangolo non isoscele e non rettangolo (1852) William BURNSIDE ABC ; sia O il centro del cerchio circoscritto, e (1807) Ernest Jean Philippe Fauque de JONQUIERE 3 S siano A1; B1; e C1 i punti medi dei lati BC ; CA ; (1897) Jesse DOUGLAS e AB ; rispettivamente. Il punto A2 è posto sul (1906) Daniel Edwin RUTHERFORD 4 D raggio OA 1 in modo tale che il triangolo OAA 1 (1917) Michail Samuilovich LIVSIC sia simile al triangolo OA 2A. I punti B2 e C2 28 5 L sui raggi OB 1 e OC 1; sono rispettivamente 6 M (1849) Alfred Bray KEMPE definiti nello stesso modo. Provate che l e linee 7 M (1816) Johann Rudolf WOLF AA 2; BB 2; e CC 2 sono concorrenti. (1906) William FELLER (1922) Vladimir Aleksandrovich MARCHENKO Perché un Regolo Calcolatore, Carta e Matita sono meglio di qualsiasi computer 8 G (1760) Christian KRAMP Non ricevete continuamente posta che vi offre 9 V (1845) George Howard DARWIN costosi aggiornamenti software per mettere a (1862) Roger COTES 10 S posto degli errori inserendone dei nuovi. (1868) Oliver Dimon KELLOGG 11 D (1857) Sir Joseph LARMOR Il Meraviglioso Mondo della Statistica (1890) Giacomo ALBANESE 29 12 L (1875) Ernest Sigismund FISCHER 1. Ogni secondo nel mondo vengono aperte (1895) Richard BUCKMINSTER FULLER 4000 lattine di birra 13 M (1527) John DEE 2. ogni secondo nel mondo sono concepiti 10 (1741) Karl Friedrich HINDE NBURG bambini 14 M Ogni volta che aprite una birra, avete una 15 G (1865) Wilhelm WIRTINGER probabilità su 400 di restare incinta. (1906) Adolph Andrej Pavlovich YUSHKEVICH It is rare to find learn ed men who are clean, 16 V (1678) Jakob HERMANN (1903) Irmgard FLUGGE -LOTZ do not stink and have a sense of humour. 17 S (1831) Victor Mayer Amedeè MANNHEIM (1837) Wilhelm LEXIS (Montesquieu about) Gottfried von LEIBNIZ 18 D (1013) Hermann von REICHENAU The imaginary number is a fine and (1635) Robert HOOKE wonderful resource of the human spirit, (1853) Hendrich Antoon LORENTZ almost an amphibian between being and 30 19 L (1768) Francois Joseph SERVOIS not being. 20 M Gottfried von LEIBNIZ 21 M (1620) Jean PICARD (1848) Emil WEYR Prob ability is a mathematical discipline (1849) Robert Simpson WOODWARD whose aims are akin to those, for example, (1784) Friedrich Wilhelm BESSEL 22 G of geometry of analytical mechanics. In 23 V (1775) Etienne Louis MALUS (1854) Ivan SLEZYNSKY each field we must carefully distinguish 24 S (1851) Friedrich Herman SCHOTTKY three aspects of the theory: (1871) Paul EPSTEIN (a) the formal logical content, (1923) Christine Mary HAMILL (b) the intuitive background, 25 D (1808) Johann Benedict LISTING (c) the applications. 31 26 L (1903) Kurt MAHLER The character, and the charm, of the whole 27 M (1667) Johann BERNOULLI (1801) George Biddel AIRY structure cannot be appreciated without (1848) Lorand Baron von EOTVOS considering all three aspects in their proper (1871) Ernst F riedrich Ferdinand ZERMELO relation. 28 M (1954) Gerd FALTINGS William FELLER 29 G 30 V 31 S (1704) Gabriel CRAMER (1712) Johann Samuel KOENIG
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31 1 D (1861) Ivar Otto BENDIXSON (1881) Otto TOEPLITZ USAMO 1995 [4] 32 2 L (1856) Ferd inand RUDIO Supponiamo q0, q1, q2, … sia una sequenza (1902) Mina Spiegel REES infinita di interi soddisfacente le seguenti 3 M (1914) Mark KAC condizioni: 4 M (1805) Sir William Rowan HAMILTON 1. m-n divide qm-qn per m>n ≥≥≥ 0 (1838) John VENN 2. Esiste un poli nomio P tale che (1802) Niels Henrik ABEL 5 G |q n|
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36 1 M (1659) Joseph SAURIN (1835) William Stankey JEVONS USAMO 1995 [5] 2 G (1878) Mauriche Renè FRECHET Supponete che in un certo gruppo ogni coppia (1923) R enè THOM di persone possa essere classificata come 3 V (1814) James Joseph SYLVESTER amichevole o ostile . Diremo che ogni membro (1884) Solomon LEFSCHETZ di una coppia amichevole è amico dell’altro (1908) Lev Semenovich PONTRYAGIN membro, mentre ogni membro di una coppia 4 S (1809) Luigi Federico MENABREA ostile è nemico dell’altro. Supponiamo inoltre 5 D (1667) Giovanni Girolamo SACCHERI che il gruppo sia composto da n persone ed (1725) Jean Etienne MONTUCLA esistano q coppie amichevoli, e che per ogni 37 6 L (1859) Boris Jakovlevich BUKREEV insieme di tre persone almeno una coppia sia (1863) Dimitri Aleksandrovich GRAVE ostile. Mostrate che esiste almeno un membro (1707) George Louis Leclerc comte de BUFFON 7 M della società i cui nemici comprendono (1955) Efim ZELMANOV 8 M (1584) Gregorius SAINT -VINCENT 4q (1588) Marin MERSENNE o meno coppie amichevoli. q1− 2 9 G (1860) Frank MORLEY n (1839) Charles Sanders PEIRCE 10 V Perché un Regolo Calcolatore, Carta e 11 S (1623) Stefano degli ANGEL I Matita sono meglio di qualsiasi computer (1877) sir James Hopwood JEANS 12 D (1891) Antoine Andrè Louis REYNAUD I Regoli Calcolatori sono progettati secondo (1900) Haskell Brooks CURRY un’architettura standard e aperta; sono 38 13 L (1873) Constantin CARATHEODORY immuni da virus, worm e qualunque forma di (1885) Wilhelm Johann Eugen BLASCHKE attacco possibile ad adolescenti dotati di 14 M (1858) Henry Burchard FINE connessione telefonica. (1891) Ivan Matveevich VINOGRADOV Q: Che cosa ha un lato solo e vive nel mare? 15 M (973) Abu Arrayhan Muhammad ibn Ahmad AL`BIRUNI (1886) Paul Pierre LEVY A: Mobius Dick. 16 G (1494) Francisco MAUROLICO (1736) Johann Nikolaus TETENS From t he intrinsic evidence of his 17 V (1743) Marie Jean Antoine Nicolas de Caritat de CONDORCET creation, the Great Architect of the (1826) Georg Friedrich Bernhard RIEMANN Universe begins to appear as a pure 18 S (1752) Ad rien Marie LEGENDRE mathematician. 19 D (1749) Jean Baptiste DELAMBRE James Hopwood JEANS 39 20 L (1842) Alexander Wilhelm von BRILL (1861) Frank Nelson COLE It is clear that Economics, if it is to be a 21 M (1899) Juliusz Pawel SCHAUDER science at all, must be a mathematical 22 M (1765) Paolo RUFFINI science. (1769) Louis PUISSANT (1803) Jaques Charles Francois STURM William JEVONS 23 G (1768) William WALLACE If it's jus t turning the crank it's algebra, but (1900) David van DANTZIG if it's got an idea in it, it's topology. 24 V (1501) Girolamo CARDANO (1625) Johan DE WITT Solomon LEFSCHETZ (1801) Michail Vasilevich OSTROGRADSKI How then shall mathematical concepts be 25 S (1819) George SALMON (1888) Stefan MAZURKIEWICZ judged? They shall not be judged. 26 D (1688) Willem Jakob `s GRAVESANDE Mathematics is the supreme arbiter. From (1854) Percy Alexand er MACMAHON (1891) Hans REICHENBACH its decisions there is no appeal.We cannot 40 27 L (1855) Paul Emile APPEL change the rules of the game, we cannot (1876) Earle Raymond HEDRICK ascertain whether the game is fair. We can (1919) James Hardy WILKINSON only study the player at his game; not, 28 M (1698) Pierre Louis Moreau de MAUPERTUIS (1761) Ferdinand Francois Desirè Budan de BOISLAURENT however, with the detached attitude of a (1873) Julian Lowell COOLID GE bystander, for we are watching our own 29 M (1561) Adriaan van ROOMEN (1812) Adolph GOPEL minds at play. 30 G (1775) Robert ADRAIN David van DANTZIG (1829) Joseph WOLSTENHOLME (1883) Ernst HELLINGER
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40 1 V (1 671) Luigi Guido GRANDI (1898) Bela KEREKJARTÒ IMO 1961 [2] 2 S (1825) John James WALKER Siano a, b, c i lati di un triangolo e sia A la sua (1908) Arthur ERDELYI area. Provate che (1944) Pierre Renè DELIGNE 3 D 2 2 2 41 4 L (1759) Louis Francois Antoine ARBOGAST a + b + c ≥ 34 A (1797) Jerome SAVARY In che casi si ha l’uguaglianza? 5 M (1732) Nevil MASKELYNE (1781) Bernhard Placidus J ohann Nepomuk BOLZANO Perché un Regolo Calcolatore, Carta e (1861) Thomas Little HEATH Matita sono meglio di qualsiasi computer 6 M (1552) Matteo RICCI (1831) Julius Wilhelm Richard DEDEKIND Potete impugnare un Regolo Calcolatore a (1908) Sergei Lvovich SOBOLEV braccio teso e darlo in testa al noioso davanti. 7 G (1885) Niels BOHR Q: Cos’è un orso polare? 8 V (1908) Hans Arnold HEILBRONN A: Un orso rettangolar e dopo una 9 S (1581) Claude Gaspard BACHET de Meziriac trasformazione di coordinate. (1704) Johann Andrea von SEGNER (1873) Karl SCHWARTZSCHILD Unfortunately what is little recognized is 10 D (1861) Heinrich Friedrich Karl Ludwig BURKHARDT that the most worthwhile scientific books 42 11 L (1675) Samuel CLARKE are those in which the author clearly (1777) Barnabè BRISSON indicates what he does not know; for an (1885) Alfred HAAR (1910) Cahit ARF author most hurts his readers by concealing 12 M (1860) Elmer SPERRY difficu lties. 13 M (1890) Georg FEIGL Evariste GALOIS (1893) Kurt Werner Friedrich REIDEMEISTER (1932) John Griggs THOMSON An expert is a man who has made all the 14 G (1687) Robert SIMSON mistakes, which can be made, in a very (1801) Joseph Antoine Ferdinand PLATEAU narrow field. (1868) Alessandro PADOA 15 V (1608) Evangelista TORRICELLI Niels BOHR (1735) Jesse RAMSDEN Newton is, of course, the greatest of all (1776) Peter BARLOW Cambridge professors; he also happens to 16 S (1879) Philip Edward Be rtrand JOURDAIN be the greatest disaster that ever befell not 17 D (1759) Jacob (II) BERNOULLI (1888) Paul Isaac BERNAYS merely Cambridge mathematics in 43 18 L (1741) John WILSON particular, but British mathematical science 19 M (1903) Jean Frederic Auguste DELSARTE as a whole. (1910) Subrahmanyan CHANDRASEKHAR Klaus ROTH 20 M (1632) Sir Cristopher WREN (1863) William Henry YOUNG It is true that a mathematician who is not (1865) Aleksandr Petrovich KOTELNIKOV also something of a poet will never be a 21 G (1677) Nicolaus (I) BERNOULLI (1823) Enrico BETTI perfect mathematician. (1855) Giovan Battista GUCCIA Karl WEIERSTRASS (1893) William LEonard FERRAR 22 V (1587) Joachim JUNGIUS (1895) Rolf Herman NEVANLINNA (1907) Sarvadaman CHOWLA 23 S (1865) Piers BOHL 24 D (1804) Wilhelm Eduard WEBER (1873) Edmund Taylor WITTAKER 44 25 L (1811) Evariste GALOIS 26 M (1849) Ferdinand Georg FROBENIUS (1857) Charles Max MASON (1911) Shiing -Shen CHERN 27 M (1678) Pierre Remond de MONTMORT (1856) Ernest William HOBSON 28 G (1804) Pierre Francois VERHULST 29 V (1925) Klaus ROTH 30 S (1906) Andrej Nikolaevich TIKHONOV 31 D (1815) Karl Theodor Wilhelm WEIERSTRASS
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45 1 L (1535) Giamba ttista DELLA PORTA IMO 1961 [4] 2 M (1815) George BOOLE P si trova all’interno del triangolo ABC . PA 3 M (1867) Martin Wilhelm KUTTA interseca BC in D, PB interseca AC in E, e (1878) Arthur Byron COBLE PC interseca AB in F. Provate che almeno uno 4 G (1744) Johann (III) BERNOULLI dei rapporti AP/PD , BP/PE , CP/PF è non (1865) Pierre Simon GIRARD maggiore di 2, e almeno uno è non minore di 2. 5 V (1848) James Whitbread Lee GLAISHER (1930) John Frank ADAMS Perché un Regolo Calcolatore, Carta e 6 S (1781) Giovanni Antonio Amedeo PLANA Matita sono meglio di qualsiasi computer 7 D (1660) Thomas Fantet DE LAGNY Nessuno vi metterà mai in crisi inventando un (1799) Karl Heinrich GRAFFE Regolo Calcola tore più piccolo, veloce o (1898) Raphael SALEM economico del vostro il mese prossimo. 46 8 L (1656) Edmond HALLEY (1846) Eugenio BERTINI Nella moderna matematica l’algebra è (1848) Fredrich Ludwig Gottlob FREGE diventata così importante che presto i numeri (1854) Johannes Robert RYDBERG avranno solo un significato simbolico. (1869) Felix HAUSDORFF 9 M (1847) Carlo Alberto CASTIGLIANO The history of astronomy is a history of (1885) Theodor Franz Eduard KALUZA receding horizons . (1885) Hermann Klaus Hugo WEYL (1906) Jaroslav Borisovich LOPATYNSKY Edwin Powell HUBBLE (1922) Imre LAKATOS The history of mathematics, lacking the 10 M (1829) Helwin Bruno CHRISTOFFEL guidance of philosophy, [is] blind, while 11 G (1904) John Henry Constantine WHITEHEAD the philosophy of mathematics, turning its 12 V (1825) Michail Egorovich VASHCHENKO -ZAKHARCHENKO (1842) John William STRUTT Lord RAYLEIGH back on the most intriguing phenomena in (1927) Yutaka TANIYAMA the history of mathematics, is empty. 13 S (1876) Ernest Julius WILKZYNSKY Imre LAKATOS (1878) Max Wilhelm DEHN 14 D (1845) Ulisse DINI Being a language, mathema tics may be 47 15 L (1688) Louis Bertrand CASTEL used not only to inform but also, among (1793) Michel CHASLES other things, to seduce. (1794) Franz Adolph TAURINUS Benoit MANDELBROT 16 M (1835) Eugenio BELTRAMI 17 M (1597) Henry GELLIBRAND Probability is expectation founded upon (1717) Jean Le Rond D'ALEMBERT partial knowledge. A perfect acquaintance (1790) August Ferdinand MOBIUS with all the circumstances affecting the 18 G (1872) Giovanni Enrico Eugenio VACCA (1927) Jon Leslie BRITTON occurrence of an event would change 19 V (1894) Heinz HOPF ex pectation into certainty, and leave nether (1900) Mi chail Alekseevich LAVRENTEV room nor demand for a theory of (1901) Nina Karlovna BARI probabilities. 20 S (1889) Edwin Powell HUBBLE (1924) Benoit MANDELBROT George BOOLE 21 D (1867) Dimitri SINTSOV Thus metaphysics and mathematics are, 48 22 L (1803) Giusto BELLAVITIS (1840) Emile Michel Hyacinte LEMOINE among all the sciences that belong to 23 M (1616) John WALLIS reason, those in which imagination has the (1820) Issac TOD HUNTER greatest role. I beg pardon of tho se delicate 24 M (1549) Duncan MacLaren Young SOMERVILLE (1909) Gerhard GENTZEN spirits who are detractors of mathematics 25 G (1873) Claude Louis MATHIEU for saying this .... The imagination in a (1841) Fredrich Wilhelm Karl Ernst SCHRODER mathematician who creates makes no less 26 V (1894) Norbert WIENER (1946) Enrico BOMBIERI difference than in a poet who invents.... Of all the great men of antiquity, Archimedes 27 S (1867) Arthur Lee DIXON may be the one who most deserves to be 28 D (1898) John WISHART placed beside Homer. 49 29 L (1803) Christian Andreas DOPPLER (1849) Horace LAMB Jean Le Rond D’ALEMBERT (1879) Nikolay Mitrofanovich KRYLOV 30 M (1549) Sir Henry SAVILE
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49 1 M (1792) Nikolay Yvanovich LOBACHEVSKY IMO 1961 [6] (1831) Paul David Gustav DU BOIS -RAYMOND 2 G Dati tre punti non allineati A, B, C e un piano (1901) George Frederick James TEMPLE p non parallelo a ABC e tale che A, B, C siano 3 V (1903) Sidney GOLDSTEIN (1924) John BACKUS tutti dalla stessa parte di p epresi tre punti arbitrari Á, B' , C' in p, siano Á' , B'' , C'' i tre 4 S (1795) Th omas CARLYLE punti medi di AÁ , BB' , CC' rispettivamente, e 5 D (1868) Arnold Johannes Wilhelm SOMMERFELD (1901) Werner Karl HEISENBERG sia O il centroide di Á' , B'' , C'' . Qual’è il luogo geometrico di O al variare di Á, B' , C' ? 50 6 L (1682) Giulio Carlo FAGNANO dei Toschi 7 M (1647) Giovanni CEVA Perché un Regolo Calcolatore, Carta e (1823) Leopold KRONECKER Matita sono meglio di qualsiasi computer (1830) Antonio Luigi Gaudenzio Giuseppe CREMONA Altra Carta e altre Matite possono essere 8 M (1508) Regni er GEMMA FRISIUS (1865) Jaques Salomon HADAMARD integrate nel sistema senza necessità di (1919) Julia Bowman ROBINSON riconfi gurare tutto. 9 G (1883) Nikolai Nikolaievich LUZIN (1906) Grace Brewster MURRAY HOPPER Legge della Gravità selettiva: Un oggetto (1917) Sergei Vasilovich FOMIN cade in modo tale da causare il maggior danno 10 V (1804) Karl Gustav Jacob JACOBI possibile. (1815) Augusta Ada KING Countess of LOVELACE The shortest path between two truths in the 11 S (1882) Max BORN real domain passes through the complex (1832) Peter Ludwig Mejdell SYLOW 12 D domain . 51 13 L (1724) Franz Ulrich Theodosius AEPINUS (1887) George POLYA Jaques Salomon HADAMARD 14 M (1546) Tycho BRAHE Abel has left mathematicia ns enough to 15 M (1802) Janos BOLYAI keep them busy for 500 years . (1804) Wiktor Yakovievich BUNYAKOWSKY 16 G Charles HERMITE 17 V (1706) Gabrielle Emile Le Tonnelier de Breteuil du CHATELET (1835) Felice CASORATI Mathematics is the science of what (1842) Marius Sophus LIE (1900) Dame Mary Lucy CARTWRIGHT is clear by itself. 18 S (1917) Roger LYNDON Karl Gustav Jacob JACOBI 19 D (1783) Charles Julien BRIANCHON Priusquam autem ad creationem, hoc est ad (1854) Marcel Louis BRILLOUIN finem omnis disputationis, veniamus: 52 20 L (1494) Oronce FIN E (1648) Tommaso CEVA tentanda omnia existimo . (1875) Francesco Paolo CANTELLI 21 M (1878) Jan LUKASIEVIKZ Johannes KEPL ER (1932) John Robert RINGROSE Number theorists are like lotus -eaters - 22 M (1824) Francesco BRIOSCHI (1859) Otto Ludwig HOLDER having tasted this food they can never give (1877) Tommaso BOGGIO it up. (1887) Srinivasa Aiyangar RAMANUJAN Leopold KRONECKER 23 G (1872) Georgii Yurii PFEIFFER There is no branch of mathematics, 24 V (1822) Charles HERMITE (1868) Emmanuel LASKER however abstract, which may not some day 25 S (1642) Isaac NEWTON be applied to phenomena of the real world. (1900) Antoni ZYGMUND 26 D (1780) Mary Fairfax Greig SOMERVILLE Nikolay Yvanovich LOBACH EVSKY (1791) Charles BABBAGE The Analytical Engine weaves algebraic 53 27 L (1571) Johannes KEPLER (1654) Jacob (Jacques) BERNOULLI patterns, just as the Jacquard loom weaves 28 M (1808 ) Athanase Louis Victoire DUPRÈ flowers and leaves. (1882) Arthur Stanley EDDINGTON (1903) John von NEUMANN Augusta Ada KING Countess of LOVELACE 29 M (1856) Thomas Jan STIELTJES The Council of the Royal Society is a 30 G (1897) Stanislaw SAKS collection of men who elect each other to 31 V (1872) Volodymyr LEVIYTSKY office and then dine together at the expense (1896) Carl Ludwig SIEGEL of this society to praise each other over (1952) Vaughan Frederick Randall JONES wine and give each other medals. Charles BABBAGE
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