One Hundred Interesting Mathematical Calculations, Number 9: Archive Entry From Brad DeLong's Webjournal One Hundred Interesting Mathematical Calculations, Number 9 One Hundred Interesting Mathematical Calculations, Number 9: False Positives Suppose that we have a test for a disease that is 98% accurate: if one has the disease, the test comes back "yes" 98% of the time (and "no" 2% of the time), and if one does not have the disease, the test comes back "no" 98% of the time (and "yes" 2% of the time). Suppose further that 0.5% of people--one out of every two hundred--actually has the disease. Your test comes back "yes." Suppose just for ease of calculation that we have a population of 10000, of whom 50--one in every two hundred--have the disease. If you test "no" you can be very happy indeed: there is only one chance in 9752 that you are the unlucky guy who had the disease and yet tested negative. If you test "yes" you are less happy. From John Allen Paulos's Innumeracy .
John von Neumann John von Neumann (/vɒn ˈnɔɪmən/; December 28, 1903 – February 8, 1957) was a Hungarian and later American pure and applied mathematician, physicist, inventor, polymath, and polyglot. He made major contributions to a number of fields,[2] including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and fluid dynamics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.[3] He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, a principal member of the Manhattan Project and the Institute for Advanced Study in Princeton (as one of the few originally appointed), and a key figure in the development of game theory[2][4] and the concepts of cellular automata,[2] the universal constructor, and the digital computer. . and
Alan Turing - Wikipedia English computer scientist (1912–1954) Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist.[5] He was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer.[6][7][8] Turing is widely considered to be the father of theoretical computer science.[9] In 1952, Turing was prosecuted for homosexual acts. He accepted hormone treatment, a procedure commonly referred to as chemical castration, as an alternative to prison. Turing died on 7 June 1954, aged 41, from cyanide poisoning. Turing left an extensive legacy in mathematics and computing which today is recognised more widely, with statues and many things named after him, including an annual award for computing innovation. Early life and education Family School
FIBONACCI "...considering both the originality and power of his methods, and the importance of his results, we are abundantly justified in ranking Leonardo of Pisa as the greatest genius in the field of number theory who appeared between the time of Diophantus [4th century A.D.] and that of Fermat" [17th century] R.B. McClenon [13]. [Numbers in square brackets refer to REFERENCES at the end of this article.] 1. During the twelfth and thirteenth centuries, many far-reaching changes in the social, political and intellectual lives of people and nations were taking place. By the end of the twelfth century, the struggle between the Papacy and the Holy Roman Empire had left many Italian cities independent republics. Among these important and remarkable republics was the small but powerful walled city-state of Pisa which played a major role in the commercial revolution which was transforming Europe. Pisa today is best known for its leaning tower (inclined at an angle of about 161/2o to the vertical).
Ludwig Boltzmann Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion). Biography[edit] Childhood and education[edit] Boltzmann was born in Vienna, the capital of the Austrian Empire. Boltzmann studied physics at the University of Vienna, starting in 1863. Academic career[edit] In 1869 at age 25, thanks to a letter of recommendation written by Stefan,[1] he was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. Ludwig Boltzmann and co-workers in Graz, 1887. In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. Final years[edit] Physics[edit]
David Hilbert _ wikipedia German mathematician (1862–1943) David Hilbert (;[3] German: [ˈdaːvɪt ˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century.[4][5] Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. Early life and education [edit] Hilbert in 1886 Hilbert in 1907 Hilbert and his wife Käthe Jerosch (1892) Franz Hilbert 1. 2. 3.
Loi de Poisson Un article de Wikipédia, l'encyclopédie libre. La loi de Poisson a été introduite en 1838 par Siméon Denis Poisson (1781–1840), dans son ouvrage Recherches sur la probabilité des jugements en matière criminelle et en matière civile[2]. Le sujet principal de cet ouvrage consiste en certaines variables aléatoires N qui dénombrent, entre autres choses, le nombre d'occurrences (parfois appelées « arrivées ») qui prennent place pendant un laps de temps donné. Si le nombre moyen d'occurrences dans cet intervalle est λ, alors la probabilité qu'il existe exactement k occurrences (k étant un entier naturel, k = 0, 1, 2, ...) est où e est la base de l'exponentielle (2,718...)k! On dit alors que X suit la loi de Poisson de paramètre λ. Calcul de p(k)[modifier | modifier le code] Ce calcul peut se faire de manière déductive en travaillant sur une loi binomiale de paramètres (T; λ/T). Il peut aussi se faire de manière inductive en étudiant sur l'intervalle [0; T] les fonctions On note Remarques : et
Bertrand Russell _ wikipedia Russell led the British "revolt against idealism" in the early 20th century.[58] He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore, and his protégé Ludwig Wittgenstein. He is widely held to be one of the 20th century's premier logicians.[55] With A. Russell was a prominent anti-war activist; he championed anti-imperialism[60][61] and went to prison for his pacifism during World War I.[62] Later, he campaigned against Adolf Hitler, then criticised Stalinist totalitarianism, attacked the involvement of the United States in the Vietnam War, and was an outspoken proponent of nuclear disarmament.[63] In 1950 Russell was awarded the Nobel Prize in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought Biography Early life and background Young Bertrand Russell Childhood and adolescence University and first marriage Early career Russell in 1907.
Andreï Kolmogorov Un article de Wikipédia, l'encyclopédie libre. Andreï Nikolaïevitch Kolmogorov Andreï Nikolaïevitch Kolmogorov (en russe : Андрей Николаевич Колмогоров ; 25 avril 1903 à Tambov - 20 octobre 1987 à Moscou) est un mathématicien soviétique et russe dont les apports en mathématiques sont considérables. Biographie[modifier | modifier le code] Enfance[modifier | modifier le code] Kolmogorov est né à Tambov en 1903. Kolmogorov fut scolarisé à l'école du village de sa tante, et ses premiers efforts littéraires et articles mathématiques furent imprimés dans le journal de l'école. Carrière[modifier | modifier le code] Après avoir terminé ses études secondaires en 1920, il suit les cours à l'Université de Moscou et à l'institut Mendeleïev. Après la fin de ses études supérieures en 1925, il commence son doctorat auprès de Nikolaï Louzine, qu’il termine en 1929. La même année, il devient directeur de l'Institut de mathématiques de l'université de Moscou. Contributions[modifier | modifier le code]
Gottlob Frege _ wikipedia German philosopher, logician, and mathematician (1848–1925) Friedrich Ludwig Gottlob Frege (;[15] German: [ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.[16] Life[edit] Childhood (1848–69)[edit] Frege was born in 1848 in Wismar, Mecklenburg-Schwerin (today part of Mecklenburg-Vorpommern). In childhood, Frege encountered philosophies that would guide his future scientific career. 1918–19.
Wiener Kreis De Wiener Kreis (Nederlands: Weense cirkel of Weense kring) (1920-1938) was een groep filosofen en wetenschappers die zich rond Moritz Schlick schaarden. Centrale figuren waren de econoom Otto Neurath, de filosoof Friedrich Waismann en de filosoof Rudolf Carnap. Ludwig Wittgenstein en Karl Popper waren regelmatig bij samenkomsten aanwezig, maar zij waren geen leden van de groep daar zij op essentiële punten afweken van het door de groep gepropageerde logisch positivisme oftewel logisch empirisme. Andere leden waren Gustav Bergmann, Herbert Feigl, Philipp Frank, Kurt Gödel, Hans Hahn, Eino Kaila, Victor Kraft, Karl Menger, Marcel Natkin, Olga Hahn-Neurath, Theodor Radakovic en Rose Rand. Twee boeken lagen aan de basis van de ontwikkelingen van deze stroming, namelijk Wittgensteins Tractatus Logico-Philosophicus (1921), en Carnaps Der logische Aufbau der Welt (1926). Doelstellingen en thema's[bewerken | brontekst bewerken] Bibliografie[bewerken | brontekst bewerken]