Оглавление
Robert Solomon. The Little Book of Mathematical Principles, Theories & Things
Contents
HOW TO USE THIS BOOK
3000 BC Global. Writing Numbers
3rd millennium BC Egypt & Babylonia. Fractions
2000 BC Babylonia. Quadratic Equations
1850 BC Eygpt. The Greatest Pyramid
c. 3rd century BC Global. π
6th century BC Greece & Italy. The Pythagoreans
6th century BC Greece. Pythagoras’s Theorem
6th century BC Greece. Irrational Numbers
6th century BC to Present Global. Perfect Numbers
6th century BC Greece. Regular Polygons
6th century BC Greece. Platonic Solids
6th century BC Global. The Golden Ratio
5th century BC Greece. Trisecting the Angle
5th century BC Greece. Doubling the Cube
5th century BC Greece. Squaring the circle
5th century BC Greece. Zeno’s Paradoxes. Zeno (c. 490–c. 430 BC)
4th century BC Greece. Plato and Platonism. Plato (428–348 BC)
4th century BC Greece. Conic Sections. Menaechmus (380–320 BC)
3rd century BC Greece. Euclid’s Elements. Euclid (c. 325–265 BC)
3rd century BC Greece. The Fifth Postulate. Euclid (c. 325–265 BC)
3rd century BC Greece. Sum of the Angles in a Triangle
3rd century BC Greece. The Fundamental Theorem of Arithmetic. Euclid (c. 325–265 BC)
3rd century BC Greece. The Infinity of Prime Numbers. Euclid (c. 325–265 BC)
3rd century BC Greece. Measurement of a Sphere. Archimedes (287–212 BC)
3rd century BC Greece. Quadrature of the Parabola. Archimedes (287–212 BC)
3rd century BC Greece. The Sand Reckoner. Archimedes (287–212 BC)
2nd century BC Greece. Trigonometry. Hipparchus (190–120 BC)
2nd century BC China. Negative Numbers
150 AD Greece. The Earth-Centered Universe. Claudius Ptolemy (83–161 AD)
628 AD India. Zero. Brahmagupta (598–665 AD)
9th century Iraq. Kitab wa al jabr wa al muqabalah (The Book of Shifting and Balancing) Al-Khwarizmi (c. 780–c. 850 AD)
4th century BC Greece & 1070 AD Iran. Cubic Equations – Geometric Solution. Menaechmus (380–320 BC) Omar Khayyam (1048–1131 AD)
1202 Italy. Fibonacci Numbers. Leonardo of Pisa (Leonardo Fibonacci; 1170–1250)
15th century & 16th century Italy. Perspective
16th century Italy. Cubic Equations – Algebraic Solution. Scipione del Ferro (1465–1526) Niccolo Tartaglia (1500–1557)
1540 Italy. Quartic Equations. Lodovico Ferrari (1522–1565)
1543 Poland. The Sun-Centered Universe. Nicolaus Copernicus (1473–1543)
1575 Italy. Mathematical Induction. Francesco Maurolico (1494–1575)
1602 Italy. Falling Bodies. Galileo Galilei (1564–1642)
1609 Austria. The Sun-Centered Universe Again. Johannes Kepler (1571–1630)
1608 Scotland. Logarithms. John Napier (1550–1617)
1619 Austria & 1974 UK. Tessellations. Johannes Kepler (1571–1630) Roger Penrose (1931–)
1619 Austria & 1809 France. Regular Solids Revisited. Johannes Kepler (1571–1630) Louis Poinsot (1777–1859)
1623 & 1673 Germany, 1642 & 1820 France. Calculating Machines. Wilhelm Schickard (1592–1635) Blaise Pascal (1623–1662) Gottfried Leibnitz (1646–1716) Charles Xavier Thomas de Colmar (1785–1870)
1637 France. Analytic Geometry. René Descartes (1596–1650)
1650 France. A Formula for Prime Numbers. Marin Mersenne (1588–1648) Pierre de Fermat (1601–1665)
1654 France. The Problem of the Points. Pierre de Fermat (1601–1665) Blaise Pascal (1623–1662)
1654 France. Pascal’s Triangle. Blaise Pascal (1623–1662)
1654 France. The Binomial Distribution. Pierre de Fermat (1601–1665) Blaise Pascal (1623–1662)
1660 France. Pascal’s Wager. Blaise Pascal (1623–1662)
1660s & 1670s England & Germany. Differentiation. Sir Isaac Newton (1642–1727) Gottfried Leibnitz (1646–1716)
1660s & 1670s England & Germany. Integration. Sir Isaac Newton (1642–1727) Gottfried Leibnitz (1646–1716)
1660s & 1670s England & Germany. The Fundamental Theorem of Calculus. Sir Isaac Newton (1642–1727) Gottfried Leibnitz (1646–1716)
1660s England. Three Laws of Motion. Sir Isaac Newton (1642–1727)
1660s England. The Law of Gravity. Sir Isaac Newton (1642–1727)
1687 England. The Precession of the Equinoxes. Sir Isaac Newton (1642–1727)
1700s Switzerland. The Law of Large Numbers. Jacob Bernoulli (1654–1705)
1734 England. The Normal Distribution. Abraham de Moivre (1667–1754)
1736 Switzerland. The Seven Bridges of Königsberg. Leonhard Euler (1707–1783)
1742 Germany. Goldbach’s Conjecture. Christian Goldbach (1690–1764)
1750 Switzerland. V + F = E + 2. Leonhard Euler (1707–1783)
1751 France. The Gambler’s Fallacy. Jean d’Alembert (1717–1783)
16th, 17th, & 18th centuries. Complex Numbers
18th century Switzerland. e. Leonhard Euler (1707–1783)
1796 Germany. Regular Polygons Revisited. Carl Friedrich Gauss (1777–1855)
1798 England. Arithmetic and Geometric Progressions. Thomas Malthus (1766–1834)
1799 Germany. The Fundamental Theorem of Algebra. Carl Friedrich Gauss (1777–1855)
1822 France. Fourier Series. Joseph Fourier (1768–1830)
1820s & 1830s UK. The Difference and Analytic Engines. Charles Babbage (1791–1871)
1824 Norway. Quintic Equations. Niels Abel (1802–1829)
1829 & 1832 Russia & Hungary. Non-Euclidean Geometry. Nicolai Lobachevsky (1792–1856) Janos Bolyai (1802–1860)
1832 France. Galois Theory. Evariste Galois (1811–1832)
1837 France. Constructible Lengths. Pierre Wantzel (1814–1848)
1837 France. Doubling the Cube and Trisecting the Angle Revisited. Pierre Wantzel (1814–1848)
1843 Ireland. Quaternions. William Hamilton (1805–1865)
1844 France. Transcendental Numbers. Joseph Liouville (1809-1882)
1850 UK. Kirkman’s Schoolgirl Problem. Thomas Kirkman (1806–1895)
1854 UK. The Laws of Thought. George Boole (1815–1864)
1858 & 1882 Germany. Twisted Shapes. August Möbius (1790–1868) Felix Klein (1849–1925)
1859 Germany. The Riemann Hypothesis. Bernhard Riemann (1826–1866)
1865 UK. Maxwell’s Equations. James Maxwell (1831–1879)
1874 Germany. The Countability of Fractions. Georg Cantor (1845–1918)
1874 Germany. The Uncountability of the Reals. Georg Cantor (1845–1918)
1882 Germany. Squaring the Circle Revisited. Ferdinand von Lindemann (1852–1939)
1888 UK. The Correlation Coefficient. Francis Galton (1822–1911)
1890, 1940, & 1963 Germany & US. The Continuum Hypothesis. Georg Cantor (1845–1918) Kurt Gödel (1906–1978) Paul Cohen (1934–2007)
1890 Italy. Space-Filling Curves. Giuseppe Peano (1858–1932)
1891 Russia. Wallpaper Patterns. Egraf Stepanovitch Fedorov (1853–1919)
1895 France “Doughnuts and Coffee Cups” Henri Poincaré (1854–1912)
1895 UK. What the Tortoise Said to Achilles. Charles Lutwidge Dodgson (also known as Lewis Carroll; 1832–1898)
1896 France & Belgium. The Prime Number Theorem. Jacques Hadamard (1865–1963) Charles de la Vallée Poussin (1866–1962)
1900 Germany. Hilbert’s Problems. David Hilbert (1862–1943)
1900 Germany. Quantum Mechanics. Max Planck (1858–1947)
1901 Russia. The Central Limit Theorem. Alexsandr Lyapusov (1857–1918)
1901 UK. Russell’s Paradox. Bertrand Russell (1872–1970)
1903–1913 Germany & UK. Mathematics as Part of Logic. Gottlob Frege (1848–1925) Bertrand Russell (1872–1970) Alfred Whitehead (1861–1947)
1904 Sweden. The Snowflake Curve. Helge von Koch (1870–1924)
1904 Germany & US. Axiom of Choice. Ernst Zermelo (1871–1953)
1905 US. The Jordan Curve Theorem. Oswald Veblen (1880–1960)
1905 Germany. Special Relativity. Albert Einstein (1879–1955)
1907 Holland. Intuitionism. Liutzen Brouwer (1881–1966)
1908 & 1922 Germany. Zermelo–Fraenkel Set Theory. Ernst Zermelo (1871–1953) Abraham Fraenkel (1891–1965)
1912 Holland. The Hairy-Ball Theorem. Liutzen Brouwer (1881–1996)
1915 Germany. General Relativity. Albert Einstein (1879–1955)
1920s Germany. The Hilbert Program. David Hilbert (1862–1943)
1931 Germany. Gödel’s Theorem. Kurt Gödel (1906–1978)
1930s US. The Traveling Salesman. Karl Menger (1902–1985)
1934 UK. Turing Machines. Alan Turing (1912–1954)
1660s Germany & 1930s US. Binary Numbers. Gottfried Leibnitz (1646–1716) Claude Shannon (1916–2001) George Stibitz (1904–1995)
1938 Poland. The Ham Sandwich Theorem. Stefan Banach (1892–1945)
1930s & 1940s Poland & UK. The Enigma Machine. Marian Rejewski (1905–1980) Alan Turing (1912–1954)
1943 UK. Colossus. Tommy Flowers (1905–1998)
1944 US. Game Theory. John von Neumann (1903–1957) Oskar Morgenstern (1902–1977)
1946 US. ENIAC. John Mauchly (1907–1980) J. Presper Eckert (1919–1995)
1950 USA. The Prisoner’s Dilemma. Albert Tucker (1905–1995)
1950s–1970s USA & Japan. Electronic Calculators
1957 US. Polya’s Principles. George Polya (1887–1985)
20th century US. Erdös Number. Paul Erdös (1913–1996)
1961 US. Chaos Theory. Edward Lorenz (b.1917)
1966 US. The Secretary Problem. F. Mosteller (1916–2006)
1968 France. Catastrophe Theory. René Thom (1923–2002)
1970 UK. Life. John Conway (1937–)
1970 Russia & US. Matiyasevich’s Theorem. Yuri Matiyasevich (1947–)
1971 US. P = NP? Stephen Cook (b.1939)
1970s UK & US. Public Key Codes
1975 US. Fractals. Benoit Mandelbrot (1924–)
1976 US. The Four-Color Theorem. Kenneth Appel (1932–) Wolfgang Haken (1928–)
1976 UK. The Logistic Model. Robert May (1936–)
1998 US. Stacking Oranges. Thomas Hales (1958–)
1998 UK & US. Fermat’s Last Theorem. Andrew Wiles (1953–)
2000 US. The Seven Millennium Prize Problems. Clay Mathematics Institute
Mathematical Threads
Glossary
Acknowledgements
General acknowledgements
Index
