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A brief history of Mathematics

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A brief history of Mathematics Before the Ancient Greeks: Egyptians and Babylonians (c. 2000 BC): Knowledge comes from papyri Rhind Papyrus – PowerPoint PPT presentation

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Title: A brief history of Mathematics


1
A brief history of Mathematics
  • Before the Ancient Greeks
  • Egyptians and Babylonians (c. 2000 BC)
  • Knowledge comes from papyri
  • Rhind Papyrus

2
Babylonian Math
  • Main source Plimpton 322
  • Sexagesimal (base-sixty) originated with ancient
    Sumerians (2000s BC), transmitted to Babylonians
    still used for measuring time, angles, and
    geographic coordinates

3
Greek Mathematics
  • Thales (624-548)
  • Pythagoras of Samos (ca. 580 - 500 BC)
  • Zeno paradoxes of the infinite
  • 410- 355 BC- Eudoxus of Cnidus (theory of
    proportion)
  • Appolonius (262-190) conics/astronomy
  • Archimedes (c. 287-212 BC)

4
Archimedes, Syracuse
5
Euclid (c 300 BC), Alexandria
6
Ptolemy (AD 83c.168), Roman Egypt
  • Almagest comprehensive treatise on geocentric
    astronomy
  • Link from Greek to Islamic to European science

7
Al-Khwarizmi (780-850), Persia
  • Algebra, (c. 820) first book on the systematic
    solution of linear and quadratic equations.
  • he is considered as the father of algebra
  • Algorithm westernized version of his name

8
Leonardo of Pisa (c. 1170 c. 1250) aka Fibonacci
  • Brought Hindu-Arabic numeral system to Europe
    through the publication of his Book of
    Calculation, the Liber Abaci.
  • Fibonacci numbers, constructed as an example in
    the Liber Abaci.

9
Cardano, 1501 1576)
  • illegitimate child of Fazio Cardano, a friend of
    Leonardo da Vinci.
  • He published the solutions to the cubic and
    quartic equations in his 1545 book Ars Magna.
  • The solution to one particular case of the cubic,
    x3 ax b (in modern notation), was
    communicated to him by Niccolò Fontana Tartaglia
    (who later claimed that Cardano had sworn not to
    reveal it, and engaged Cardano in a decade-long
    fight), and the quartic was solved by Cardano's
    student Lodovico Ferrari.

10
John Napier (1550 1617)
  • Popularized use of the (Stevins) decimal point.
  • Logarithms opposite of powers
  • made calculations by hand much easier and
    quicker, opened the way to many later scientific
    advances.
  • MirificiLogarithmorumCanonisDescriptio,
    contained 57 pages of explanatory matter and 90
    of tables,
  • facilitated advances in astronomy and physics

11
Galileo Galilei (1564-1642)
  • Father of Modern Science
  • Proposed a falling body in a vacuum would fall
    with uniform acceleration
  • Was found "vehemently suspect of heresy", in
    supporting Copernican heliocentric theory and
    that one may hold and defend an opinion as
    probable after it has been declared contrary to
    Holy Scripture.

12
René Descartes (1596 1650)
  • Developed Cartesian geometry uses algebra to
    describe geometry.
  • Invented the notation using superscripts to show
    the powers or exponents, for example the 2 used
    in x2 to indicate squaring.

13
Blaise Pascal (1623 1662)
  • important contributions to the construction of
    mechanical calculators, the study of fluids,
    clarified concepts of pressure and.
  • wrote in defense of the scientific method.
  • Helped create two new areas of mathematical
    research projective geometry (at 16) and
    probability theory

14
Pierre de Fermat (16011665)
  • If ngt2, then
  • an bn cn has no solutions in non-zero
    integers a, b, and c.

15
Sir Isaac Newton (1643 1727)
  • conservation of momentum
  • built the first "practical" reflecting telescope
  • developed a theory of color based on observation
    that a prism decomposes white light into a
    visible spectrum.
  • formulated an empirical law of cooling and
    studied the speed of sound.
  • And what else?
  • In mathematics
  • development of the calculus.
  • demonstrated the generalised binomial theorem,
    developed the so-called "Newton's method" for
    approximating the zeroes of a function....

16
Euler (1707 1783)
  • important discoveries in calculusgraph theory.
  • introduced much of modern mathematical
    terminology and notation, particularly for
    mathematical analysis,
  • renowned for his work in mechanics, optics, and
    astronomy.
  • Euler is considered to be the preeminent
    mathematician of the 18th century and one of the
    greatest of all time

17
David Hilbert (1862 1943)
  • Invented or developed a broad range of
    fundamental ideas, in invariant theory, the
    axiomatization of geometry, and with the notion
    of Hilbert space

18
John von Neumann ) (1903 1957)
  • major contributions set theory, functional
    analysis, quantum mechanics, ergodic theory,
    continuous geometry, economics and game theory,
    computer science, numerical analysis,
    hydrodynamics and statistics, as well as many
    other mathematical fields.
  • Regarded as one of the foremost mathematicians of
    the 20th century
  • Jean Dieudonné called von Neumann "the last of
    the great mathematicians.

19
Norbert Wiener (1894-1964).
  • American theoretical and applied mathematician.
  • pioneer in the study of stochastic and noise
    processes, contributing work relevant to
    electronic engineering, electronic communication,
    and control systems.
  • founded cybernetics, a field that formalizes
    the notion of feedback and has implications for
    engineering, systems control, computer science,
    biology, philosophy, and the organization of
    society.

20
Claude Shannon (1916 2001)
  • famous for having founded information theory in
    1948.
  • digital computer and digital circuit design
    theory in 1937
  • demonstratedthat electrical application of
    Boolean algebra could construct and resolve any
    logical, numerical relationship.
  • It has been claimed that this was the most
    important master's thesis of all time

21
What does the future hold?
  • Applications..
  • Biology and Cybernetics

22
Clay Millenium Prizes
  • Birch and Swinnerton-Dyer Conjectureif ?(1) is
    equal to 0, then there are an infinite number of
    rational points (solutions), and conversely, if
    ?(1) is not equal to 0, then there is only a
    finite number of such points. The Hodge
    conjecture asserts that for particularly nice
    types of spaces called projective algebraic
    varieties, the pieces called Hodge cycles are
    actually (rational linear) combinations of
    geometric pieces called algebraic cycles.
  • Navier-Stokes Equationhe challenge is to make
    substantial progress toward a mathematical theory
    which will unlock the secrets hidden in the
    Navier-Stokes equations.
  • P vs NP Problem
  • Poincaré Conjecture
  • The Riemann hypothesis asserts that all
    interesting solutions of the equation
  • ?(s) 0
  • Yang-Mills and Mass Gap

P vs NP Problem
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