# Famous mathematicians

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- Created by: Elena
- Created on: 07-07-20 10:23

## Pythagoras (569-500BC)

- Leader of a Greek religious movement that believed all relations could be reduced to number relations "all things numbers"
**Pythagorean theorem**was known and used by the Babylonians- He is credited with the first recorded proof of this theorem

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## Zeno (495-430BC)

- Conceived a number of
**paradoxes**as an attempt to support the doctrine that all evidence of the senses is illusory (especially motion) - One famous example of such a paradox is the race between the famous Greek hero Achilles and a tortoise
- His paradox is resolved with the insight that a sum of infinitely many terms can nevertheless yield a finite result - calculus
- He reasoned that if the tortoise was given a headstart, Achilles would never be able to overtake it, simply reaching points the tortoise had already reached and moved on from

- This provided an early entree into the mathematics of limits

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## Archimedes (287-212BC)

- Created many inventions, including compound pulley systems, war machines, and even an early planetarium
- His major mathematical writings contributed to understanding the principle of buoyancy, plane equilibriums, and the
**parabola** - Was the first to give a
**scientific method for calculating pi**, by measuring circumscribed polygons approaching a "limit"- One of the earliest approaches to "integration"

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## Euclid (330-275BC)

- His treatise on mathematics,
*The Elements,*endured for two millennia as a principle text on geometry- Commences with definitions and 5 postulates
- First three deal with
**geometrical construction** - Fourth asserts that all right angles are equal
- Fifth states that parallel lines will never meet

- Euclid also proved
**Pythagoras' theorem**independently

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## Descartes (1596-1650)

- Viewed all physical bodies as machines operated by mechanical principles (including the human body)
- In
**analytical geometry**, Descartes proposed that a point in a plane could be determined by distances from two fixed lines ('x' and 'y')- Such coordinates are referred to as "
**Cartesian coordinates**"

- Such coordinates are referred to as "
- Similarly, a point in 3-dimensional space could be determined by three coordinates (x,y,z)

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## Fermat (1601-1665)

- Number theorist who worked on maxima/minima, tangents, and stationary points to become a father of calculus
- Discovered analytic geometry independently of Descartes
- Co-founded
**probability theory**through correspondence with Pascal - Well-known for his "
**Enigma**", also known as Fermat's Last Theorem- x
^{n}+y^{n}=z^{n}has no solution when n>2

- x
- Investigated a type of Archimedean spiral, named
**Fermat's spiral**

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## Pascal (1623-1662)

- Principle contribution was
**probability theory**, the foundations of which were established in a long exchange of letters with Fermat - Created
**Pascal's Triangle**to calculate odds governing combinations- Sum of any row gives the total number of combinations
- Pairs of numbers at the end of each row gives the "odds" of the least likely combinations, with each succeeding pair giving chances of combinations which are increasingly likely

- Work in
**binomial coefficients**lead to Newton's later discovery of the general binomial theorem for fractional and negative powers - Invented the first digital calculator, the "
**Pascaline**"

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## Newton (1643-1727)

- "If I have seen further it is by standing upon the soldiers of giants"
*Principia Mathematica*(The Mathematical Principles of Natural Philosophy), contains his "**Laws of Motion**" and philosophical rules- His
**binomial theorem**dealt with expanding expressions of (a+b)^{n} - Regarded as inventing modern
**calculus**with Leibniz, who developed his own version in the same time frame, resulting in a dispute

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## Leibniz (1646-1716)

- Developed calculus coincident with but independently of Newton, though the
**integral notation**Leibniz developed is more elegant- Integral sign and derivative notation still in use today

- Attempted to develop an '
**alphabet of human thought**' in which all fundamental concepts would be represented by symbols

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## Euler (1707-1783)

- Revised almost all areas of mathematics: filling up details, adding proofs, and arranging the whole in a consistent form
- Euler's famous equation:
**e**^{i(pi)}+1 = 0- In which 'i' is the sign for the
*impossible*square root of -1

- In which 'i' is the sign for the
- Solved a puzzle of how to cross seven bridges without re-crossing them by mathematically representing and formalizing it, in doing so he gave birth to
**modern graph theory**

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## Lagrange (1736-1813)

- Revelled in and put on display the sheer beauty of mathematics
- The"
**Euler-Lagrange equation**" concerns itself with paths, curves, and surfaces for which a given function has a stationary value **Lagrangian points**define a position in space where the pulls of two rotating gravitational bodies combine to form a point at which a third body of comparatively negligible mass would remain stationary- These are valuable in positioning satellites for synchronous orbit and may enable practical interplanetary missions with less fuel

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## Laplace (1749-1827)

*Mécanique Céleste*(Celestial Mechanics), translated the geometrical study of mechanics by Newton to one**based on calculus**- Used calculus, among other things, to explore probability theory
- Laplace's partial differential equation, often referred to as
**Laplace's Equation**has been used for tasks as diverse as describing the stability of the solar system to the field around an electrical charge

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## Gauss (1777-1855)

- Discovered that valid self-consistent geometries could be created in which Euclid's fifth
*parallel postulate*did not hold- These came to be known as '
**non-Euclidean geometries**'

- These came to be known as '
- Gaussian
**distribution curve**, referred to as '**normal distribution**', is wildly applicable in experimental situations where it describes the deviations of repeated measurements from the mean - Positive and negative deviations are equally likely, and small deviations are much more likely than large deviations
- Also known for work on primes, integers, integration, and elimination, which were named Gaussian after him

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## Lovelace (1815-1852)

- Regarded as the first person to anticipate the general-purpose computer and as the first "
**computer programmer**" - Through her acquaintance with Mary Somerville (who translated Laplace's works into English), she met Charles Babbage, the inventor of the calculating machine known as the "
**Difference Engine**" - Babbage later reported at a conference plans for a machine that could not only foresee but act: the "
**Analytical Engine**" - Lovelace translated an article written on this machine adding her own notes, which became the definitive work on computing
- When the United States DoD completed an advanced new computer language in 1980, they named it after her

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