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56 Cards in this Set

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  • Back
Associated with number theorem that states if 2^m+1 is prime, them m=2^n. Ex: The nth number of this type equals 2^2^n+1. He thought (incorrectly) that all numbers of this form were prime.
Fermat; it's called the Fermat Numbers Theorem

Ex: F_6=2^2^6+1=2^64+1=641*6700417
Assoc. with theorem: Let n be odd, n≥3. Then a regular n-sided polygon can be inscribed in a unit circle (with a straight edge and compass) iff n is a product of 1 or more distinct ________ primes. (His name goes in the blank.)
Fermat
Called for a new branch of math that was arithmatic instead of geometric
Fermat
Born a frail infant in 1642; his father died when his mother was 3 months pregnant. She remarried and her new husband didn't want to raise ______; he was raised by his grandparents.
Newton
Succeeded Isaac Barrow as holder of the Lucasian chair at Oxford
Newton
Shy and wary of conflict, he didn't put things in writing
Newton
Came up with F=ma
Newton
Developed calculus with derivatives and limits
Newton
Used dots in derivative notation; for example, dx/dt was written as an x with a dot over it
Newton
Was a member of the Royal Society in London
Newton
Objected to the Catholic leaders at Oxford
Newton
Ended up being warden of the Royal Mint
Newton
His calculus called derivatives "fluxions"
Newton
Was unable to get a medical license, but practiced medicine anyway
Cardano
Lived 1501-1576
Cardano
Convinced Tartaglia (aka Niccoso of Fontana) to share his formula for finding the roots of cubic equations
Cardano
Was a gentleman soldier before getting into philosophy
Descartes
Tutored Queen Christina of Sweden
Descartes
Considered the founder of number theory
Fermat
Imprisoned for heresy for publishing the horoscope of Christ
Cardano
Son was executed for wife-poisoning
Cardano
Mainly gambled in his youth
Cardano
Teaching posts often interrupted by scandal; eventually he was forbidden to lecture publicly or to write or publish books
Cardano
Became an astrologer to the papal court in Rome
Cardano
According to various accounts, he predicted he would die on a certain day and so felt obliged to commit suicide to authenticate the prediction
Cardano
Published the solution to the cubic in Ars Magna
Cardano
Wrote Practica Arithmeticae, a book on numerical calculation
Cardano
Wrote the Book on Games of Chance, which broke ground for probability theory 50 years before Fermat and Pascal
Cardano
Was the first to take notice of negative roots
Cardano
Was the first to recognize that a cubic might have 3 roots
Cardano
Made the realization of the existence of complex/imaginary numbers
Cardano
Introduced in Ars Magna the trick of changing a cubic equation to one in which the second-degree term was absent
Cardano
Arrived at the general solution of the reduced cubic
Cardano
Wed algebra and geometry to produce analytic geometry (2 ppl)
Fermat and Descartes
Was a mathematician, physicist, and astronomer
Galileo
Name is assoc withthe birth of modern science
Galileo
Assoc with the Copernican revolution
Galileo
Assoc with the dethronement of Aristotle as the supreme authority in the schools
Galileo
Assoc with the struggle against external restrictions on scientific inquiry
Galileo
Father of analytic geometry
Descartes
Left France for Holland around the time Galileo was sentenced to house arrest
Descartes
Tutored Queen Christina of Sweden
Descartes
Used a theory of vortices to describe planetary motion
Descartes
Amateur mathematician; had a law degree, was a government official, judge
Fermat
Never gave away his solutions
Fermat
Never wrote anything official; all we have is his correspondence
Fermat
Born in Toulouse, France
Fermat
Found the tangent line to a polynomial curve
Fermat
Developed theory of probability with Pascal
Fermat
Issued a challenge problem in 1657 to England, Holland, Germany, France
Fermat
Challenge problem concerned ...
Pell's Equation
Solved challenge problem
Wallis
Wallis didn't like him
Fermat
Father of number theory
Fermat
Had a Little Theorem
Fermat
Used Method of Descent for proving the nonexistence of solutions to Diophantine equations (ex: x^4+y^4=z^2)
Fermat