Ancient Math
Who gave the earliest known formula for area of a circle?
The Egyptians. They would compute volumes and areas of figures using proportions, and though they did not think they were formulas, the proportions did give rise to algorithms for calculating these values.
What was Barrow's conjecture, which was proved by Newton?
Fundamental Theorem of Calculus
Who wrote to Fermat about The Problem of the Points?
Blaise Pascal
Who defined group?
Galois
What two individuals proved the following:
We cannot determine if there is a set of cardinality greater than the natural numbers and rational numbers but less than the real numbers
Godel and Paul Cohen (20th century)
What was the Method of Two's given in the Rhind Papyrus?
Main method of multiplication worldwide for at least 3000 years (even when the base 10 number system was introduced)
Only requires ability to double a number and divide it in half
Often done on an abacus
What was the motivation of Leibniz in the creation of calculus?
To study curves and analytic geometry
Who wrote the first book on Mathematical Probability?
Huygens
On Reasoning in Games of Chance
Who's theorems are often used to show that a subgroup is a normal subgroup?
hint: it pertains to prime factorizations of the order of finite groups
Sylow (Ludwig Sylow)
Who proved that every positive definite function can be written as the sum of functions that are squares of functions.
Emil Artin
Who introduced the "Why?" in mathematics? ie Who decided proof was a great idea?
Greeks
more specifically, Thales of Miletus began feeling the need to demonstrate why he was valid
Pythagoras introduced the postulational method
What were the areas of interest of Leibniz (besides calculus)?
Imaginary numbers, symbolic algebra, solving of linear equations using numerical arrays/matrices
Who created a pamphlet with a table that had the first "naive logarithms?"
Napier
What is Representation Theory and who created it?
(represents groups as matrices under multiplication where matrices have complex coefficients or coefficients modulo primes)
Cayley and Frobenius
Is there a packing of 3-d space using spheres with maximum density? How was the answer to this question proved?
Thomas Callister Hales found this packing via computer proof
What was the sexagesimal system used for by the Babylonians?
Measuring geometric angles
What were Newton's original interests that led him to create calculus?
Optics and physics
What was the slide rule, and who created it?
A mechanical device used for multiplying
Gunter and Briggs
What is The Baby Monster?
The 2nd largest simple sporatic group
Are the solutions of regular problems in the calculus of variations always analytic? Who answered this?
Bernstein, De Giorgi, and Nash prove that they are
According to the Greeks, what is a perfect number.
A positive integer which is amicable with itself. ie it equals the sum of its factors
Who attended the famous London "coffee house meeting" regarding force at a distance, which went against Aristotle?
Edmond Halley, Hooke, and Wren
Who created a quick method of multiplication using trig tables and trig identities?
Tycho Brahe and Paul Wittich
Who created the quaternions? What are they an example of?
Hamilton
Division Algebra
State the Birch and Swinnerton-Dyer Conjecture.