Calculus
The instantaneous rate of change of a function.
Derivative
The set of all points equidistant from a given point forms a..?
Circle
The set of positive integers, with or without 0 included depending on your definition, is known as this.
The natural numbers
Largely debated on who discovered calculus first, name one of the two main independent discoverers of calculus.
Newton/Leibniz
What's 1004*996? Solve without a calculator.
999,984
Theorem that guarantees that a function f(x) takes on every value between f(a) and f(b) if it is continuous over an interval [a, b].
Intermediate Value Theorem
A helix, a type of spiral, has a constant distance and angle from a central axis. What is the smallest dimension it can exist in?
3-dimension
This boolean operation results in true if exactly one of its two inputs is true.
XOR (exclusive or)
This theorem was famously unproven for many many years, and had the proof omitted from a book because of failure to fit into the margins, this was proven by Andrew Wiles in 1994 and he later corrected his mistakes in that proof in 1995.
Fermat’s Last Theorem
This number's additive inverse is also its multiplicative inverse.
i or -i
The theorem that relates a line integral around a simple closed curve to a double integral over the enclosed region and is a 2D special case of Stokes.
Greene’s Theorem
Which lines in a triangle, when constructed, intersect at the center of the inscribed circle?
Angle bisectors
If a set has n elements, its power set has this many elements.
2^n
This mathematician had so many publications that it inspired the concept of the blank number, named after the degree of separation you had from writing a paper with him.
Erdos
A geometric figure formed by rotating the curve y = 1/x (for x ≥ 1) around the x-axis. What is the surface area of this figure?
Infinite surface area
The mode of convergence of a sequence of functions is strong enough to allow exchanging the limit with a definite integral (and to justify termwise integration).
Uniform Convergence
In spherical geometry, you are given a "line" (a great circle) and a point not on that line. How many lines can you draw through that point that are parallel to the given line?
Zero.
Under the Peano axioms, this is the only integer directly stated to exist.
0
Arguably the most prolific mathematician of all time, Leonhard Euler, became famous for solving this famous problem which the Bernoulli family proposed.
The Basel Problem
This paradox in set theory shows that a hotel with infinitely many rooms can still accommodate infinitely many new guests.
Hilbert’s Hotel
A classic example of a continuous function that is nowhere differentiable.
Weierstrass function
A helix (e.g., a spiral staircase) and a circle are both curves with constant curvature. The torsion (the twisting of the curve out of its plane) of a circle is equal to 0. What is the torsion of a circular helix?
A constant
This rule of inference states that if you know P implies Q, and you know that Q is false, you can conclude P is false.
Modus tollens
This curve is known as being the “curve of quickest descent” which was famously debated throughout the late 1600s and early 1700s.
Brachristochrone Curve
This number is the smallest number of vertices n in a complete graph such that you cannot avoid a two coloring which has a k complete graph the same color.
Ramsey of k, k.