Index of Large Numbers
Famous Mathematicians
Famous Proofs
Match the Professor
to the Dissertation
to the Dissertation
Solve
100
The (current) U.S. national debt totals out to 35 of this number
What is trillion
100
The founder of the most well-known geometry (think middle school - high school), the author of Elements
Who is Euclid?
100
Why does a2 + b2 = c2?
100
Studies in Dynamical Systems
Who is Dr. Lee?
100
1+1
What is 2?
200
Sharing a name with a search engine, this number is represented by 10 followed by 100 zeros
What is A googol
200
This German mathematician came up with dy/dx notation for derivatives
Who is Gottfried Wilhelm von Leibniz?
200
ln(y)=ln(x^n)
ln(y)=nln(x)
y′/y=n*1/x
y′=y(n/x)=(x^n)(n/x)=nx^(n−1)
Why does the power rule work?
200
Online and First-Fit Coloring of Bounded Tolerance Graphs
Who is Dr. Saoub?
200
Let n=82022. Find n/4
What is 26064 (or 43032)?
300
This number is represented as G64 and at the time of its discovery, was the largest number ever used in a proof.
What is Grahams number
300
Named the Father of Computer Science and Artificial Intelligence, worked on decrypting the German Naval Enigma Code during WWII
Who is Alan Turing?
300
Assume √c=p/q, c is prime, p/q is simplified
c=p²/q²,
p² must be a multiple of c, so p must be a multiple of c
cq²=p², cq²=(cm)²
cq²=c²m², q²=cm², q must be a multiple of c
√c=p/q, √c=cm/cn, √c=m/n, m/n more simple than p/q, that is a contradiction
Why does √2 have to be Irrational?
300
Parameter Identification and the Design of Experiments for Continuous Non-Linear Dynamical Systems
Who is Dr. Childers?
300
The number of 4-digit (between 1000 and 9999) positive multiples of 5 with only even digits.
What is 100?
400
Sharing a name with a type of large plant, this function can take the number 3 and output a number unfathomably larger than grahams number.
What is TREE(3)
400
Famous for an insane number of things, including the Polyhedral Theorem, the totient function, proving e to be irrational, and this formula: eix = cos(x) + isin(x)
Who is Leonard Euler?
400
assume e=a/b, a,b>0, a,b∈ℤ
Why does e have to be irrational?
400
On Demazure Crystals of the Quantum Affine Algebra
Who is Dr. Maggie?
400
∫(5e^5)/x +(e^5)ln(x)dy
What is (y)((5e^5)/x +(e^5)ln(x))+c ?
500
Created in the 2007 MIT “big number duel”, this number is the largest number that can be created using a googol symbols of first order set theory notation and is named after its creator.
What is Rayos number
500
This mathematician is famous for his Incompleteness Theorem
Who is Kurt Gödel?
500
The base step, that 0p ≡ 0 (mod p), is trivial. Next, we must show that if the theorem is true for a = k, then it is also true for a = k + 1. For this inductive step, we need the following lemma.
Lemma. For any integers x and y and for any prime p, (x + y)p ≡ xp + yp (mod p).
The lemma is a case of the freshman's dream. Leaving the proof for later on, we proceed with the induction.
Proof. Assume kp ≡ k (mod p), and consider (k+1)p. By the lemma we have
(k+1)p≡kp+1p(modp).
Using the induction hypothesis, we have that kp ≡ k (mod p); and, trivially, 1p = 1. Thus
(k+1)p≡k+1(modp),
which is the statement of the theorem for a = k+1. ∎
In order to prove the lemma, we must introduce the binomial theorem, which states that for any positive integer n,
(x+y)n=∑i=0n(ni)xn−iyi,
where the coefficients are the binomial coefficients,
(ni)=n!i!(n−i)!,
described in terms of the factorial function, n! = 1×2×3×⋯×n.
Proof of Lemma. We consider the binomial coefficient when the exponent is a prime p:
(pi)=p!i!(p−i)!
The binomial coefficients are all integers. The numerator contains a factor p by the definition of factorial. When 0 < i < p, neither of the terms in the denominator includes a factor of p (relying on the primality of p), leaving the coefficient itself to possess a prime factor of p from the numerator, implying that
(pi)≡0(modp),0<i<p.
Modulo p, this eliminates all but the first and last terms of the sum on the right-hand side of the binomial theorem for prime p. ∎
The primality of p is essential to the lemma; otherwise, we have examples like
(42)=6,
which is not divisible by 4.
Why does Fermat's little theorem have to be true?
500
An Operator Approach to Linear-Quadratic Stochastic Control Theory
Who is Dr. Minton?
500
dy/dx =-(6xy-y^3)/(4y+3x^2 - 3xy^2)
what is 3(x^2)y - x(y^3 )+ 2(y^2) = C?