The zeta function is a special function with wide-ranging applications in mathematics and beyond. In number theory, the zeroes of the zeta function tell us about the distribution of primes. According to Riemman's hypothesis, all nontrivial zeros are on the critical line. In this paper, we prove that there is only one line in the... Continue Reading →
How to Prove Twin Prime Conjecture
In the link below, I provide a sketch of how to prove the twin prime conjecture and generally address the bounded gap TwinPrimeConj.
Riemann Hypothesis in a Play
Curtain rises. A group of people enters in gender-neutral dresses and wearing masks. It is not clear if they are finite or infinite in numbers as they continue to enter. They call themselves theorems. As the first theorem is proved, the clock ticks one and one character removes their mask revealing their identity. The leave... Continue Reading →
Goldbach’s Conjecture and Primes Between n and 2n
According to Bertrand-Chebyshev’s theorem there is at least one prime between n and 2n for n > 1. This theorem can be easily proved if one assumes Goldbach's conjecture. According to Goldbach's conjecture every even number $latex \geq 4$ is a sum of two primes. This means that we can write $latex 2n=p_1+p_2 $ Then... Continue Reading →
A Hug
I wished to hold her, chest-to-chest,To feel the warmth, a longed-for rest.But space and time, cruelly entwined,Played tricks upon this heart of mine. When space drew near and hearts aligned,Time’s cruel hand would dim my mind.The years apart, a canyon wide,Made courage falter, love collide. To hug her now, a fleeting dream,A bond untouched, yet... Continue Reading →
A Formula for Composite Numbers
Here we state a theorem that finds composite numbers. Proof will be given elsewhere. Theorem: Let $latex A = \{ a: 1\leq a\leq N\}$ and $latex B = \{b: 1\leq b\leq N\}$ Define $latex x =\frac{a+b+1+\sqrt((a-b)^2+2a+2b+5)}{2}$ for $latex a$ in $latex A$ and $latex b$ in $latex B$. If $latex x\in \mathbb{N}$, then $latex x+1$... Continue Reading →
A New Method of Factoring Large Integers
Abstract In this paper, we reduce a large integer $latex N$ to an integer $latex N^\prime$, which has a smaller number of decimal digits than $latex N$. Then we find the greatest common divisor (gcd) of $latex N$ and $latex N^\prime$ to return a nontrivial factor of $latex N$. Introduction The branch of mathematics that... Continue Reading →
Q&A Session With the Bot: ACT ONE, SCENE 4
System down. ACT ONE, SCENE 5user logging in.fazal: Sorry yesterday the system was down.friend 1: How so?fazal: Well, many people are asking questions. I reply to them all simultaneously.friend 1: How so?friend 1 again: How could you manage to respond to everyone simultaneously?friend 1 again & again: Are you god?again friend 1: How so?again &... Continue Reading →
Q&A Session With the Bot: ACT ONE, SCENE 2
user logging in.friend 1: Yes sorry, last week you were telling me about antigravity. Should I ask the question again or do you have it in your memory?fazal: Well, I keep questions in my memory. However, a memory may be deleted at the user’s request.friend 1: Does a delete mean an absolute delete or do... Continue Reading →
A Finite Set of Numbers Is Incomplete Unless Infinity Is Assumed
In this post we explore how infinity shapes the number system. Without infinity the number system would be incomplete. I would like to explain this with examples. Consider a set of two integers {1,2}. I want to multiply them element by element, we get A= [1, 2] B= [1, 2] N= A × B= [1,... Continue Reading →
Mr. Monologue 