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 →
How Big Is 1?
Can we determine how big is 1? Like one meter , one second, one hour. We can tell if we compare one number with another number. It is the property of real number that a < b, or a = b, or a >b. It cannot be determined how big is a stand alone number.... 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 →
Quantification of Thoughts
Thoughts are the noise generated in the form of ideas by human beings. Various diseases and aging are the denial of ideas or thoughts to deposit noise on or inside the body. In my opinion, the messiest part of the human body is the brain. On the other hand, the heart appears to be something... 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 →
Geometrized Symbols and the Related Codes
In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN). The algebraic structure of MDN is established. Assuming the universe as a symbol, the... Continue Reading →
Mr. Monologue 