# Category: My Math Studies

• ## Some Number Theory

Advertisements Let prime number p be a factor of positive integer m. The integer m has an expression as the difference between two perfect squares s and t, with s greater than t, such that either s+t or s-t equals p. When m=p×1, this will be the only such s and t, and s=t+1. Define […]

• ## Math Insight, After a Morning “Off”

Advertisements Early Tuesday morning, I popped awake, but no mathematical insight was waiting to compel me to stay awake. However, i did walk quietly downstairs to work on my mathematical study, as I have been doing every early morning since the insights started coming – about a week and change now, I think. I took […]

• ## This Morning’s Math Realization

Advertisements Azarya’s Angels did not give me a realization as the result of a train of thought that seized me upon popping awake very early. However, I did pop awake early, and began studying data while enjoying coffee and a donut, and by about 7 a.m., the realization for which the Angels apparently awakened me […]

• ## Math Study Progress

Advertisements I have added all the information I have figured out so far about splitting roots and ceiling discrepancy, as well as the colorful chart I shared here earlier, to the report on Telescoping the Integers. (link) So far, it contains nothing suggestive of new advances in integer factorization, but time and further study will […]

• ## What Hath Eratosthenes Wrought?

Advertisements Numbers sieve us, this table and chart are something he hath wrought! Not bad for a nearly-2300-year-old dead man, eh? P.S. – Hey, Aleister Crowley! Did you know that the discrepancy between the ceiling root of 79 – which is one more than the number of cards in a tarot deck, a.k.a. The Book […]

• ## Mathematical Thoughts: This Morning’s Gifts

Advertisements This morning’s gifts (which I could consider to be from the Queen of the Sciences Herself or from “Azarya’s Angels” who appear to serve as Her messengers to me), the mathematical insights it occurred to me in the early morning hours to ponder, relate to two concepts I have newly discovered: ceiling discrepancy and […]

• ## New Math Paper in Progress

Advertisements The new report on Telescoping the Integers is in progress, and you can go see what’s there so far, if you wish. I shall be exploring and writing a good bit more on it as soon as tonight. https://docs.google.com/document/d/1jpcGfykv5sQl4OPAEx2k8On0oN17cmKGuCI_9xdUaqI/edit?usp=sharing

• ## A New Math Study: Telescoping the Integers, and the Series of Ceiling Roots

Advertisements Yes, it appears mathematics is not done with giving me a flood of ideas in the early morning hours. This time, it was in the form of interesting observations, some of which I felt compelled to work out while I was trying to get back to sleep in preparation for my church choir job, […]

• ## Math Study: Number Pegboards and Series of Ceiling Squares

Advertisements I have put a new mathematical study paper up on Google Docs. This is my “Eureka” moment, even though I feel like I have been having a continuing series of those lately. (Is this what enlightenment feels and acts like?) To Ms. Rebecca Newberger Goldstein (https://twitter.com/platobooktour): Remember your character Azarya in “36 Arguments for […]

• ## A New Math Study: Numbers on a Pegboard

Advertisements For my latest mathematical explorations, the inspiration for which have come like the Ceiling Squares study in the form of ideas demanding me to pursue them in the early hours of morning, I have come up with a way to assign odd integer values to integer points on the Cartesian grid of x>0 and […]