About yamResearch
Idea
The idea of yamResearch is to serve as an accessible, interactive portfolio of research and ideas by Lyam Boylan in the form of a wiki. It was inspired by the need
- to modernize research papers by making them more digitally interactive and accessible to a wider audience, and
- to organize my thoughts.
Unless otherwise mentioned, all research on this site was conducted by me. However, as is the case with a lot of things in mathematics, much has already been done before. Hence, sections which do reference research by others are either there because they were coincidentally discovered before me, so I have linked to their work out of respect, or are incidentally in theme with - or generally helpful to - the main idea of the article.
Presentation style
The presentation style of this site is inspired by traditional online wikis, especially
nLab (not affiliated).
Internal links are orange, whereas
external links are blue. Two unique integrations are
MathJax, for rendering expressions such as
$$\int_{-\infty}^\infty e^{-x^2}=\sqrt{\pi},$$
and
Desmos, for interactive graphing such as
$$\text{Graph 1. Interactive graph of $\int e^{-x^2}dx$.}$$
I tend to use the pronoun "we" when presenting ideas objectively (that is, "we" as inclusive to author and reader, and anyone following the same lines of reasoning). "I" is reserved only for when something specifically pertains to me as the subject. The focus of most articles are about the research itself, rather than me
as a researcher, so "we" is used almost everywhere.
Themes
As
opposed to, say, having special interest in a specific area like
number theory,
geometry, etc., my research tends to be from a
higher point of view. That is to say, I am interested in
structures, in the most general sense. Despite this level of abstraction, I generally take a more
constructivist approach.
Isolating
By
isolating (the essence of), I mean distilling some structure into some
canonical form.
Some examples include:
Enumerating
By
enumerating (espcially in regards to an isolated family of structures) I mean constructing some
map between a
number set and a family of structures (or the elements of a structure).
Some examples include:
Generalizing
By
generalizing (especially in regard to an enumerated family of structures) I mean realizing some family of structures as a
special case of a more abstract
superset.
Some examples include:
A call to action
We would like to call to action other researchers to modernize and make more-accessible their work.
