Greetings, everyone, and welcome to Mathyrious!! On this website and its accompanying YouTube channel, I explore the mysterious web of pure mathematics for an audience that is not restricted to those within what is today called STEM (Science, Technology, Engineering, and Mathematics). Thus, I hope to offer something of interest regardless of your prior level of mathematical knowledge.
From the outset, I want to make it clear that I make no claim to be either a mathematician or some undiscovered mathematical genius. As far as mathematics is concerned, I am an amateur dilettante fascinated by its place in the Western intellectual tradition. I want to explore how mathematics arose within that tradition not only among intellectuals but also from less academic areas of the culture. In particular, I want to examine how it grew to include the abstract form known as “pure mathematics.”
I am quite aware that mathematics is not everyone’s favorite subject. Even those who wish to learn more about advanced mathematical topics face an array of technical jargon, arcane symbols, and “mathematical truths” that appear designed to elicit bewilderment. I hope to use my humble corner of the internet to clarify such matters and dispel some of the confusion.
I named this website (and an accompanying YouTube channel) Mathyrious, conflating mathematics and mysterious, to allude to the aura of hidden knowledge that has always accompanied mathematics in general and its pure form in particular. The website’s motto (… exploring the web of pure mathematics) uses the metaphor of a spider’s web to highlight the interconnected nature of its subdisciplines.
Many content creators on YouTube and elsewhere provide excellent expositions at varying levels of mathematical maturity. I do not seek to repeat what has been presented satisfactorily elsewhere. I will concentrate more on the ideas behind the mathematics than detailing the nuts and bolts of its theorems. Presenting these ideas must include placing mathematical developments within their cultural context. This would include not only broad historical and philosophical currents, but also how mathematics interacted with everyday life. Thus, the discussions may range from how mathematics has interacted with the natural sciences, the social sciences, and computer science to philosophy, religion, and the arts, and even business and aspects of entertainment.
Mathematics has never operated in a cultural vacuum, and a closer examination of its development should offer insight into how and why mathematicians have believed what they believed about their subject. In particular, this context should reveal the assumptions underlying the current consensus among mathematicians. Such insight does not require anyone who disagrees with that consensus to conform to it, but it will separate those approaching their disagreements intellectually from those who do so ideologically.
While I will try to keep requirements for prior mathematical knowledge to a bare minimum, some exposure is helpful. In particular, it would be helpful if you had prior exposure to the material usually covered in primary and secondary school mathematics curricula. This would include basic arithmetic, algebra, and geometry. This allows mathematical concepts not yet covered to be offered as examples. In any case, this basic material will be covered.
Given my priorities, I will spend more time on the philosophy and foundations of mathematics than most mathematical curricula. This matters because underlying assumptions shape how one may reach conclusions. If there are disagreements, both sides should be clear on why the final results vary.
There are seven planned content areas on this website as follows:
● News
● Blog
● Videos
● Notes
● Books
● Articles
● Links
● Downloads
If you are viewing on a mobile device, a dropdown menu for access to the home page and the main page for each area appears above with three horizontal lines. For other devices, an equivalent menu bar appears on the right-hand side of each page.
The News appears first and is a good starting point for returning readers. This page announces any changes or additions to the website with corresponding links. You can check there for new posts since your last visit.
The Blog, Videos, and Notes contain the website’s primary content. Blog posts and Videos are self-contained discussions and opinions on a topic. The Blog covers material from foundational to basic to advanced concepts. The Videos are more scattershot in their approach and are often dictated by what other content creators are discussing. There will often be overlap between them, but material may Once a sufficient amount of material is covered through either the Blog or Videos, I may choose to edit and expand on them and issue them in a set of notes. In addition to my own material, I will also call attention to material in books, online articles, and from other content creators. These will appear in Books, Articles, and Links, respectively. Occasionally, I may post material in PDF format that may be accessed under Downloads.
Pages for some content areas may not yet be accessible. Links to inaccessible pages will lead to a Coming Soon page. All current area pages will be operational by the end of 2026. The website may add other areas and corresponding pages in the future.