Greetings, everyone, and welcome to Mathyrious!! On this website and its accompanying YouTube channel, I explore the mysterious web of pure mathematics for those whose primary academic interests fall outside what is today called STEM (Science, Technology, Engineering, and Mathematics). Instead, I will harken back to an earlier era by situating mathematics firmly within the liberal arts.
From the outset, I want to be transparent that I claim neither to be a mathematician nor some undiscovered mathematical genius. I am an amateur dilettante fascinated by mathematics and its place in the Western intellectual tradition. I want to explore how mathematics has interacted with other areas within that tradition and how it has grown to include the abstract form known as “pure mathematics.”
Unfortunately, those engaging with mathematics from outside STEM often encounter a bewildering array of technical jargon, arcane symbols, and “mathematical truths” that violate common sense. I will use my humble corner of the internet to post my own musings on such matters and hopefully 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 merely repeat what has been presented satisfactorily elsewhere. Since the fruits of mathematics in the applied sciences are self-evident to anyone who has followed the development of technology in the last few decades, the role of mathematics in these areas hardly needs defending. The same applies to its use in business, from the simpler math of bookkeeping to the more advanced uses by actuaries and statistical analysts. This does not mean I will ignore these applications, but I need not draw attention to their existence.
My approach will be to use a broader brush, focusing on the ideas behind various areas of mathematics without necessarily requiring the reader to engage in all the murky details. For those who want more detail, I will present some in a separate area of the website and provide sources for further reading.
Along with these presentations on “pure mathematics,” I will also write about how these ideas have been applied in other academic areas and in everyday life. For example, this wider intellectual net might include how mathematics interacted not only with science and technology, but also with philosophy, religion, the arts, and even entertainment. Mathematics has never operated in a cultural vacuum, and a closer examination should offer insight into how and why mathematicians believe what they believe about their subject. This does not force anyone else to conform to that view, but any deviation from the mainstream consensus must be explained.
While I will try to keep requirements for prior mathematical knowledge to a minimum, some expectations of a shared background are necessary as a starting point. I will presume readers are familiar with material usually covered in primary and secondary school mathematics curricula. This would include basic arithmetic, algebra, and geometry. This material will be reviewed as necessary.
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
● Notes
● Books
● Articles
● Videos
● Links
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 here for new posts since your last visit.
The Blog and Notes contain the website’s primary content. Blog posts are self-contained discussions and opinions on a subject. Notes are more comprehensive treatments. Many (but not all) extend what has previously appeared in the Blog. Additional areas include recommended Books, Articles, and Links to other sources on mathematics and related fields. The Videos page will embed my YouTube videos to allow for easier access. The material from the videos will overlap with the website but may not be identical in specific content.
Some website area pages 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.