Welcome to Mathyrious !!!  This website is a project explaining pure mathematics to an educated but not necessarily mathematically inclined audience.  This would not only include those unfamiliar with advanced mathematics, but also those with an applied mathematics background who lack an understanding of its theoretical basis.  My approach will initially be far less logically rigorous and technically precise than that of a mathematics textbook.  This does not mean that I believe logical rigor and technical precision are unimportant.  It is just that when first introducing concepts, some rigor and precision may be sacrificed at the altar of clarity.  Both qualities will appear later in this project.

I plan to present developments in pure mathematics within its historical, cultural, and philosophical contexts.  Hopefully, this will not only provide the proper motivations for these developments but also reinforce an understanding of pure mathematics as a human activity that transcends the usual limitations of our understanding.  Regardless of personal beliefs on the nature of mathematical objects and mathematical truth, pure mathematics is transmitted within boundaries set by the aforementioned contexts.

Another focus of mine is to emphasize the interconnected nature of pure mathematics, which serves as the logic of abstract quantitative structures.  This firmly defines pure mathematics as a formal rather than an empirical discipline.  Thus, not only are the truths of pure mathematics assumed prior to any empirical measurements, but the notion that any specific area (or areas) of pure mathematics is necessarily understood as the sole foundation point (or points) for all other areas is rejected.  The common use of axiomatic presentations of pure mathematics is not to be understood as setting a necessary foundation, but rather as choosing one among many possible starting points from which to operate.  The specific choice of a starting point may be set according to the project’s purpose and intended audience, and effectively discarded as the project matures.  Thus, my choices for this project, intended for a more general audience, will differ from those intended for mathematics majors, mathematicians, or computer-aided proof verification.  In any case, I reject the claims for any area of pure mathematics (e.g., set theory, category theory, type theory, etc.) to have an ordained place of privilege within pure mathematics as its sole foundation. 

Any consideration of mathematics (or any academic topic) must be built upon some shared knowledge.  The intended audience should guide this choice of background assumptions.  Given that I am aiming at an educated but not mathematically advanced audience, the material typically covered in an academic track that prepares for college would be sufficient.  Thus, I will assume some familiarity with material usually covered in primary and secondary school mathematics curricula.  This would include basic arithmetic, algebra, and geometry.  This basic material will be reviewed in the Basic Mathematics section of this website

New topics will usually be introduced on the Mathyrious Blog.  Each topic will be examined informally to illustrate its theoretical underpinnings.  Once sufficient material on a given topic has been discussed, it will be presented again in a more rigorous, technical manner in the Notes section of the website.   I will provide problems (with solutions) in the Test Your Knowledge section of the website for you to use to test your understanding.  

Within the Notes area of the website, a set of notes titled Start Here (also appearing in its own area for easy access) serves as an introduction to this project.  I recommend that those new to the website begin there.  Even for readers with advanced knowledge of mathematics, it will provide some indication of the perspectives taken throughout this project and help avoid misunderstandings.  

Additional areas include recommended Books, News, and Links on mathematics and related fields.  Quick summaries of contentious topics online will be provided in the Frequently Asked Questions section of the website.   Selected material from the website serves as the source for videos on the Mathyrious YouTube channel and is mirrored in the Videos area on this website.  Eventually, I hope to open an online store for books and merchandise related to mathematics.  As new material accumulates, returning readers are recommended to check the New at Mathyrious section of the website for announcements and updates.

This website will begin going online in March 2026 and all areas should be functional by the end of the year..