Who we are and what we do

Welcome to the Differential Geometry online math store! I hope you enjoy perusing our ever-growing collection of mathematical images and objects, and that you share your good experiences here with friends. Because I depend on sales to earn a living, I hope some of our products appeal to you enough that you buy them. But although this is a store, selling mathematical products for profit is secondary to sharing the beauty of mathematics.

Professionally I go by Andrew D. Hwang. (Hwang rhymes with song, more or less.) Informally I go by Andy. I love mathematics, geometry and analysis particularly. In 1993 I earned a PhD in mathematics at the University of California, Berkeley. After a 30-year career in academia, I founded Differential Geometry LLC to create original, distinctive, high-quality mathematical images and objects. Our products are designed to arouse curiosity and wonder, to cultivate appreciation for the beauty of modern geometry, analysis, and algebra. Our primary inspiration is form (shape), accessible to everyone without technical training, as an invitation into abstract realms often seen only at the university level.

Mathematics is awesome in the pre-1980 sense. Tens of thousands of people worldwide devote their professional lives to the discipline. If you ask why, you'll hear as many reasons as people you ask, generally encompassing that mathematics is beautiful, compelling, richly subtle.

On the other hand, I have had this exchange many times, and am far from alone:
What do you do?
I'm a mathematician.
Oh. [Pause] I always hated math. (Or: I'm terrible at math.)
If you substitute music for math, you may better appreciate the real human tragedy here.

Mathematics should belong to everyone as a shared cultural gift. Unlike many cultural gifts, mathematics is formally taught, whether students want to learn it or not. Because math is both formally taught and compulsory, there are stakes involved, pressures exerted, assessments exacted, judgments issued. To be candid, there is no joy in any of those things.

One major goal of the Differential Geometry store is to make mathematics beautiful to people who think it is not. To many Americans (and possibly others), math means formulas and algorithms. Formulas and algorithms do have a beauty to them, but (typographical symmetry aside) that beauty is indirect, the result of translating symbols into concepts or operations, and comprehending the resulting structure or process. Form, by contrast, more directly engages human senses of sight and touch.

By and by in this sequence of blog posts we'll get to the actual mathematics behind our images and objects. To round off this short introduction, let me relate a couple of more human details.

First, pricing. While giving away products is incompatible with earning a living by running the store, I have deliberately made all our images available in some version at the lowest retail price that makes them feasible to carry.

The store's pricing is intentionally straightforward. The prices at the Differential Geometry store are set monotonically, in a way designed to encourage you to select the specific product wanted, not to encourage "buying more to save more" or other consumerist mind games.

Second, sourcing. Money should be a tool of well-being. If commerce increases exploitation or environmental damage to increase profit, then the system is badly-incentivized. Our products are manufactured by firms that, to the best of my ability to distinguish, behave with social and environmental responsibility.

You didn't ask, but the software used to create our images and objects is largely "home grown" over my years in academia.

Finally, why the name? Maybe you have never heard the phrase differential geometry and find it obscure. Maybe you work in the field of differential geometry and find the name uninspired.

In mathematics, differential geometry refers generally to the use of differential calculus to study shape. My own area of training was complex differential geometry, especially extremal Kähler metrics. There were natural professional reasons for choosing an appealing name evoking the great love of my intellectual life.

On the other hand, mathematical terms get borrowed outside mathematics, perhaps because they carry a trustworthy or authoritative cachet. I spent a number of days brainstorming company names and domain names, then web searching to see if they existed. They did, but uniformly belonged to firms in fields such as medical devices, architecture, cosmetics, fabrics, engineering, or business consultancy.

Differential Geometry appealed both for its technical meaning, and for its colloquial association, distinctive geometry. After a few months of sitting with it as a prospective name I still liked it.

So why is the domain diffgeom.com? For one thing, it's shorter, snappier, easier to remember and type than the full name. But there is another reason: A domain name homesteader had already purchased differentialgeometry.com, not for use but for sale. You may be able to guess the ballpark asking price if you imagine the budget of a large, well-established company.

That's a capsule summary of who we are and what we do. I look forward to designing and creating differential geometric images and objects for many years to come, sharing them with you, and helping you and those you know build your own love of math.