Snapshots of modern mathematics from Oberwolfach
imaginary.org
imaginary.org
* Wolfram Alpha: For quick, very short definitions from a variety of perspectives, but probably you already know that. https://www.wolframalpha.com
* Wolfram's Mathworld: Encyclopedia originally by Eric Weisstein; Wolfram acquired and expanded it. Good for brief, precise definitions and broad coverage, but it can be a bit terse: http://mathworld.wolfram.com/
* Encyclopaedia of Mathematics wiki: "The original articles are from the online Encyclopaedia of Mathematics, published by Kluwer Academic Publishers in 2002. With more than 8,000 entries, illuminating nearly 50,000 notions in mathematics, the Encyclopaedia of Mathematics was the most up-to-date graduate-level reference work in the field of mathematics. / Springer, in cooperation with the European Mathematical Society, has made the content of this Encyclopedia freely open to the public." IME, an excellent, reliable reference; only downside is that it's a bit uneven in breadth and depth: https://www.encyclopediaofmath.org/
* Encyclopaedia Britannica: Excellent, accurate, and in-depth, especially for basic topics. https://www.britannica.com
* Stanford Encyclopedia of Philosophy: Encyclopedia by professional philosophers, covers many mathematics topics. Dense but certainly in-depth. https://plato.stanford.edu/
...
And a few that you have to pay for:
* The Princeton Companion to Mathematics, edited by Timothy Gowers: You probably already know about this one. It's an amazing opus that covers pure mathematics.
* Mathematics: Its Content, Methods and Meaning by Aleksandrov, et al: Encyclopedia, in the form of a large collection of survey articles, by Soviet mathematicians in the mid-20th century. Strong on historical context. Highly regarded at the the time; from the review in Science: "Whether a physicist wishes to know what a Lie algebra is or how it is related to a Lie group, or an undergraduate would like to begin the study of homology, or a crystallographer is interested in Fedorov groups, or an engineer in probability, or any scientist in computing machines, he will find here a connected, lucid account." http://store.doverpublications.com/0486409163.html
* Oxford English Dictionary: As surprising as it sounds, often I've found no better source for learning new mathematical terms. For each term, the comprehensive variety of definitions from many angles along with the historical quotes, often from mathematicians you'd recognize, provide great context, depth, and insight; the competitors above can't match the OED's research. And yes, the definitions are mathematically accurate as far as I've been able to tell. http://oed.com
do you have an example?
Coincidentally, Wiktionary had a math session last month. How do you like https://en.wiktionary.org/wiki/triangulation for example?
Mathematicians like Don Knuth take great care to source etymologies of mathematical terms, too. In some cases it seems necessary to avoid confusion over different, similarly named ideas.
> do you have an example?
Off the top of my head and IIRC, harmony and root.
> Wiktionary
While I respect the efforts of Wiktionary and Wikipedia, I don't use them for mathematics. Mathematics is a field whose distinguishing feature, in a sense, is its exact precision. I don't have the expertise to read crowd-sourced material and identify which information reaches that level of precision, which is a little off, which is fringe, and which is just nonsense. In the case of mathematics, information of uncertain accuracy is worse than no information at all, IMHO.
I once read an article by a mathematician reviewing Wikipedia. One page they looked at contained some good information, some imprecise information, and some nonsense: The thing I remember was a section about a discovery in the field; the discovery was insignificant, if it was real, and it was attributed to someone nobody heard of. The reviewer speculated that the person to which it was attributed must have added the section.
> Mathematicians like Don Knuth take great care to source etymologies of mathematical terms, too
That's great. It's hard to imagine he has the resources and expertise in etymology of the OED.
When I want to learn something on a scholarly level, there's no substitute for resources who already have done some of the scholarly heavy lifting for me.