We have benefited tremendously from the wisdom and tools freely shared by experts online and wished to use our first substantive post as a tribute to those resources that remain. Many pages have proved fleeting: blogs and services abandoned for want of time and money, forums overgrown with spam, small pages forgotten by search engines focused on views… This website will undoubtedly meet the same fate, but in the meantime, perhaps it will serve as a hopping point for a visitor?

Software

Maxima, an open source computer algebra system
Pix2Text, to convert images and PDFs to TeX and other formats
Snip, a freemium alternative

Proofs and tricks

AMS Notices
Math Overflow
Proof Wiki
Tricki, a repository of mathematical know-how

Academic papers

arXiv math
zbMATH

Recorded expert presentations

Banff International Research Station (BIRS)
Hausdorff Center for Mathematics (HCM)
Institut des Hautes Études Scientifiques (IHÉS)
Simons Laufer Mathematical Sciences Institute (formerly MSRI)
Pacific Institute for the Mathematical Sciences (PIMS)

Teaching videos

Math Overflow’s list of free video lectures
3blue1brown’s linear algebra videos
Math Curator Zanachan

Upcoming conferences

Research Seminars (filter by topic)

Other resources

Postbaccalaureate Bridge Programs (pdf)

Blogs

Antoine Chambert-Loir (Freedom Math Dance)
Daniel Litt
Djalil Chafaï
George Lowther (Almost Sure)
George Shakan (Mathematical Research Blog)
Gil Kalai (Combinatorics and more)
Izabella Laba (The Accidental Mathematician)
Maria Gillespie (Mathematical Gemstones)
Mark Sapir
Nick Higham
Peter Cameron
Qiaochu Yuan (Annoying Precision)
Shiraz Khan
Terence Tao (What’s new)
Yaghoub Sharifi

> Meta-blogs

Carnival of Mathematics, a monthly summary of math blogs
AMS blog on math blogs

Podcasts

It’s Not Just Numbers
Random Walks

Forums

math subreddit(s)
les-mathematiques.net (in French)

Books We Really Like

A. Y. Khinchin, Three Pearls of Number Theory
Joseph H. Silverman, A Friendly Introduction to Number Theory
Saban Alaca, Kenneth S. Williams, Introductory Algebraic Number Theory
Walter Rudin, Principles of Mathematical Analysis
Charles Pinter, A Book of Abstract Algebra (skip the last chapters)
Paolo Aluffi, Algebra: Chapter 0
Joseph J. Rotman, An Introduction to the Theory of Groups
Oleg Bogopolski, Introduction to Group Theory