Resources

References for mathematics:

The “periodic table of finite simple groups”, by Ivan Andrus: https://irandrus.wordpress.com/2012/06/17/the-periodic-table-of-finite-simple-groups/
Chapters 2 and 3 of the ATLAS are probably a more useful reference
Or see the whole ATLAS in PDF form (1985) or online form
Sage quickref: https://wiki.sagemath.org/quickref
Spacebook: https://topology.jdabbs.com/ (“Does first countable and separable imply second countable?”, etc)
Design database: designtheory.org

References for writing:

The grammar according to West (guide to writing in mathematics, particularly for non-native speakers): https://faculty.math.illinois.edu/~west/grammar.html
Google ngrams: “Is it more usual to say ‘well known’ or well-known’?”, etc. https://books.google.com/ngrams
TeXample: http://www.texample.net/. Treat somebody else’s work as a template.
Detexify: “What’s the latex command for the symbol [some scribble]?” http://detexify.kirelabs.org/classify.html
latex2wp: Compile basic latex –> wordpress. https://github.com/seaneberhard/latex2wp
MRLookup: “Give me a bibtex-formatted citation, please”: https://mathscinet.ams.org/mrlookup (or maybe even better: see https://mathoverflow.net/a/319982/20598)
Digital timestamp: Need to certify that you have a proof of the Riemann hypothesis (or whatever) today, but not yet ready to go public? http://www.itconsult.co.uk/stamper.htm (and then don’t email it to me)
mathgen: In case of writer’s block, use this to generate a random math paper: https://thatsmathematics.com/mathgen/

References for speaking:

How to give a colloquium according to John McCarthy: http://www.ams.org/profession/leaders/workshops/gcoll.pdf
Name pronunciation for famous mathematicians: http://www2.onu.edu/~m-caragiu.1/bonus_files/Names.pdf

General advice:

Ten lessons I wish I had been taught, by Gian-Carlo Rota: https://www.ams.org/notices/199701/comm-rota.pdf
Similar: advice on being a mathematician from Paul Halmos: http://www.ams.org/notices/200709/tx070901136p.pdf