These are links to some online tools and resources that I find useful from time to time and recommend to whoever has not yet heard of them.

• Ferdinand Ihringer's math blog: https://blog.ihringer.org/ (formerly https://ratiobound.wordpress.com/).

• The Grammar According to West (a lot of nice advice on mathematical English writing): https://dwest.web.illinois.edu/grammar.html

• A database of interesting graphs and their properties, featuring a search by a graph drawing: https://houseofgraphs.org/

• Datasets of highly symmetric objects: https://graphsym.net/

• A simple online visual tool for working with graphs, easy to try some classic algorithms, highly recommend for those doing their first course in graph theory to play around and learn: https://graphonline.ru/

• A very nice and extensive wiki-type website devoted entirely to group theory, covers a lot of terminology, properties and classical results with proofs, and information on popular small groups: https://groupprops.subwiki.org/

• Online visual editor that can generate a tikz code of the picture: https://www.mathcha.io/editor

• Websites for drawing (visual to png/svg/tikz) and simulation of finite state automata: https://madebyevan.com/fsm/ and https://automatonsimulator.com/

• Another AI-equipped note-taking and PDF-annotating online tool, and one other free feature it has is generating Python code from a text prompt (and it's often not terrible!): https://app.avidnote.com/

• Citation generator (including but not restricted to DOI -> BibTeX): https://quillbot.com/citation-generator.

• Google Scholar browser extension is also very useful for generating BibTeX from the page that hosts the paper, although sometimes it identifies papers or some information about those papers incorrectly: https://chromewebstore.google.com/detail/google-scholar-button/ldipcbpaocekfooobnbcddclnhejkcpn

• For weird people like me who read pdf files in a browser: The Google Scholar PDF reader is quite convenient as it recognizes citations in text and makes them hyperlinks, which open a small pop-up with info about the paper on google scholar (does not close or scroll anything!). You can also see info on how to cite the paper and who has cited it within the reader: https://chromewebstore.google.com/detail/google-scholar-pdf-reader/dahenjhkoodjbpjheillcadbppiidmhp

• WebTeX is a Chrome extension which uses KaTeX to compile TeX code on websites that do not have it as a build-in feature. Useful for emails that contain TeX code: https://chromewebstore.google.com/detail/webtex-%E2%80%93-render-latex-any/cbcpbegaepelbhjfkikhbhhoemegdbim

• Not quite research or math related, but has been very useful for me, in the work context as well: the Context Reverso online digital translation tool has a PC app which translates any text you highlight on a Ctrl+C+C input, very useful when browsing in an unfamiliar language: https://www.reverso.net/windows-mac-app/en.