Saturday, May 05th, 2012 | Author: Konrad Voelkel
This is a list of resources available on the web for research mathematicians, which used to be updated regularly. The first version was published May 5, 2012. The last update was on March 12, 2015, marked by [UPDATE 15-03-12]. It is now no longer actively maintained.
If you have any recommendations on what to add to this list, please leave a comment below or write an email. Anything resembling advertising will be deleted without comment.
Reference & Bibliography tools
Doing research (and even preparing seminar talks), you need to check the available literature. There are many tools to do this, most notably MathSciNet to get correct bibliographic data, reviews of articles and links to journals to download articles, if possible.
- MathSciNet Mathematical Reviews (MR), paper reviews (subscription required).
- MathSciNet Lookup, bibliographic information (no subscription required).
- Zentralblatt MATH (Zbl), paper reviews.
- swMATH, mathematical software citations. [UPDATE 14-04-02]
- Oberwolfach References on Mathematical Software [UPDATE 14-04-02]
- Google Scholar, a citation search engine.
- The Selected Papers Network, a federated approach to reviewing and discussing articles and preprints.
- Paperscape, an awesome visualization of the arXiv as a galaxy/universe map.
- Eigenfactor, a website with tools to work with "new" metrics.
- Mendeley's mathematics section - Mendely is a reference management tool (now owned by Elsevier).
- CiteSeer, a citation search engine.
- RetractionWatch mathematics section - RetractionWatch is tracking retractions as a window into the scientific process.
- Allyn Jackson: From Preprints to E-prints (AMS Notices 2002, PDF)
- JabRef, an open source bibliography manager (written in Java).
- Nature Special: Science Metrics, like citation count, eigenfactor and h-index.
- Bookworm arXiv, search for trends in the arXiv.
- Google Books NGram Viewer, to see when a specific term was used a lot.
- GitHub: make your code citable, on how to get a DOI for code. [UPDATE 14-06-11]
Open Access Journals & Preprint Archives
Nowadays many publications are discussed as soon as they reach a preprint archive, or an e-print archive. It can take years until journal publication of a preprint, so you will most likely work with preprints anyway.
- ArXiV | How to use ArXiV RSS Feeds
- K-Theory Preprint Archive
- NUMDAM, digitalised math articles, mostly from France.
- Publications of the AMS at JSTOR, open access
- The full JSTOR list, many open access journals
- Project EUCLID, offers access to many open access journals as well as many subscription-only journals.
- Publications on the nLab, a web-based journal for peer-reviewed publication of original research and expository writing.
- DOAJ - directory of open access journals, mathematics section.
Open Access Textbooks & Videos
Sometimes there is no need to buy that expensive textbook.
- Allen Hatcher: Algebraic Topology
- Charles Weibel: The K-book: An introduction to algebraic K-theory, a graduate textbook in progress
- EGA at NUMDAM, Elements de Géometrie Algébrique
- WikiBooks on University-level Mathematics
- J. S. Milne's Course Notes, mostly on algebraic topics.
- Trillia: Alexandre Stefanov's list of textbooks
- The Catsters, a classic resource for category-theory lovers
- David Ben-Zvi's list of Langlands resources, including lecture videos and many course notes
- Lecture videos from the Isaac Newton Institute for Mathematical Sciences, University of Cambridge
- Lecture videos from the IHES
- Lecture videos from the Institute for Advanced Study, School of Mathematics
- VMath video lectures from the MSRI
- OpenCourseWare (OCW) at the MIT
- A MathOverflow thread with lots of links to math videos
- Wolfram MathWorld, an encyclopedia of mathematics.
- Encyclopedia of Mathematics, a wiki-format encyclopedia of mathematics, in collaboration of Springer with the EMS.
Recommend this to non-mathematicians
If you encounter people who seem to like math but aren't (yet) ready for research, send them to these places to play around:
- TED Talks: Numbers at play
- Khan Academy, the online math education website, with videos and exams
- The Art of Problem Solving, intriguing mathematical problems and solutions
- AMS Recommendations for Undergrads, a linklist (US-centric)
- List of interactive math websites @ Reddit (thanks to Anton Maier)
- List of useful free math resources @ Reddit
- Reddit's Math Subreddit, a forum
Innovative Projects & Experiments & Various
A collection of partly well established (MathOverflow), and partly more experimental projects which might change the way you do mathematics, collaboratively, on the web.
- MathOverflow, the question&answer site for research math | customize RSS Feeds like this one.
- math.SE, the StackExchange question&answer site for undergrads.
- Pronunciation of Mathematicians' Names, famous mathematicians and their theorems are pronounced here.
- Polymath, massively collaborative mathematics.
- Tricki, a repository of mathematical know-how.
- Seems to be offline: Open Problem Garden, a collection of open math problems, ranging from easy to millenium-prize class.
- Wolfram Alpha, a computational knowledge engine.
- nCatLab Wiki, the n-Category Café open lab notebook.
- MathBlogging.org, your one-stop shop for mathematical blogs.
- The Stacks Project, an open source textbook and reference work on algebraic stacks and the algebraic geometry needed to define them.
- MFO (Oberwolfach) Photo Collection
- Mathematics Genealogy Project
- Boole's Rings Researchers. Connecting.
- Subject Wikis | most developed: Group Properties
- Mathematicians on Google+ | another such list.
- The On-Line Encyclopedia of Integer Sequences (OEIS)
- LMFDB, the database of L-functions, modular forms, and related objects.
- The Mathematical Atlas, a gateway to modern mathematics.
- The Manifold Atlas, a wiki project
- We Use Math, non-profit website that helps to answer the question "When will I use math?"
- SciGit, easy paper collaboration for scientists
- TrueShelf, educational website focused on crowdsourcing exercises and puzzles in undergraduate and graduate curriculum
- Symbolab, scientific equation search
- π-Base: Counterexamples in Topology, a database version of the popular book - expandable by you! [UPDATE 15-03-12]
- Graded Rings Database [UPDATE 15-03-12]
Some Math Blogs
I warmly recommend clicking through this list and then through the blogrolls of each blog, until you found your niche in the blogosphere. There are vast amounts of content, and there is always some quality content hidden, deep inside. It is really worthwile to search once and to grab the RSS feeds of the 2-3 most interesting blogs. I also recommend to browse through the archives of interesting blogs, sometimes an article from some years ago might inspire you!
- MathBlogging.org Weekly Picks
- Timothy Gowers
- Terence Tao - What's New
- Burt Totaro - Geometry Bulletin Board
- Gil Kalai - Combinatorics and more
- Joel David Hamkins - Mathematics and Philosophy of the Infinite
- Andreas Holmstrom - Motivic Stuff
- Akhil Mathew - Climbing Mount Bourbaki
- Qiaochu Yuan - Annoying Precision
- Charles Siegel - Rigorous Trivialities
- Tanya Khovanova - Math Blog
- Martin Orr's Blog
- Adriana Salerno - PhD+Epsilon, an early-career mathematician blogs about her experiences and challenges.
- Low Dimensional Topology, a group blog
- n-Category Café, a group blog on math, physics and philosophy.
- Azimuth, John Carlos Baez' blog on what scientists can do to help save a planet in crisis.
- Secret Blogging Seminar, a group blog
- ResearchBlogging.org Mathematics section
- Researcher's blog, career advice.
- AMS Graduate Student Blog
- Cathy O’Neil - mathbabe
- Automorphic Forum
The Cost of Knowledge - The Academic Spring
In January 2012, Fields medallist Timothy Gowers wrote a blog post about the academic publisher Elsevier, its bad business practices and that he decided to boycott them. This lead to the creation of a boycott movement website "The Cost of Knowledge" and a discussion forum to change the world of mathematical publishing. The Academic Spring it was called.
- T.Gowers: Elsevier — my part in its downfall.
- the cost of knowledge (dot com)
- Math2.0 Forum, a place to discuss publishing.
- Rehmann's Math Journal Price Survey.
- J.C.Baez: What We Can Do About Science Journals.
- M.Nielsen's comprehensive linklist on the academic spring, really a good starting point to get involved.
- T.Gowers: The Elsevier Boycott one year on.
How to give a talk
Beware that there are many kinds of mathematics talks: seminar talks (audience should understand), workshop talks (experts should understand), colloquium talks (mathematicians should understand most), general public talks (non-mathematicians should understand most) - and all mixtures of these. Most talks take about 45 up to 90 minutes, although some plan only 20 to 30 minutes. It is crucial to know what kind of talk is expected and who the audience is. Besides that ... there are some tips & tricks:
- Matilde Marcolli: The (Martial) Art of Giving Talks, (PDF).
- William T. Ross: How to give a good 20-minute talk
- John E. McCarthy: How to Give a Good Colloquium (PDF)
- P.R. Halmos: How to talk Mathematics, a classic
- Joseph A. Gallian: How to Give a Good Talk, comes with a handy preparation check-list (PDF).
- David Tong: How to Make Sure Your Talk Doesn’t Suck (PDF)
- Read the AMS Notices, in particular the "What is ..." series. It is very good at explaining concepts to the general mathematical public.
How to fail graduate school / obtaining a PhD
Inspired by this MO thread, but mostly stuff I actually read and can recommend. Most of these advice articles seem to think of the US system, where you stay in grad school for a while and then look for an advisor, while it's different in many other countries. However, much advice is useful, and I recommend to read it early on, before entering anything similar to grad school at all!
- Scott Hanselman: It's not what you read, it's what you ignore (not particularly for mathematicians, more for programmers, but still valuable)
- Bob L. Sturm: 25 points for PhD students
- Marie desJardins: How to Be a Good Graduate Student (for computer scientists)
- Secret Blogging Seminar: Thoughts on Graduate School - read the comments!
- Secret Blogging Seminar: Thoughts on Graduate School, addendum
- Terence Tao's career advice
- Ravi Vakil's career advice comes with many links
How to write mathematics teXnically
If you have to write math, you either do it on paper, on a blackboard or on a computer.
On any computer, you'll likely use LaTeX, since the days of trying to use ASCII are long over.
TeXing is an art to be learned, but the basics are pretty easy and it's no longer limited to creating PS or PDF files, but you can literally TeX the web.
- American Scientist: The Science of Scientific Writing [UPDATE 14-03-19]
- TeX StackExchange, the question-answer forum.
- TeXample.net, ample resources for TeX users, especially for TikZ graphics.
- XyJax, an enhancement of MathJax to support (large parts of) xypic.
- HTML escape codes for math | HTML escape codes for greek letters
- LaTeX for WordPress Plug-in, the one I currently use (implemented with MathJax).
- Instiki, a wiki that supports LaTeX+Markdown syntax (implemented in Ruby, with MathJax)
- Detexify - LaTeX symbol classifier, you draw a math symbol with your mouse pointer, then you get LaTeX code.
- MathJax Bookmarklet, to enable LaTeX rendering via MathJax on any website.
- ShareLaTeX - Real Time LaTeX Collaboration is a LaTeX-enabled cloud document editor.
- Make big maths [UPDATE 14-03-19]
- Math IM, TeX-enabled chats [UPDATE 14-03-24]
- Aww app, a sharable whiteboard (without TeX) [UPDATE 14-03-24]
Some conference & summer school listings
You should choose which one is most useful to you, then check that one more often and maybe ignore the rest.
- Meetings and Conferences of the AMS
- Andreas Holmstrom's list of lists
- K-Theory Calendar
- Conferences in Arithmetic Geometry
- Conferences and meetings on Topology and related topics
- Upcoming conferences in algebraic geometry
They still exist. And they're mostly used for job offers and conference announcements.