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Oct 23, 202415 min read

A big list of online resources

A while ago I was wondering, what should I do on the internet? I realized, I liked math, teaching and the internet. I also saved up a relatively long list of webpages which might be interested to mathematicians. I therefore figured, it would hurt to add some commentary and upload them here. The goal is to put all of the URLs I want to save somewhere. This should explain why this is more of a hoard than a well-thought-out collection.

Well, I might do a mathematics web pages tier list someday in the future. Also YouTube channels and blogs are not listed. In my opinion they deserve their own page.

If you are wondering, how I collected all of the pages. For a given category I went to Google to search for results. I put the pages below. If a page contained a resources subpage I went to look for it. I try to prioritize this recursive process on pages which seem important and central, like the Wikipedia pages of a topic or national societies. In mathematics it might happen, that the page no longer exists. In such cases we use the Wayback machine to find an old copy. Sometimes the pages are archived elsewhere but then they are pretty hard to find. Instead of following links we can also backtrack links by using a backlink finder. This often results in pages listing mathematics resources (yummy!).

List of lists

I am not the first one to think of collecting online math resources. I want to direct some attentions to similar projects.

My current learning spaces

I want to highlight some pages which I use for my daily life and where I’d like to have quick access.

News and Magazines

Events

  • European Math Society: The European Math Society has a fantastic calendar containing math events. Interestingly those encompass not only research meetintgs but also events aimed at bachelor and high school students. A similar page is MathMeetings.net
  • Topology project: If you want a definite page for conference in Japan this is it. It contains all important conferences discussing topology. If you go up a level you also find some other things on topology which I haven’t read yet because I often find something better to do than to use my Japanese for reading purposes.
  • COMS: This page has a curated list of all kinds of math conferences. Sadly conferences from the global east are oftentimes not includes. I guess I have to check out Japanese pages then.
  • TUM Math Calender: I have to swallow my pride here. The math calendar of TUM is really something else. It gives a list of all math talks scheduled in and around Munich (with a lot of talks in Garching)
  • UR Wochenplan: The same as above but for Regensburg.

Mathematical Communities

  • Math Stack Exchange: A very good place to ask questions.
  • Matheducators Stack Exchange: The same but for questions concerning math teaching
  • Illustrating Mathematics: Do you want to join a community working towards making mathematics more accessible by computer graphics, 3D-prints and mathematical art? This page might interest you then.
  • Mathematical Society of Japan: Hosts some events (mostly in Tokyo but sometimes in Osaka). I recently learned of the spring meeting. I would have been very sad if I managed to miss that.
  • German Mathematical Society: I am currently not in Germany but before I come back I have to check it out in more detail. The German society takes a more holistic approach to mathematics, doing more outreach in elementary and secondary school than other math societies. This is very nice to see but it makes the links I want to find a little bit harder.

List of open problems

Databases and Wikis

  • Google Scholar: The biggest upside of using Google Scholar is its comfortability. When searching for keywords you usually get pretty satisfactory results.
  • zbMATH Documents: One problem of Google Scholar is that oftentimes articles outside of mathematics find their way into the search results. This is why I use the zbMath Document search for specific literature. Just remember to sort by relevance instead of newest. The documents are reviewed by fellow mathematician and provide insight into the resource. Google scholar also allows you to set up alerts when new results appear under a search (especially helpful to stay updated on specific authors!)
  • zbMATH Classification: Besides documents zbMath also offers a nice view of the Mathematics Subject Classification 2020. This is nicely integrated with the document search. I organize my Obsidian Vault based on the MSC so this is incredibly helpful for me.
  • Arxiv: Very useful. The fact that mathematicians share their work as preprints on Arxiv is a fantastic thing. Besides downloading documents I haven’t found any other uses though. I wish it were more of a social platform with possibilities for subscriptions
  • Approach Zero: Did you ever wonder how to enter Latex-Equations in google? This tool gives you a really simple way to do this. My primary use case is to search explanations on obscure mathematical notations.
  • ProjectEuclid: I understand ProjectEuclid mainly as a place where I could download mathematical journals… If I had any journals I follow! Nonetheless, it seems ProjectEuclid has quite a few quality of life features such as an email alert when journals publish new volumes.

Wikis

  • Wikipedia: As for wikis, Wikipedia is obviously the best bet. It has a familiar layout, making it very comfortable to use. Sadly the definitions can sometimes be very hard to grasp
  • Encyclopedia of Math: The Encyclopedia of Math is usually even harder to read, copying definitions directly out of text books. Which is useful if you don’t want to fetch the book yourself.
  • Wolfram MathWorld: Similar to the Encyclopedia of Math but with a greater focus on picture and understanding. Sadly it does not have the same amout of information.
  • Tungsteno: Tungsteno might have one of the prettiest homepages of any mathematical wiki. I might honestly steal some ideas for my own website. The contents are pretty impressive but since this is managed by only one person there is sadly not much to see.
  • Math Counterexamples: This page offers a big list of counter examples for many different fields of mathematics. If you ever wondered, why can’t the implication be reversed then you might want to check out this site. In case you are looking for something more topological in taste try Pi-Base.
  • ProofWiki: To be honest, I am the kind of person who avoids proofs as much as possible. I am most happy if the definition is elegant enough to make the proof obvious. Still, I know many mathematicians who vehemently disaggree with that statement. The ProofWiki might comfort you then.
  • nLab: The nLab is a wiki exploring mathematics from the higher point of view. In one sense by focusing on everything category theory related. In another sense the page also gives fantastic overviews over broad mathematical fields with tons of hyperlinks and references. Very similar is the Rough Guide Project
  • Quanta Magazines Map of Mathematics: The YouTuber Domain of Science once published a Map of Mathematics. On the search for a better version of it I stumbled on the map by Quanta magazine. It’s nothing like I was searching and honestly, a little bit disappointing. But, it’s steadily growing, I’m looking forward, how the map is going to evolve.
  • Virtual Math Museum: Has a big collection of art pieces and visualizations displaying objects from topology, geometry and much more.

Literature and Lecture Notes

  • List of Lecture Notes
  • MIT Open Cource Ware: MIT Open Course Ware is a platform to download courses and materials (that have been used at MIT?). I haven’t used it myself yet but the selections seems to be very plentiful.

On Latex

  • Quiver: Drawing commutative diagrams can be a pain. Especially I have been asking myself for a long time how I could add commutative diagrams into Obsidian. This is the solution. Just draw the commutative diagram using a friendly UI and continue your studies!
  • Upmath Markdown & Latex editor: So I drew a commutative diagram but how to transfer it to Obsidian? Sadly not all applications support TikZ drawings. One idea is therefore to convert Latex into html. There, the equation are rendered as svg which can be copied. You might find this useful if you want to add latex to your PowerPoint-presentation.
  • Overleaf: My favourite tool to write long Latex documents
  • [Detexify](http://detex: ify.kirelabs.org): You see a mathematical symbol and don’t know how to recreate it in Latex? Just draw it by hand and this website gives you the correct code!
  • Mathpix: A tool to convert screenshots of equations into Latex formulas. I haven’t tried this tool out but it seems to be very useful.

Tools

  • Cinderella: Cinderella is a software that takes GeoGebra to the university level. Looking at the example page, it seems to be useful in many different mathematical disciplines. It can even be used for hyperbolic geometry.
  • Fermatslibrary: A chrome extension to improve the arxiv-experience. Sadly, I using firefox, so this is not really useful to me but I don’t want to remove it from this list.
  • Old Inverse Symbolic Calculator and New Inverse Symbolic Calculator: With an inverse symbolic calculator you can enter a floating point number and get back a formula describing that number. It has the same use cases as the OEIS
  • OEIS: The OEIS is probably the most important resource for the average street fighting mathematician. You want to understand something from your research? Convert it somehow to a sequence and enter it into the OEIS to find connections to completely unrelated fields of math.
  • The GAP System: A very powerful computer algebra system.
  • Wolfram Alpha: I use Wolfram Alpha if I want to get any kind of simple computation done. The natural language input helps because I don’t want to learn a new programming language for a triviality.
  • Braiding: Braiding is a tool which allows the calculation of normal form of braids as well as some other things. It was a pain to set up but it has some features which are not part of the MathLab implementation.
  • SnapPy: Yes, I know. I am watching Henrys videos as soon as they come out. I have met him on a conference. I am studying low-dimensional topology, I admire Thurston’s work, I do mathematical visualizations myself so trust me, I’ll start the application someday.

Professional stuff

  • Jobs from the EMS: The EMS posts jobs for mathematicians. I am currently not at that point but it might come in handy. For a greater focus on the American continent try the portal of the AMS

Cute pages from cute mathematical disciplines

Here are some cute pages from a few mathematical comunities that interest my.

  • Groupprops: Groupprops collects material of group theory. Its goal is to list as many groups and their properties as possible.
  • The House of Graphs: This page aims to collect all interesting graphs.
  • Combinatorial Game Theory: Are you interested in combinatorial games? David Eppstein lists a lot of them and gives details on them.
  • KnotInfo: KnotInfo lists many knots and their properties, similar to this is the KnotAtlas
  • The Geometry Junkyard: A page which lists a lot of (interesting) junk from geometry
  • MacTutor: MacTutor is a online resource containing biographies of more than 3000 mathematicians. Currently I am stuffed with reading materials but in a few years I might come back to the offer. If you are in the mood for something more specific why not check out the Euler Archive dedicated entirely to the work of Leonhard Euler?
  • Number Theory Web: Contains a lot of information on number theory. Most interestingly it contains a list of more resources, related to number theory!
  • Group Names: A list of finite groups for all groups with order less than 500.
  • LMFDB: This stands for The L-functions and modular forms database. It aims to give a wiki and classification of all we know about both topics and aid the Langlands program
  • Collections of Combinatorics Videos: This page collects talks related to combinatorics. I didn’t have time to dive deep into combinatorics but the website references many video portals which might be of interest to me. I have to look into it when I find time to do so.
  • Stack Project: Something, something algebraic geometry. Check it out if you are into that kind of stuff!
  • ETC: This is really stupid. The Encyclopedia of triangle centers lists a lot of possible centers of a triangle. It’s insane.

Books

As already mentioned somewhere at the top. I really don’t have time for books but that doesn’t mean that I am unwilling to collect recommendations.

Funny Homepages

When it comes to their homepages, some mathematicians do the bare necessities whereas others seem to go over the top with design and ideas.

  • Sebastian Hensel: A very average page. Shoutout to my bachelor thesis advisor!
  • Eiko Kin: Maybe the best mentor there is. I am learning much from her. Her page is also quite funny.
  • Alan Hatcher: I like the colour palet.
  • Steven Strogatz: This might be one of the cleanest homepages I have seen.
  • Henry Segerman: Henry Segerman does some sort of quare packing to show off his works. Quite creative indeed!
  • Nathan Carter: Not really a special page but he was the author who drew me into math so he deserves some sort of spotlight
  • John Hubbard: There is a lot of Graduate-Texts-Yellow. (Frankly, I get a headache when I see one of these books)
  • Erich Friedman: Erich Friedman presents a lot of disparate and weird stuff on his page. (With the quare packing being by far the most cursed)
  • John Baez: John Baez does a lot of stuff on the internet. His webpage is so big, it is intimidating but his tips for young researchers is probably a good place to start. Most impressive however, is that there is no CSS file to be seen.
  • Paul Bourke: I have no idea where I found this persons page. Some voice in my head tells me he is the person who makes all of the illustrations on Wikipedia. I have no proof of this but looking through his page you definitely get that feeling
  • Keenan Crane: Another person from the illustrating mathematics community. His page is so crammed, I love it.
  • Kento Nakamura: He likes mathematical visualizations, therefore I like him. But honestly, he created incredible stuff at a young age.

Dumb stuff

Sometimes I need a break from serious mathematics to escape into its dumb side. Like, what is the collaboration distance of my favourite professors? What are my advisors great-great-great-great parents?

  • Collaboration Distance: This page allows you to see how big the collaboration distance between two people is. I notives that this is not really a good indicator of how close they are in any sense but its a funny thing to calculate. Especially amusing is the Erdös number which represents you collaboration distance to Paul Erdös. You can find more information on The Erdös Number Project
  • Math Genealogy Project: The genealogy project allows you to trace the advisor and students of mathematicians. Going through the tree really gives you the feeling as if all mathematicians are part of a big family (especially here in Germany :P ). What is the closest famous great-…-great-advisor of your advisor? My advisor seems to be a descendant of David Hilbert.
  • The Springer GTM Test: Which Springer Graduate Texts in Mathematics Volume are you?
  • Etudes: I can’t read anything off of that page but the toys seem indeed very funny.
  • Mathe-Landkarte: Map showing things the current math outreach landscape in Germany
  • Das Topologikon: A brilliant comic about topology. The images are fantastic and the explanations actually very decent.

Unclassified

Topology Atlas Magnitude: a bibliography Research Rabbit BibBase Veering Home - SLMath - https://www.slmath.org/# Mathigon – Der mathematische Spielplatz - https://de.mathigon.org/ AMS :: Elias M. Stein Prize for Transformative Exposition - https://www.ams.org/prizes-awards/paview.cgi?parent_id=57 Joint European Master’s in Interdisciplinary Mathematics - https://www2.daad.de/deutschland/studienangebote/international-programmes/en/detail/8442/ Asymptote - https://asymptote.sourceforge.io/ Rhino - Rhino.Python Guides - https://developer.rhino3d.com/guides/rhinopython/ Grasshopper 3D - Wikipedia - https://en.wikipedia.org/wiki/Grasshopper_3D Kat in the Hat does a rhyme - Twitch - https://www.twitch.tv/katdoesmaths arminstraub.com - The “What Is…?” column - http://arminstraub.com/math/what-is-column SageMath - Open-Source Mathematical Software System - https://www.sagemath.org/ GDR Tresses The Geometry Center Welcome Page - http://www.geom.uiuc.edu/ The Mathematical Society of Japan - https://www.mathsoc.jp/en/ TAKAGI LECTURES --- Video Archives - https://www.ms.u-tokyo.ac.jp/~toshi/jjm/JJM_HP/contents/takagi/takagi-video.htm 3DXM Virtual Math Museum - https://www.virtualmathmuseum.org/ Portal:Mathematik Cayley Graphs Plotter | JuliaPoo

Train tracks on a torus | Low Dimensional Topology https://www.math.unl.edu/~mbrittenham2/ldt/ldt.html https://web.archive.org/web/20150403103025/http://www.math.niu.edu/~rusin/known-math/index/mathmap.html

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