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Show HN: Discover the World of Mathematics (mathpendium.org)
108 points by CatsAreCool 13 days ago | hide | past | web | favorite | 36 comments

The front page is too empty. You must add some links to popular topics (quadratic equation? topology?) and some link to random topics. Something like the Wikipedia main page.

There is an error in https://mathpendium.org/view/5e33c092981ec41bc6b27939 (two missed $ and the rendered is unhappy with \subset)

Can I edit without an account? Please. I'm too lazy to create one :) . I guess it's a tradeoff between spam and making it easy to make small contributions.

Thanks for the feedback. Yes, it seems I need to redesign the site to make it easier to navigate and feel less empty. I like your suggestions about adding popular topics.

Thanks for letting me know about the error. Right now Mathpendium has around 1000 entries, and so it is easy for some errors to slip through the cracks.

I was debating about whether or not to require an account to make a contribution. As you mentioned, making an account helps decrease the chance of spam. However, I am open to allowing anonymous contributions, and it is good to know that others would appreciate that.

I searched for "voronoi" and got no results. I don't know if this is because the site doesn't have any content about voronoi polygons, or if search is broken. I assume it's the former.

That then leads me to ask - how do I discover what content the site has, and what content is it likely to have in the near future?

There appears to be quite a lot of missing (basic) content. Try searching "Cauchy-Schwarz" (or its variants). Nothing. Same for "Fourier".

Thanks for the feedback. The site's growth model more like Wikipedia's growth model in that it grows by user contributions.

This is something that I need to better communicate on the site and explains why the site currently has some content, but not others.

I just searched for "game theory" and got no results which is jarring even though I understand why. Indexing LaTex snippets has its use but is too far removed from higher level concepts to be generally useful. Mathworld (http://mathworld.wolfram.com/) had a huge number of high quality, high level articles. It would be very interesting if the top-down and bottom-up approaches respectively between the two could be combined.

If Eric Weisstein (http://mathworld.wolfram.com/about/author.html) is out there reading, thank you for your work. I can't believe the longevity and quality of Mathworld.

Thanks for the feedback. Yes, I agree that Mathworld is great. Mathpendium is not meant to replace sites like Mathworld, but to work with them. I think this is something I need to make more clear on the site.

That is, sites like Mathworld are great for finding information and an overview about a topic.

For example, it is a great place to learn about what a solvable group is.

Mathpendium, on the other hand, is designed to help you if you only want a concise definition of a solvable group, want to find all theorems that describe when a group is solvable, or find all conjectures related to solvable groups.

That is, Mathependium is used for when you want to get a list of all theorems related to a topic, with links to other sides for a deep dive or overview.

In a sense, theorems are the tools of mathematics, Mathpendium is a toolbox that helps you find those tools, and each item on the site has links to other sites to learn more about the tool.

> Yes, I agree that Mathworld is great.

Slighty OT but,

Apart from the fact that it looks and feels like 2006 (that latex renderer is so, so horrible, it's a distraction), and that you can't copy anything meaningful out of it, Mathworld is great. But honestly, as of 2020, I would have thought we'd have much better tools to learn a domain as thoroughly defined as mathematics (interactive, intuitive, etc etc etc). As it stands, it's still really hard without a teacher, but it shouldn't: a rich web experience with text as a basis should be able to produce at least as good understanding as a video (whose only major difference is voice).

I'd expect to be able to hover over anything and get a tooltip definition, be able to move things in equations and sliders for constants to see real-time graphs or limits or edge cases etc; with formulas that self-update in real time.

I mean, it's a poor state of affairs that the combined body of mathematicians on Earth still haven't come up together to find a way to explain and teach mathematics at least as well as a freaking catalog website can show and sell products. It's not that hard to leverage decent frontends...

I love your efforts because I think they're truly headed in the right direction; we need so many more of these tools, innovation on the way to building an actual "base of mathematical knowledge" that's not Wikipedia (too general) nor Matlab (too specific) nor YouTube (good thing but not enough).

Back on topic:

- are you considering a public-facing API?

- I think "discover" (in your title) is misleading and explains some slightly harsh reactions here (failing to honor a promise is really bad marketing). I'd suggest something more like "pro tools for pro math", I mean make the promise that it's a tool for people who already know these things, who don't "discover" but rather "reference", "recall", sort of a modern lookup table. Like, say I've forgotten formula or theorem X, I'd really value being able to get that info as fast as possible.

Thanks for your support. I share your views too, which is why I am creating Mathpendium :)

Right now I haven't thought about a public API. I am currently focusing on how users use the site since this will provide good feedback for how an API could be used.

I think you make a really good point for the discover title, and I really like your suggestion. This is definitely I will address. Thanks for the feedback. It is really helpful.

I noticed some issues rendering LaTex. Also if I were you, I would probably prioritize curated annotation.

For example:

* I searched for "Lebesgue integral" and got no results. I searched for "Lebesgue" and got results on Lebesgue measures. I would expect the first search to ... say return an outbound link to the mathworld/wikipedia article for the high level overview. Then I would expect it to toss "integral" as too generic and show all following results for just "Lebesgue"

* I searched for "Zeta function" and got no results. I search for "zeta" and found some relevant material but not much. Similar expectations as I had around Lebesgue integral searches.

* I search for "Banach space" and got no results, nor anything for "Banach" which makes me think you have a lot more indexing to do.

* If you search for "Riemann" the first page/second result and second page/first results have rendering issues:

"\<astyle="text−decoration:underline;color:black;"href="javascript:globalEntitySelected( ′ bedb7aa7−eb4f−47fe−9de0−e50e262c3289 ′ , ′ 5e33c092981ec41bc6b27930 ′ )">sum</a> j=1 n

f(c j

)[g(x j

)−g(x j−1

)]−L ∣ ∣ ∣

<ϵ, "

and "\newline{}For all x\geq 2.01x≥2.01" respectively

* Finally, I understand the cookie notice, but don't have it overlap the page selector on paginated results. Until I hid the element I didn't realize there were multiple pages of results in some cases.

Thanks for the feedback. I need to work on better communicating that the site is grown through user contributions. That is why the results are currently limited.

Also, thanks for pointing out the LaTeX issues. There are a lot of edge cases to address.

As for the cookie notification, I agree with your feedback. I am using a third party component for that. I will need to see what customization I can do.

So Mathpendium is geared more toward the practicing mathematician?

It is more like a reference and a jumping point to books and articles. After understanding the general ideas of a topic it lets you dive deeper.

It is definitely targeted towards professional mathematicians, but also those learning math that already have an overview of a topic and want to dive deeper.

Wow, thanks for sharing that article about Eric Weisstein. Very interesting.

> He is also a prolific communicator of mathematics, having authored most of MathWorld's nearly 13,000 articles.

That's amazing. Reminds me of Salman Khan a full decade before.

> Weisstein is an advocate for author's rights, especially in the area of electronic publication

When I read this I cringed as it sounded like he was in favor of stronger copyrights, instead it seems like the opposite—some slimey Intellectual Monopoly troll once sued him and nearly ended MathWorld (http://www.ericweisstein.com/authors-rights/authors_note.htm...).

> What if you could easily answer the question "what is everything currently known in mathematics."

I love this. I work on this problem a lot. More generally of the form "what is everything currently known in X"?

I would love to be able to make statements like "I am familiar with X/Y/Z% of the nodes in Computer Science/Medicine/Arrested Development Season 2". I would love it if the abstract idea of the "dent" (http://matt.might.net/articles/phd-school-in-pictures/) a researcher makes could actually be concretely measured as nodes added/updated/subtracted from some corpus of knowledge.

Have you thought about moving the content to a git repo and allowing people to contribute via a pull request?

Yes, the goal is to help people know what is known in an area. I will update the docs to make this more clear.

I am open to supporting pull requests, but my thoughts were that the custom user interface Mathpendium has allows for an easier contribution process.

I’m not convinced about the usefulness of this format, but I’ll reserve judgement for now. However, one thing I’m almost certain is that categorization and navigation by topic is a must-have; serendipity just doesn’t cut it (unless you have made some truly groundbreaking advancements in search). Btw, I searched quite a few keywords in algebraic geometry and found nothing; maybe you could look into converting the Stacks project (they even have an API[1]) into your format and contemplate usefulness in the process.

Another meta suggestion: IMO knowing who you are is usually pretty important for establishing trust in academic circles. Maybe link to your personal homepage on the about page? Right now all we get is a project-specific email so you’re basically anonymous.

[1] https://stacks.math.columbia.edu/api

Thanks for the feedback. I have a lot of feedback on the need for searching by topic, and it us something I will add.

Also, I can add a bio page about myself.

When I landed on the front page i thought it hadn't loaded properly. Had no idea what to do.

Is this just for people who already know lots about math? If so maybe that's why I didn't get it.

Thanks for the feedback. Yes, it seems others too have felt the home page was hard to navigate because it was too empty. I will explore ways to make it more clear how to use the site.

I'm thinking perhaps a list of categories to explore (calculus, real analysis, abstract algebra, etc.) could be helpful if one doesn't have a specific term to search for.

Do entries have categories? Searching for e.g. "calculus" only brings up one result.

I think the home page needs to say what the site is for and what kinds of things are on it, otherwise we have no idea what to search for. Maybe start with something in the search box and the results already below?

Are you using MathJax to display the equations? Why do I not get the MathJax context menu when I right-click on the equations?

It's using Katex, which is smaller and faster: https://katex.org/

Yes, I'm using katex because I found the API easier to work with.

Are you rendering the LaTeX on server-side or on client-side using JavaScript? I am asking these questions because I find MathJax code in your website:

  <script type="text/plain" cookie-consent="strictly-necessary">
    window.MathJax = {
      tex: {
        inlineMath: [['$', '$'], ['\\(', '\\)']]
      svg: {
        fontCache: 'global'
  <script type="text/javascript" id="MathJax-script" async

Actually, that code should be deleted. At one time, I was experimenting with MathJax but don't use it anymore.

It's a little lacking in content. I searched for 'Bernoulli' and came up with nothing, so widened this to 'probability' and nothing still.

It would benefit from some kind of taxonomy on the front page to give an indication of what content areas are available.

Thanks for the feedback. I have learned that I need to add a way to view things by category.

Also the site is grown similar to Wikipedia with user contributions, which is why there isn't as much content now.

This is something I need to better communicate on the site.

Category -> search -> no results found.

I searched for 'logic' and 'proof', and all I got was a request to consent to their use of cookies.

Interesting. The consent for use of cookies dialog should appear the first time you open the site. After agreeing to the use of cookies, the dialog shouldn't be displayed anymore. If you don't mind me asking, what browser and system are you using?

Chrome/OS X. I didn't agree to the cookies, and wouldn't do so until I was satisfied that the site was of interest and value. Give people a chance to test drive it before requiring consent.

"probability" search term doesn't give a useful result. How is data fed into the system?

The system is mostly fed by user contributions. Better communicating this is something I need to improve on the site.

Long equations break out of the content box. E.g., view/5e33c093981ec41bc6b279b7

Thanks for the feedback. This is a known issue, but I am working on other higher priority issues at the time.

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