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Like many other mathematicians I use mathematical software like SAGE, GAP, Polymake, and of course $\LaTeX$ extensively. When I chat with colleagues about such software tools, very often someone has an idea of how to extend an existing tool, what (non-existent) tool would be useful, or which piece of documentation should be (re)written. Due to lack of time & energy and often also programming expertise, these ideas rarely materialize.

On the other hand, every now and then I meet programmers with a strong interest in mathematics (who are often actually trained mathematicians), and who are looking for a software project to work on. However, normally they don't really know what's needed and end up doing a non-mathematical project.

This gave me the idea to ask the mathematical community to compile a wish list for mathematical software. Wishes can be very small or or something bigger. Just try to make sure that it's realistic and maybe also give an explanation why you consider your project as interesting.

And if you happen to be a programmer fulfilling one of the wishes, please leave a comment.

It would be great if you could also include an estimate on how complex your project and what the math/coding ratio is -- but this is optional.

tl;dr

  • What software tool would you like to see created?
  • What existent software tool would you like to see extended by what feature?
  • What piece of documentation is missing or should be updated/extended?

One suggestion per answer, please.

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    $\begingroup$ It would be great to have software that serves up a website where mathematicians can ask other mathematicians questions that come up during their research. $\endgroup$ – Yoav Kallus Aug 7 '15 at 20:30
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    $\begingroup$ As a programmer, I really like this question, but all of the responses so far look like they would take teams of people months to complete. :( But I guess if it could be done by a single programmer in a week, it would already have been done, right? $\endgroup$ – Jashaszun Aug 7 '15 at 21:15
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    $\begingroup$ This question is way too broad. There are some subquestions that could work, but I think you really need to restrict the scope. For example "What existent software tool would you like to see extended by what feature?" would seem to allow as answer: "I would like to see feature X in Software Y (that already is present in Software Z)." I do not really believe it is useful to create a wishlist for the numerous differing software-packages in a single Q&A. $\endgroup$ – user9072 Aug 8 '15 at 9:31
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    $\begingroup$ Likewise "What piece of documentation is missing or should be updated/extended?" solicits feedback on the documentation of a multitude of different software. Even for a single piece of software these two questions combined seem too broad, I could see one of them for one software as a very broad question (though it is not quite clear it fits here). Anyway the scope of this Q needs to be reduced drasticaly in my opinion. $\endgroup$ – user9072 Aug 8 '15 at 9:36
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    $\begingroup$ @quid: While I agree that my question is fairly broad, I must admit that this is by intention. The idea is to compile a list that mathematically inclinced programmers can pick a project idea from to work on. In this regard I also find it useful to have a collection of feature requests that covers more then one software tool. If this list becomes too confusing one can still split it up into several later. $\endgroup$ – eins6180 Aug 8 '15 at 21:07

21 Answers 21

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I think some aspects of math would be revolutionized by having a good math search engine. Recently, a question was asked on Meta.MathStackExchange about what they perceived as the greatest problems facing the site. The biggest response was that there was no search engine that indexed mathematics.

This is partly reasonable, since math is stored and documented in $\TeX$ and this can be taken as a standard. But this is also problematic, as there are multiple noncanonical ways to do things in $\TeX$. I would be remiss if I didn't say there are very many other challenging aspects of this.

As an example use case, I often have to look things up in the Gradshteyn and Ryzhik Table of Integrals and Series. It would be remarkable if there were a reasonable way to search for my expressions within the book. Even if I had to attempt multiple searches, it would almost certainly be faster. Taking it up a step, it would be great to search through TeX on the arXiv for certain expressions as well.

I think that even a relatively mediocre math search engine would be a handy start.⠀⠀⠀⠀⠀

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    $\begingroup$ A related discussion meta.mathoverflow.net/q/1564. $\endgroup$ – Name Aug 7 '15 at 20:06
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    $\begingroup$ You might look at search.mathweb.org $\endgroup$ – Robert Israel Aug 7 '15 at 22:21
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    $\begingroup$ @shardulc ideally, all three. That is, I'd like a search engine that indexes both normal language and latex. In my example in GR, I was thinking along the lines of your second question about a specific formula, which is (as far as I know) not at all an available service. $\endgroup$ – davidlowryduda Aug 9 '15 at 1:30
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    $\begingroup$ A review of some current math search engines have been uploaded to arXiv recently: arxiv.org/abs/1609.03457 $\endgroup$ – Shamisen Sep 18 '16 at 2:51
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    $\begingroup$ If one had a search engine which indexes all theorems/lemmas/... in all articles and which allows to search for (assumptions) with (conclusions). $\endgroup$ – TKe Jan 26 '18 at 15:28
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A more modern typesetting language to replace $\TeX$. TeX is basically impossible to parse and its internals are really odd and difficult to work with, when one tries to do something advanced.

Knuth is a genius, and it was a really neat hack for the time, but, with all due respect, after 30 years of experience with computer typesetting I am sure it is possible to put together something better.

If not, at least a TeX compiler with better error messages.

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    $\begingroup$ TeX is certainly not a "neat hack". $\endgroup$ – the_fox Aug 7 '15 at 19:18
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    $\begingroup$ Please not. TeX is perfect as it is. The change of format of mathematical papers is undesirable. $\endgroup$ – juan Aug 7 '15 at 19:30
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    $\begingroup$ Tex was and is an extraordinary achievement, and is fantastic for what it is, and almost certainly superior to the alternatives, but (like any long-lived project) it has acquired a huge accumulation of cruft, much of which is rather dated. So if a dedicated team led by a clone of Knuth could write a new system, from the ground up, following the same principles as TeX and learning from what TeX’s many contributors have done in the mean time — I suspect we could end up with a significantly better system still. But there’s probably too much intertia for this to happen any time soon. $\endgroup$ – Peter LeFanu Lumsdaine Aug 7 '15 at 20:04
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    $\begingroup$ Isn't exactly this done by the developers of systems like Context, LuaTeX, ... ? $\endgroup$ – Johannes Hahn Aug 7 '15 at 20:16
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    $\begingroup$ While a better system does exist in the platonic realm, given the bug-free monolothic design of TeX any realistic change is extremely likely to be for the worse, for there are essentially no known examples of big software that do not suffer from bugs, design-by-committee, backward- and forward-incompatibilities, poor manuals, etc. Better is enemy of good. $\endgroup$ – Boris Bukh Aug 8 '15 at 12:02
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I always thought it would be nice to have a real-time virtual blackboard (supporting digitizer pen), say, as an extension of Skype or similar service, where you can not only talk with a colleague but also do math together over great distances.

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A vastly improved support for handwritten math (e.g. via digitizer pen) incl. its conversion to typeset math would be awesome! In a long run, ideally it should be able to replace LaTeX. Just think of how much of researchers' time is spent on inputting math.

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    $\begingroup$ One existing tool in this direction is Detexify, which can recognize handwritten symbols and tell the TeX code. This is often much faster than consulting a symbol list. Maybe the Detexify project could help build the required math recognition software? $\endgroup$ – Joonas Ilmavirta Aug 7 '15 at 20:00
  • $\begingroup$ I agree, it is a start. But I think it will take some years before we get a complete solution. Recognizing 'normal' handwriting properly is already a difficult problem (but it has improved a lot over the past few years, especially with handheld devices and 'apps' and such). And then, on top of it, one has the whole particularity of the mathematical notation. $\endgroup$ – M.G. Aug 7 '15 at 20:09
  • $\begingroup$ @JoonasIlmavirta Detexify's recognition is not so great, though the idea is. About half the time I try to use it, I give up and do a web search or consult a symbol list. $\endgroup$ – Kimball Aug 8 '15 at 3:28
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    $\begingroup$ Another one: myscript.com/technology/technical-demonstrations $\endgroup$ – Stephen Aug 11 '15 at 8:41
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    $\begingroup$ I doubt that handwriting math and then digitalizing it is much faster than writing it in TeX. $\endgroup$ – 6005 Sep 24 '16 at 5:39
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An improved version of latexdiff

A good diff software is essential for collaboratively writing articles. Latexdiff takes two tex files and outputs a new tex file with the differences highlighted (additions are underlined in blue and deletions are crossed out in red). This is very useful since it facilitates viewing the changes that coauthors have made during a round of editing, especially if some of your coauthors are not super computer-savy (e.g., they don't use diff themselves) since you can just pass them the output PDF with the marked changes.

However, my experience with using latexdiff is that the output file usually requires some manual editing before it can be compiled into a PDF, since the diff markup algorithm often messes up the latex syntax. It would be useful to have a more user-friendly latexdiff.

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  • $\begingroup$ The online TeX Editor Sharelatex has a history feature that sounds a lot like what you are asking for. This of course helps only if all collaborators use this editor and it is only available if you pay a monthly fee or manage to recruit enough participants. $\endgroup$ – HenrikRüping Jul 25 '18 at 12:52
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I would like software that makes the specific job of managing mathematical references easier.

When I've looked, there are BibTeX and its relatives for making sure that the whole process stays under control; many tools for managing references; tools for pulling BibTeX from MathSciNet; tools for creating BibTeX from arxiv identifiers; tools for searching these places for papers; tools for merging BibTeX files; and so on.

Using these individually simplifies individual parts of the process. But I always find that I need to:

  • copy my bibliography from my previous paper, and maybe another one,

  • merge in some more bibliography entries from my other previous paper where my coauthor managed the file, and eliminate the duplicates and inconsistencies,

  • try to figure out which papers have moved from preprints to arXiv preprints to being published, and update their entries,

  • go through new published references I'm adding, hunt them down, and copy-paste BibTeX from MathSciNet,

  • create new entries for the arXiv preprints,

  • and then some misc. extra jobs that always show up, like fixing tildes and putting capitals in braces and adding hyperlinks to bib entries that lack them because they date all the way back to my thesis.

The process is exhausting and the tools don't click together enough to make it much easier - e.g. automating pulling references from MathSciNet seems almost not worth the trouble because it involves firing up special-purpose software that's only useful for half of the new entries that I'm referencing.

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    $\begingroup$ I haven't really used it much but the postdocs at my last lab used mendeley.com to organize the papers they've read. You can export BibTeX from it, too. $\endgroup$ – Sumyrda Aug 8 '15 at 7:02
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    $\begingroup$ We mathematicians are already extremely lucky to have MathSciNet. As far as I know, in most other fields there is basically no publication database that can produce Bibtex entries of reasonable quality (names in the correct format, capitals properly escaped, consistent journal names). $\endgroup$ – Federico Poloni Aug 8 '15 at 7:07
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    $\begingroup$ There is Zotero. It is not without problems (multilingual search could be better, BibTeX export is very mediocre), but in my experience it has been the best among available software. $\endgroup$ – Boris Bukh Aug 8 '15 at 11:55
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    $\begingroup$ @FedericoPoloni We are doubly-lucky: we have not only MathSciNet, but also Zentralblatt. It has an advantage over MathSciNet that the first three search results are free (require no subscription) --- many here are in sufficiently wealthy institutions that this does not matter, but for some it is valuable. $\endgroup$ – Boris Bukh Aug 8 '15 at 17:21
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    $\begingroup$ DBLP now indexes most of theoretical computer science and, unlike MathSciNet, is free to use. $\endgroup$ – András Salamon Aug 15 '15 at 17:03
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I find it particularly cumbersome to produce good-looking mathematical illustrations. I know of several ways to make decent cartoon images in bitmap format with little hassle, but I prefer the image quality provided by vector graphics. TikZ seems to be the go-to for math-based vector graphics, but this is incredibly time consuming, even after climbing the learning curve.

I would very much like a bmp-to-tikz "converter."

Depending on the quality of the bitmap, the converter might need to iteratively suggest a vector-graphics interpretation for the user to evaluate. The user could then fine tune the TikZ code after conversion if he's extremely picky.

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    $\begingroup$ Or maybe an xfig-like visual editor for tikz? $\endgroup$ – Kimball Aug 8 '15 at 15:11
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    $\begingroup$ @Kimball Inkscape has an extension to export to tikz. $\endgroup$ – Federico Poloni Aug 8 '15 at 16:53
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    $\begingroup$ Inkscape also has a feature to turn bmp to svg (e.g. by color) and then you can use the svg to tikz feature. $\endgroup$ – Sumyrda Aug 8 '15 at 17:36
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    $\begingroup$ Here is an example of bmp to TikZ way via potrace: tex.stackexchange.com/questions/172336/… $\endgroup$ – percusse Aug 8 '15 at 22:17
  • $\begingroup$ Even though it costs money, for some illustrations Omnigraffle is pretty nice! There's also an MO thread on tools for mathematical illustration (for quick drawing IPE is also quite good, but not easy to get fine grained enough)... $\endgroup$ – Suvrit Aug 10 '15 at 13:23
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LaTeX support (or mode) in voice-recognition softwares for people with upper limb disabilities. Maybe via Dragon NaturallySpeaking or something new entirely. Something similar for coding as well!

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15
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It would be nice to have a pdf viewer which gave the user the option to collapse and also restore individual proof sections.

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    $\begingroup$ I think this can be better achieved by moving away from PDFs to something like XHTML. $\endgroup$ – David Ketcheson Aug 12 '15 at 12:24
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    $\begingroup$ Philipp Kühls PhD Thesis is about algebraic surgery. However for fun he also coded his own pdf viewer with features very similar to what you are asking for. www.surgery-hotel.de $\endgroup$ – HenrikRüping Jul 25 '18 at 12:56
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There should be $\LaTeX$-browsers. The (relatively) new HTML 5 is great. It'd be still wonderful to have both: HTML-browsers (as today) and $\LaTeX$-browsers.

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    $\begingroup$ What is a LaTeX browser? $\endgroup$ – Federico Poloni Aug 9 '15 at 20:03
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    $\begingroup$ What is an HTML browser? $\endgroup$ – Włodzimierz Holsztyński Aug 10 '15 at 3:11
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    $\begingroup$ A program that takes HTML as an input and display on the screen formatted text. So, according to my definition, pdflatex + any pdf reader of your choice is a LaTeX browser. That's why I asked for your definition, not for a counter-question. $\endgroup$ – Federico Poloni Aug 10 '15 at 8:21
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    $\begingroup$ how about sharelatex.com ? "LATEX-browser" inside your "HTML browser" =) $\endgroup$ – Sigrlami Aug 11 '15 at 6:24
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    $\begingroup$ There's no real point in doing a whole browser for this. Just use a plugin or a dedicated website to compile LaTeX source code to an output format on the spot. $\endgroup$ – xji Aug 12 '15 at 18:36
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A wiki-like mathematical structure/example data base

I can imagine this better as an online service than a locally running software, but nevertheless I imagine it to be very useful.

You ever wondered (because of your research or out of curiosity) whether there is an example of a structure A (e.g. a topological space, graph, group, ...) which has the properties B, C and D, but not E? If Yes, what is an example of such a structure? If No, how can this be proven?

Wouldn't it be nice to have an online service, something like Wikipedia, where you can enter that you are browsing the database of structures A, and you specify the filters [B], [C], [D] and [not E]. You press enter and it spits out:

  • Here is an example of such a structure: ...
  • These structures are exactly the 3-dimensional compact manifolds. An example would be: ...
  • No structure can have this combination of properties. Source: ...
  • It is conjectured that no such structure exists. Source: ...
  • It is a known open problem whether there is such a structure: Read more here: ...
  • Property [B] and [C] imply [D] and [not E]. Hence you are actually looking for structures A with only [D] and [not E].
  • The database does not contain information on this combination of properties. Do you want to extend the knowledge?

"wiki-like" means that the database's knowledge can be extended/corrected by anyone $-$ like in Wikipedia. Even though this might seem like a complicated semantic search engine, I think that the strong formalization we have in mathmatics enables us to choose a strict syntax for the input.

  • We always specify the general structure we are looking for, e.g. vector space, topological space, metric space, group, ring, field, graph, function $\Bbb R\to\Bbb R$, subset of $\Bbb R$, curve (in metric space), field-automorphism, ...
  • It follows a list of properties, e.g. finite, compact, 3-dimensional, connected, Hausdorff, has inner point, metrizable, bijective, ... . Every such property can be suffixed with a [not]-operator. The listed properties are joined by conjunction.

The structures and property names are no free-form input, but chosen from a pop-up menu or by auto-completion, so that the users know what to input. The database should implement very basic reasoning, e.g.

  • If a property A implies B, and B implies C, so does A imply C.
  • If A and B contradict each other and C implies A, so C and B contradict each other too.
  • The structures can be linked, e.g. every metric space is a topological space (by its induced topology). Hence, every property which is available for topological spaces, is also available for metric spaces.

I know of several such services of varying generality: e.g. for rings, groups, graphs (here and here), polyhedra, or general counterexamples. The differences to what I am looking for can mostly be described by the following points:

  • General: I want a combined database for all/most structures. All this under a common interface.
  • Extendable: I think everyone should be allowed to add his knowledge to the database.
  • Searchable: Most of the time I know only the names (or some names or vague descriptions) of some properties of the desired structure. I do not know the structures name. Hence I want to filter by these properties. Sometimes I might be not even interested in examples, but in the relation between two properties: e.g. do they contradict each other, are they the same, does one imply the other, ...?
  • Structured: Not a loose collection of examples/counterexamples/articles, but highly interconnected and analysable data.
  • Userfriendly/Beautiful: I think mathcounterexamples and of course StackExchange is a good demonstration of these goals.

I once had an idea how this can be realized. I even asked a question on Computer Science StackExchange to see whether useful data structure for this kind of task already exist. I would love to realize such a project, but I am definitely lacking the web-developer skills, and currently also the time.

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    $\begingroup$ There is also Groupprops among the "things which aren't quite what you're asking for but are at least somewhat in the right direction". But the whole thing should be part of a larger "semantic web" effort: Wikimedia made a step in this direction by creating Wikidata which should, ultimately, make it possible to query Wikipedia-and-sisters in semantically useful ways (like "give me a list of French painters born between 1800 and 1835"), so maybe if this takes off, math can benefit from the infrastructure. $\endgroup$ – Gro-Tsen May 20 '18 at 18:05
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What I think would be most useful to address this issue is improving the system to make requests and contributions to such software packages. I'm sure many of these systems would be happy to have more help with development.

For instance, I found that the Sage implementation of computation of zeta functions of graphs is horribly slow and I wrote a much faster implementation (using Sage), and I wanted give Sage my code so they could use it a subsequent release, but after looking at the amount of effort required to contribute code, I decided I didn't want to spend that much time on it. I was just hoping to submit my code with some comments, which an interested developer could revise to conform to standards, test and implement.

One example of something I would like implemented (say in Sage) is computation of $p$-adic integrals. E.g., given a compact open subgroup $K$ of $GL_2(\mathbb Q_p)$ and a character $\psi$ on the upper unipotent $N$, compute $\int_N 1_K(n) \psi(n) \, dn$. (Some simple cases like basic character sums might be implemented, but possibly they are only implemented mod $p$.) I once thought about trying to automate calculations for a highly computational project I had, but then decided it wasn't worth the development time for just that one project.

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    $\begingroup$ William Stein was so put off by the Sage contribution standards, that he forked purplesage (psage) to be his own sandbox, with lower conformity. $\endgroup$ – ABCDveve Aug 8 '15 at 4:41
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    $\begingroup$ Code Standards are different from maintainer to maintainer, but as a professional software developer, I will tell you they absolutely exist for a reason. Relaxing code standards across the board purely for the sake of making it easier for amateur developers to make contributions would result in your software having more bugs than features. $\endgroup$ – nhgrif Aug 8 '15 at 12:49
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    $\begingroup$ @nhgrif I also believe in coding standards. I am just saying I would like the contribution system be improved to make it easier for mathematicians to contribute (which possibly includes a level of vetting by developers). Maybe already the system for this is good, but this wasn't clear from the documentation, so perhaps the documentation on this should at least be made more friendly for well-meaning but busy/lazy laymen. $\endgroup$ – Kimball Aug 8 '15 at 13:38
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    $\begingroup$ Hi -- purple sage didn't work due to lack of time. Regarding dumping useful code on us, that we have to understand and get up to snuff for inclusion, if we had more time and bandwidth, then we would make that easy. However, we don't -- I have almost not grant support, and almost all effort is researchers in their spare time. Maybe if we someday have funding... $\endgroup$ – William Stein Aug 10 '15 at 19:37
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    $\begingroup$ @LSpice Obviously we should let William Stein comment himself, but my reading of the situation was that at the time (2010-ish), Sage had established enough momentum that it's future was assured, so he (Stein) could focus primarily on (software for) his own research area. $\endgroup$ – Gordon Royle Aug 12 '15 at 11:48
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For the sake of searching mathematical texts one could create a purely auxiliary language sTeX, a simplified $\LaTeX$ -- just a software tool (not directly for people). Then one would add a "translator" (or rather a simplifier) from $\LaTeX$ into sTeX. Then search engines (like Google) can search texts in $\LaTeX$ by first obtaining the intermediate sTeX.

Mathematicians may learn just a little bit about sTeX to make mathematical searches still more efficient (but even without knowing anything about sTeX, the mathematical searches will be much easier to handle than without sTeX anyway).

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    $\begingroup$ It would have to be called something else, though: ctan.org/pkg/stex . Also, it seems like the mathematical (La)TeX understood by MathOverflow's flavour of Markdown is already a pretty bare-bones version. $\endgroup$ – LSpice Aug 10 '15 at 20:39
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A blog comment hosting service that supports MathJax in comments.

Currently most of the services uses iframes, making comments with MathJax impossible to render (unless the service provides native support for MathJax.)

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  • $\begingroup$ I understand that you are suggesting an externally-hosted comment system, but WordPress comments could likely be MathJax-enabled with little effort. This doesn't help with services like Medium or other blog hosting services, though. $\endgroup$ – Josh The Geek Aug 8 '15 at 20:21
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[In short, a place we can find a more modern proof, or a proof with a different approach, than the original paper that is customary to cite.]

One of the comments mentioned moving LaTeX from PDF to an XHTML sort of environment (Stacks Project is a good example). It may be worth expanding on that as a separate answer.

One obvious advantage is that words in text mode can be searched. And it may be a step towards making LaTeX code searchable (the current top answer). Most of the non-mathematical TeX codes (bullet points, italic, include pictures) we can use markdown like here on MathOverflow.

But the real game-changer is to make it more like GitHub, where one can fork a proof in order to add missing details, or make more substantial rewriting, and "publish" it for all to see. The rest of us can vote on them. Eventually the platform should have sufficiently many of the basic theorems (with many different proofs) in all branches of mathematics that we can cite directly, instead of citing the original paper or a textbook. The citations can also be used to generate a "dependency graph", barring circular reasonings (It may not be as exhaustive in the details as in Stacks Project, or we'd lose the big pictures).

If we want to say a certain result (say, in a certain abstract theory) is important, we can just point to it and see how many important results—or results that you care about—are connected to it. It may be more fun to learn new mathematics this way, combining the best of all textbooks, old and new.

Aside from the theorems, there would be special pages that are more expository, giving historical context (say of a problem) and connecting different theorems into a coherent narrative without getting bogged down in the details of proofs.

Now, wouldn't that be the new publishing model that we have all wished for? Credit may be traced from the forking history. (Of course if we are "importing" or rewriting a proof in the literature we should give proper citations.)

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  • $\begingroup$ You might want to check out openmathematics.org, which doens't have GitHub support for files and comments yet, but soon will have. $\endgroup$ – James Smith May 20 '18 at 18:23
  • $\begingroup$ I think the Stack Project just made their underlying system available, called Gerby github.com/gerby-project/gerby-project.github.io/blob/master/… They are now working with Jacob Lurie's (yet to unveil) project Kerodon. This is still a single narrative type of math writing. $\endgroup$ – liuyao May 23 '18 at 18:17
  • $\begingroup$ This is very interesting! Do you know anything more about Kerodon? Googling quickly, I see that he's gotten the logo sorted, but not much else is visible. $\endgroup$ – James Smith May 23 '18 at 19:24
  • $\begingroup$ Also, I see you have started your own project. Can you go into some more detail about what you hope to do with it? $\endgroup$ – James Smith May 23 '18 at 19:28
  • $\begingroup$ @JamesSmith, sorry I don't know anything about Kerodon. (I don't have the time or means to make my own project; I'm just trying out what others have set up. I used brilliant.org for a bit, but their active user base is too elementary. Now I use observablehq, which is for coding/data analysis/visualization. I think it has great potential, even as a model for some scientific publishing but perhaps not for math.) $\endgroup$ – liuyao May 24 '18 at 20:48
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Another thing I would like to see (not strictly math only) is a proper editor for .djvu (for all platforms) documents the way there are such editors for .pdf documents. Especially for bigger scanned documents (like many historical stuff in math), .djvu offers much better compression and much smoother viewing performance. To my knowledge, there is only one program that comes close to a .djvu editor, but unfortunately it is lacking in many regards.

On a related note, it would be nice to have a proper .pdf editor, native for Linux (there is one that comes close to the Windows ones, but it is not developed and has many problems, including usability ones), so that one does not need to use (the somewhat unstable) wine.

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  • $\begingroup$ In terms of PDF editors, would QPDF (en.wikipedia.org/wiki/QPDF) or iText (en.wikipedia.org/wiki/IText) provide any of the desired functionality? $\endgroup$ – LSpice Aug 10 '15 at 20:42
  • $\begingroup$ Agree. It is a shame there is still no free and professional tool to at least highlight and comment pdf, and save/print the changes. The best I could find is Xournal that simply converts pdfs to images. $\endgroup$ – Valentas Aug 12 '15 at 7:32
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    $\begingroup$ Regarding your second request, I'd like to mention "Master PDF Editor" (code-industry.net/free-pdf-editor). $\endgroup$ – Daniel Gerigk Aug 12 '15 at 11:27
  • $\begingroup$ Thanks, but I've used Master PDF Editor before. It used to be a bit slow and buggy and the gui was suboptimal. Maybe that has changed by now. I have not tried @LSpice 's suggestions yet, but I will soon (when I am again in Linux). $\endgroup$ – M.G. Aug 12 '15 at 11:34
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    $\begingroup$ @LSpice: It is called Document Express Desktop from Cuminas, it includes Document Express DjVu Editor among other things like .djvu printer and shell extensions. It's not free, but they offer a trial. The shell extensions can be had separately and free of charge IIRC. $\endgroup$ – M.G. Apr 3 '18 at 19:04
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It would be great if mathematical plotting programs like gnuplot would support both mouse based zoom-in and mouse based zoom-out. I once tried to describe what I mean in a German post titled Zoom-out could be so easy, but the description is too incomplete. One issue of that post is that you normally want to keep the aspect ratio. And the concrete formulas are also missing. Both issues could be solved easily, but the principal issue that people don't understand why this would be important is much harder to address.

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    $\begingroup$ To try to put in one sentence what Thomas wants, for non-readers of German: just as many programs allow one to zoom in by drawing a rectangle in the current viewport over the part one wants to zoom in on, one should be able to zoom out by drawing a rectangle to show which part of viewport should contain the current image. $\endgroup$ – Max Aug 10 '15 at 19:36
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    $\begingroup$ Isn't this more or less pinch-to-zoom as found on touchscreens? Just for the special case where the starting points of the two fingers are two corners of the viewport. $\endgroup$ – Max Aug 10 '15 at 19:37
  • $\begingroup$ @Max Probably yes. But the most important point is that the touchscreens have a well working zoom-in and zoom-out. For some strange reasons, programs like gnuplot (and matlab) do have well working zoom-in, but miss well working zoom-out. $\endgroup$ – Thomas Klimpel Aug 10 '15 at 21:37
  • $\begingroup$ Have you looked into interactive plotting tools like Bokeh? It's a Python library, but there are ports to a few other languages. $\endgroup$ – Daniel Watkins Aug 11 '15 at 16:52
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Idea generator using generative machine learning. If it can generate new art, lets give it a try with math.

enter image description here

Using new techniques from machine learning's aspect of generating new data (eg. GAN networks), it would be very interesting to devise algorithms that input massive amounts of theorems and problems and combine them in various ways to output new statements.

  • As in supervised machine learning, the human will be labeling whether the output was helpful in giving them novel perspectives.

  • A first step in the algorithm would be rephrasing the theorem's and problem's statements in as many different ways as possible. Often big bridges in math are build because we managed to find equivalent problems from distinct areas that allowed an exchange of techniques.

Related:

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  • $\begingroup$ Since GANs shown remarkable success on images inputs, I wonder if this project could be used to have new applications in the field: mathpicture.fas.harvard.edu $\endgroup$ – Shamisen Jan 31 '18 at 3:22
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I'd like to have on a usb key a user friendly software that could parse a math article to check the proofs in it without having to learn how to use stuff like Coq and highlight the possible gaps. But this may sound unrealistic, at least for now.

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    $\begingroup$ If a computer could parse an English document and understand if something could be possibly formalized as a proof, it would be half-way to being a mathematician itself. $\endgroup$ – PyRulez Aug 8 '15 at 1:16
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    $\begingroup$ Indeed, the question itself is sort of like: "What can make my life as a mathematician easier, but without obsoleting me?" $\endgroup$ – ABCDveve Aug 8 '15 at 4:43
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    $\begingroup$ Well anyway, this would be extremely difficult. It won't be like some programmer is looking for something to do and he says "oh, let me just create a skynet to check Sylvain Julien's articles for errors." $\endgroup$ – PyRulez Aug 8 '15 at 15:51
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    $\begingroup$ It's very likely that this would necessarily be almost as creative as a mathematician. Note how difficult it is to train humans to do this task: almost all of them who we successfully train to being able to assess math articles, also reach the epsilon-higher level of being able to generate some. $\endgroup$ – Max Aug 10 '15 at 19:40
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    $\begingroup$ Yeah, this is as "AI Complete" as it gets. In other words, if you build this thing, you should build a couple other multi-billion dollar industries around it. $\endgroup$ – Wouter Lievens Aug 11 '15 at 10:32
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The website

swmath.org

helps in finding existing mathematical software and documentation.

From their website:

What is swMATH?

swMATH is a freely accessible, innovative information service for mathematical software. swMATH not only provides access to an extensive database of information on mathematical software, but also includes a systematic linking of software packages with relevant mathematical publications.

The intention is to offer a list of all publications that refer to a software recorded in swMATH. In particular, all articles are given, which are included in Zentralblatt MATH (zbMATH). It can be both, articles that describe the background and technical details of a program, as well as those publications in which a piece of software is applied or used for research.

In this way, swMATH provides information on actual use of the software that is otherwise impossible or very difficult to obtain. At the same time the documentation of literature referring to a software is a valuable source of information for the authors of the software about where their software is used. Moreover, if software is cited in scientific publications, this is also an important quality criterion, which is used by swMATH for software selection.

swMATH sees itself as a service to the mathematical community. Additions, corrections and other notes from authors and users of mathematical software can be communicated under 'Feedback' and are very welcome.

For more detailed information, we refer to the following article.

[...]

Project Information

swMATH is a project of the Mathematical Research Institute Oberwolfach (MFO) and FIZ Karlsruhe (FIZ), funded by the Leibniz Association 2011-2013.

Project leader: Gert-Martin Greuel (MFO); Wolfram Sperber (FIZ) Concept, programming, design: Michael Brickenstein, Christoph Knoth (MFO); Sebastian Bönisch, Hagen Chrapary (FIZ)

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I would like to have a feature in a (La)TeX IDE that would allow one to ``collapse" one's document tree into a single file. I modularize my typesetting: I have separate files for definitions, lemmas, \newcommands, etc., and it is not convenient to share all of the separate files with others.

Uploading one's document tree to the arXiv--one file at a time--is a tedious chore. Also, some editors request that submissions be put into a single file for publication. The ability to work modularly and then readily convert the corpus to a single file would be useful.

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protected by Community Aug 8 '15 at 10:35

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