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Software for Math Research

calebm 5y ago
Python is conspicuously missing from this list.
- aexl 5y ago
  As well as Julia.
- capitalsigma 5y ago
  SageMath is python with some handy builtins for doing symbolic calculations
  - deleted 5y ago
    [deleted]
xvilka 5y ago
I would add also nlgebra[1] and Simba[2]. [1] https://github.com/dimforge/nalgebra https://github.com/dimforge/nalgebra [2] https://github.com/dimforge/simba https://github.com/dimforge/simba
xiaodai 5y ago
No mention of Magma. My favourite
outlace 5y ago
No proof assistants like Lean and Coq?
- sadfev 5y ago
  I was wondering about that too. They are perhaps most important tools for both CS and pure mathematics. It’s very interesting that Lean has exploded in the mathematics community. Kevin Buzzard talks about it a lot, but I haven’t seen a talk which explains why Lean succeeded in creating a gargantuan math library whereas Coq only recently got respectable math library in “MathComp” (I am also including Analysis library). I would like to know apart from social reasons what technical choices lead to Lean dominating (ordinary/regular/pure) mathematics. I hear “quotients” but no one actual explains with a concrete example.
  - maxwells-daemon 5y ago
    In my experience: one of Lean's main advantages is developer experience. It's convenient by design, with lots of automation to make easy proofs trivial. You do your work in VSCode or Emacs rather than some outdated IDE, and the server mode makes it easy(ish) to integrate with other software.
    - sadfev 5y ago
      I think CoqIDE is great and ProofGeneral (Emacs) is something all Coq experts use. I have the opposite experience with Lean 4, the VSCode integration is horrid and documentation is awful. The only good sources are papers for Lean4. Granted I can go back to Lean3 but why would I?
      - outlace 5y ago
        But Lean4 is in alpha stage and there are no official stable releases yet, of course it's not well-documented nor polished yet. Lean3 works perfectly well and has everything you need.
  - outlace 5y ago
    I think it all comes down to the aesthetics and user experience. The Lean webpage is inviting and modern. Coq’s website looks like it’s from the 90s. Lean’s integration with Visual Studio Code is clean and user friendly. The language itself is familiar and polished. The imprimatur of a Microsoft team producing Lean being makes it seem more sophisticated.
dr_kiszonka 5y ago
Nice list! Scilab looks pretty interesting, especially the Simulink-like part. I only wish there was something Python-based for Dynamical/Hybrid Systems.
- linspace 5y ago
  Not python and not my field, but in Julia you have https://juliadynamics.github.io/DynamicalSystems.jl/dev/ https://juliadynamics.github.io/DynamicalSystems.jl/dev/
  - dr_kiszonka 5y ago
    Neat - thanks for the link! Also, nice username :)
agambrahma 5y ago
Recently (re-)discovered Mathematica, and found spanning a much larger set of domains than I expected (also, very approachable).
- linspace 5y ago
  The first time I used Mathematica (20 years ago) it blew my mind. To be fair it was the first time I used a CAS and so the very idea of a computer crushing me at several calculus tasks was incredible. From the open source alternatives the better supported I think is (wx)Maxima, which for the simple tasks I usually require (i.e some Taylor series, check cumbersome trigometric equations, ...) it's more than enough although it's true it lacks by a long margin the polish of Mathematica. Recently I'm considering buying an educational version of Mathematica just for the convenience. It sucks it's a closed source program but it's rare, although not impossible, for open source alternatives to have the same good documentation and ease of use. I guess that the attention to these details is not something people usually do unless being paid. Now, tangentially related, this is extremely cool (and previously posted in HN I think): https://ai.facebook.com/blog/using-neural-networks-to-solve-advanced-mathematics-equations/ https://ai.facebook.com/blog/using-neural-networks-to-solve-...
  - jjgreen 5y ago
    I've never liked Mathematica, it gets notation all wrong, Sin[x] where it should be sin(x), Maple got this right.
    - DerekL 5y ago
      That's probably because they wanted to use juxtaposition for multiplication. Otherwise, “f(x)” could mean either f applied to x or f times x in parentheses.
  - billfruit 5y ago
    What about Axiom, it seems to have been worked on for many decades.
linspace 5y ago
There are a several comments saying "no mention of X", and actually they are right. This list is defeated by the simplest of google queries.
MayeulC 5y ago
xcas is very good (though the UI shows its age), based on giac: https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac.html https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac.htm... In addition to software in the comments, not even WolframAlpha is listed.
- prirai 5y ago
  The list mentions free software alternatives, not the proprietary ones which would be probably on everyoneeveryone's mouths.
ai_ia 5y ago
The list is missing Manim for visualization. I tried it out because I was curious how 3b1b creates his videos and was blown away by the simplicity of the tool. For simple visualization and teaching aid, Manim is a great tool.
- prirai 5y ago
  Adidng this to my list. Thanks. Btw I use Sage and it has most of the packages written below.
deleted 5y ago
[deleted]
amathres_info 5y ago
I think you are all missing the context here. The "Association for Mathematical Research" is a new organization created by various people who got in trouble on woke math twitter. Nobody had heard of it until yesterday. (Their crimes are mostly opposing diversity statements in job applications, or favoring gifted programs.) It looks like a schism with the AMS (which more-or-less publicly takes the opposite view on these things), though they deny it. The impetus for the new group is clearly political. They got a few big names on there, but everybody on the board is already known for holding retrograde political views and I think they all signed one of the dueling petitions about this in the AMS Notices a year or two ago. This is just a filler page to make it look like they have some content. It's not a serious list of mathematical software. There are good ones of those done elsewhere.
- coolgeek 5y ago
  > Their crimes are ... favoring gifted programs I looked around on the AMS site, and I'm not seeing anything about the AMS opposing gifted education. Would you please provide a link to this? (To be perfectly clear, I do not want links to opposition in the wider world. I've come across references to that before. I just find it hard to believe that the AMS would oppose gifted education.)
- JoeyBananas 5y ago
  The amount of leftist political content in the AMS notices is pretty annoying. I wish them well in this endeavor.
gooby_snacks 5y ago
Not sure what the criteria is to be included in this list, but I've used this software for dynamical systems and there doesn't appear to be anything listed for that category. https://juliadynamics.github.io/JuliaDynamics/ https://juliadynamics.github.io/JuliaDynamics/

Python is conspicuously missing from this list.

aexl 5y ago
As well as Julia.
capitalsigma 5y ago
SageMath is python with some handy builtins for doing symbolic calculations
- deleted 5y ago
  [deleted]

I would add also nlgebra[1] and Simba[2]. [1] https://github.com/dimforge/nalgebra https://github.com/dimforge/nalgebra [2] https://github.com/dimforge/simba https://github.com/dimforge/simba

xiaodai 5y ago

No mention of Magma. My favourite

outlace 5y ago

No proof assistants like Lean and Coq?

sadfev 5y ago
I was wondering about that too. They are perhaps most important tools for both CS and pure mathematics. It’s very interesting that Lean has exploded in the mathematics community. Kevin Buzzard talks about it a lot, but I haven’t seen a talk which explains why Lean succeeded in creating a gargantuan math library whereas Coq only recently got respectable math library in “MathComp” (I am also including Analysis library). I would like to know apart from social reasons what technical choices lead to Lean dominating (ordinary/regular/pure) mathematics. I hear “quotients” but no one actual explains with a concrete example.
- maxwells-daemon 5y ago
  In my experience: one of Lean's main advantages is developer experience. It's convenient by design, with lots of automation to make easy proofs trivial. You do your work in VSCode or Emacs rather than some outdated IDE, and the server mode makes it easy(ish) to integrate with other software.
  - sadfev 5y ago
    I think CoqIDE is great and ProofGeneral (Emacs) is something all Coq experts use. I have the opposite experience with Lean 4, the VSCode integration is horrid and documentation is awful. The only good sources are papers for Lean4. Granted I can go back to Lean3 but why would I?
    - outlace 5y ago
      But Lean4 is in alpha stage and there are no official stable releases yet, of course it's not well-documented nor polished yet. Lean3 works perfectly well and has everything you need.
- outlace 5y ago
  I think it all comes down to the aesthetics and user experience. The Lean webpage is inviting and modern. Coq’s website looks like it’s from the 90s. Lean’s integration with Visual Studio Code is clean and user friendly. The language itself is familiar and polished. The imprimatur of a Microsoft team producing Lean being makes it seem more sophisticated.

dr_kiszonka 5y ago

Nice list! Scilab looks pretty interesting, especially the Simulink-like part. I only wish there was something Python-based for Dynamical/Hybrid Systems.

linspace 5y ago
Not python and not my field, but in Julia you have https://juliadynamics.github.io/DynamicalSystems.jl/dev/ https://juliadynamics.github.io/DynamicalSystems.jl/dev/
- dr_kiszonka 5y ago
  Neat - thanks for the link! Also, nice username :)

agambrahma 5y ago

Recently (re-)discovered Mathematica, and found spanning a much larger set of domains than I expected (also, very approachable).

linspace 5y ago
The first time I used Mathematica (20 years ago) it blew my mind. To be fair it was the first time I used a CAS and so the very idea of a computer crushing me at several calculus tasks was incredible. From the open source alternatives the better supported I think is (wx)Maxima, which for the simple tasks I usually require (i.e some Taylor series, check cumbersome trigometric equations, ...) it's more than enough although it's true it lacks by a long margin the polish of Mathematica. Recently I'm considering buying an educational version of Mathematica just for the convenience. It sucks it's a closed source program but it's rare, although not impossible, for open source alternatives to have the same good documentation and ease of use. I guess that the attention to these details is not something people usually do unless being paid. Now, tangentially related, this is extremely cool (and previously posted in HN I think): https://ai.facebook.com/blog/using-neural-networks-to-solve-advanced-mathematics-equations/ https://ai.facebook.com/blog/using-neural-networks-to-solve-...
- jjgreen 5y ago
  I've never liked Mathematica, it gets notation all wrong, Sin[x] where it should be sin(x), Maple got this right.
  - DerekL 5y ago
    That's probably because they wanted to use juxtaposition for multiplication. Otherwise, “f(x)” could mean either f applied to x or f times x in parentheses.
- billfruit 5y ago
  What about Axiom, it seems to have been worked on for many decades.

linspace 5y ago

There are a several comments saying "no mention of X", and actually they are right. This list is defeated by the simplest of google queries.

MayeulC 5y ago

xcas is very good (though the UI shows its age), based on giac: https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac.html https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac.htm... In addition to software in the comments, not even WolframAlpha is listed.

prirai 5y ago
The list mentions free software alternatives, not the proprietary ones which would be probably on everyoneeveryone's mouths.

ai_ia 5y ago

The list is missing Manim for visualization. I tried it out because I was curious how 3b1b creates his videos and was blown away by the simplicity of the tool. For simple visualization and teaching aid, Manim is a great tool.

prirai 5y ago
Adidng this to my list. Thanks. Btw I use Sage and it has most of the packages written below.

deleted 5y ago

[deleted]

amathres_info 5y ago

I think you are all missing the context here. The "Association for Mathematical Research" is a new organization created by various people who got in trouble on woke math twitter. Nobody had heard of it until yesterday. (Their crimes are mostly opposing diversity statements in job applications, or favoring gifted programs.) It looks like a schism with the AMS (which more-or-less publicly takes the opposite view on these things), though they deny it. The impetus for the new group is clearly political. They got a few big names on there, but everybody on the board is already known for holding retrograde political views and I think they all signed one of the dueling petitions about this in the AMS Notices a year or two ago. This is just a filler page to make it look like they have some content. It's not a serious list of mathematical software. There are good ones of those done elsewhere.

coolgeek 5y ago
> Their crimes are ... favoring gifted programs I looked around on the AMS site, and I'm not seeing anything about the AMS opposing gifted education. Would you please provide a link to this? (To be perfectly clear, I do not want links to opposition in the wider world. I've come across references to that before. I just find it hard to believe that the AMS would oppose gifted education.)
JoeyBananas 5y ago
The amount of leftist political content in the AMS notices is pretty annoying. I wish them well in this endeavor.

gooby_snacks 5y ago

Not sure what the criteria is to be included in this list, but I've used this software for dynamical systems and there doesn't appear to be anything listed for that category. https://juliadynamics.github.io/JuliaDynamics/ https://juliadynamics.github.io/JuliaDynamics/