Open Source Math 352
An anonymous reader writes "The American Mathematical society has an opinion piece about open source software vs propietary software used in mathematics. From the article : "Increasingly, proprietary software and the algorithms used are an essential part of mathematical proofs. To quote J. Neubüser, 'with this situation two of the most basic rules of conduct in mathematics are violated: In mathematics information is passed on free of charge and everything is laid open for checking.'""
Openness is Fundamental to Mathematics (Score:2, Interesting)
It is fundamental to mathematics that other mathematicians in the same field can check a proof, and the use of closed source software makes that logically impossible, for without access to the source of the application, it is not possible to guarantee that any particular operation has been implemented correctly.
He's also plugging his own open source project, SAGE [sagemath.org] - I might have to download it and see if the rusty old brain cells can figure out how to play with it ;)
Welcome to the world of modern research ... (Score:4, Interesting)
Then again, I must really ask if the mathematician in question understands what they are doing if they are using software as a shortcut for difficult analytic solutions. After all, if they don't understand the algorithms well enough to do the work themselves, who is going to say that they understand the limitations of the rules that they are asking the computer to apply.
Proof exchange format (Score:2, Interesting)
Re:Python is part of the answer (Score:5, Interesting)
The insidious thing about that particular result was that it looked very similar to the correct. In fact the difference would not have been found if two people did not run different versions of code independently (and more or less coincidentally) arriving to slightly different error rates.
openmodelica.... (Score:3, Interesting)
OpenModelica [ida.liu.se]
a very nice modelling package that can help you with practical mathematics issues like mathematica might.
cheers.
Peter
Ruby could be the answer as well (Score:5, Interesting)
There is one special feature of Ruby, that I miss in every single programming language I used since: iterator methods. Any time I want to iterate over elements of an array or hash I just do: That's it, instant "anonymous function" given as a parameter in estetically pleasing syntax. In fact, "for" loop in Ruby is just obfuscated way of calling method #each on an object. But the madness doesn't stop here: It's a pity that so many people disregard Ruby as a "platform for Rails". It is a feature complete countepart to Python, and as my company high volume systems can attest, can handle anything other languages can handle.
Robert
Re:Python is part of the answer (Score:3, Interesting)
I fear you and/or the AMS are giving too much credit to the big names in mathematical software. Sure, they have some bright people and they do some useful research in their own right, but they're still only human. They make mistakes, their software has bugs, and they don't know lots of deep secrets that the rest of academia don't. In fact, the development practices at certain high profile mathematical software companies leave a lot to be desired; they tend to hire PhD types, who know a lot about mathematics but may or may not know jack about how to write good software. I rather doubt they're about to kidnap all the leading edge research and make it disappear from everyone not working for them.
Disclosure: I work for a mathematical software firm well known in its industry, and I've encountered some of the others in a professional context. I am speaking personally and not on behalf of anyone else here.
look at who's speaking... (Score:2, Interesting)
Re:Welcome to the world of modern research ... (Score:2, Interesting)
Re:Python is part of the answer (Score:2, Interesting)
I can see why you might think that, but my point had little to do with commercial software houses. My main point was that computer-assisted "proofs" are not proofs in the mathematical sense. They're "results" that rest "scientifically" on the software and hardware and real world. It really doesn't matter whether I use my implementation of Newton's Method or Mathematica's. Neither should be trusted in a proof.
I forget who it was (Wiles maybe?), but a famous mathematician once described doing mathematical research as groping around a dark cave, trying to find an exit. A computer program is like a flashlight. Not an exit, but a helpful tool for finding it.
Re:Python is part of the answer (Score:2, Interesting)
Disclaimer: IANAM (I am not a mathematician), but I'm applying to grad schools in math, and I work with mathematicians who use computer-aided proofs on a daily basis. Most mathematicians are not concerned with such loose and squirrely concepts such as colliding universes. We care about actual mathematical objects.
For instance, the proof of the four-coloring theorem -- first it was proved by purely mathematical means that every planar graph is essentially the same as one of a few thousand small "representative" graphs. By "essentially the same", I mean that if the representative graph is four-colorable, than the original graph is, too. Then, use a computer program to color each graph with four colors. Finally, give the results to a couple of independent teams and have them verify that your coloring contains no errors.
This isn't the mess of tweaks & hacks that you describe. Now. With closed-source math software, one can never be sure that provable methods are used. With open source, one can.
Sage [sagemath.org] has bugs. You can fix them [sage-trac.org]. Try that with Mathematica.
Re:PDF rant. (Score:4, Interesting)
Open Source Software in Machine Learning (Score:3, Interesting)
The article is in the Journal of Machine Learning Research. [mit.edu]
spss (Score:1, Interesting)
Re:Libraries are NOT FREE. (Score:5, Interesting)
Would these be the same kind of good-for-nothing, lazy, worthless asses who brought us Special Relativity while working in a lowly position in the Patent Office in Bern? You know, the kind who got together with friends to peruse and discuss the latest freely available scientific texts, the same texts that led him to revolutionise science more than anyone since Newton?
The books in the Princeton Library are free, thanks to the generousity of far-seeing individuals who realised that their money was better spent on a library than a new yacht. They, at least, saw the benefit of sharing knowledge with everyone, regardless of their means. I can only hope that, somewhere in that misanthropic little husk you call a heart, you will some day find room for a similar spirit of openness and sharing.
Re:Python is part of the answer (Score:3, Interesting)
Furthermore the advent of computers has made the illustration of concepts much easier through high quality and even interactive graphics.
In other words, we not only stand on the shoulders of giants, but we take their work and compress it into more easily understood pieces. Often upon reaching the next higher level of understanding, the shortcuts that we could have taken to get there become more apparent. Today, the number of pages of derivation between basic axiomatic logic and the proof of Fermat's last theorem is perhaps a few thousand. But maybe, in another hundred years, we will actually find that "simple" proof that Fermat hinted at (or not, who knows).
For what its worth, some people lament the "loss" of the old texts, but I think this is misguided. That material has no place in modern education.
As for devious paradoxes, these seem to be more a problem in physics, where models are incomplete, but taken to be complete, than in mathematics where incompleteness is intentionally controlled to avoid paradox. We also have, for example, the completeness theorem showing that all well-formed expressions can be evaluated. And, for the most part the possible locations of devious paradoxes seem to be known (e.g. continuum hypothesis etc).
Automated theorem provers are first proven to be correct given the allowed operations and assumptions before they can be allowed to prove anything. There is no magic here; they could just as easily be replaced by a warehouse full of German mathematicians (German mathematicians were famous for solving intensely mechanical problems before the advent of computers (e.g. taylor expansions to hundreds of terms and huge integrals, etc).
Re:Python is part of the answer (Score:3, Interesting)
Try reading books from the early 20th century [uni-bielefeld.de], and ask yourself how much overlap there is with a recent textbook. You won't find that much.
In other words, we're not so much compressing the past as merely picking the bits we're interested in and ignoring the others.