alt Hacker NewsThere's a lot of value in the implementation of many strong and fast algeorithms in computer algebra in proprietary tools such as Maple, Wolfram, Matlab. However, I (though of course believe that such work needs to be compensated) find it against the spirit of science to keep them from the general public. I think it would be good service to use AI tools to bring open source alternatives like sympy and sage and macaulay to par. There's really A LOT of cool algorithms missing (most familiar to me are some in computational algebraic geometry)
Additionally I think because of how esoteric some algorithms are, they are not always implemented in the most efficient way for today's computers. It would be really nice to have better software written by strong software engineers who also understands the maths for mathematicians. I hope to see an application of AI here to bring more SoTA tools to mathematicians--I think it is much more value than formalization brings to be completely honest.
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I think the current generation of tools have a long way to go before I trust any numerical algorithm they implement, based on our recent experiments trying to make it implement some linear algebra by calling LAPACK. When we asked it to write some sparse linear algebra code based on some more obscure graph algorithms it produced some ugly stepchild of dijkstra's algorithm instead, which needless to say did not achieve the desired aim.
Computer algebra of the Mathematica/Maple variety is not formally rigorous: it will get things wrong due to conflating function domains, choices of branch cuts for 'multi-valued functions' and other assumptions that are required for correct results but not exposed or verified. The work of providing "strong and fast algorithms" that are comprehensively described ought to be done as part of building proof systems for the underlying mathematics that will ensure correctness.
> against the spirit of science
Unfortunately, the bank doesn't accept spirit of science dollars, and neither does the restaurant down the street from me either.
People need to eat.
That's the main flaw in open source. Yes, its a great idea, but why am I working a real job to eat, and spending nights and weekends on a project just as a hobby.
Science doesn't progress very fast using the 'hobby' model of funding. Unless you are rich, and it is a hobby, much like Wolfram Alpha was. He wanted to play with math/physics stuff and was rich enough to self fund.
> against the spirit of science to keep them from the general public
Within science, participants have always published descriptions of methodology and results for review and replication. Within the same science, participants have never made access to laboratories free for everyone. You get blueprints for how to build a lab and what to do in it, you don't get the building.
Same for computation. I'm fairly sure almost all (if not all) algorithms in these suites are documented somewhere and you can implement them if you want. No one is restricting you from the knowledge. You just don't get the implementation for free.