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Open Source Math
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.'""
I am no a mathematician but surely if you're going to submit a computer aided proof you must submit a full copy of the program. The are all manor of subtle mistakes that can be made in a program that could cause serious problems with a proof.
Suppose you inspect the source and find it to be faultless, how can you trust the compiler. And if you hand compile the compiler, how can you trust the CPU? Surely it's turtles all the way down.
In many ways, establishing the correctness of a computer-aided proof is very much like security engineering. You want to verify that the whole software stack is operating correctly before you can trust the result. Having the source-code is a pre-requisite to this exercise.
Changing to topic slightly, I was particularly heartened to see that the open-source mathematics framework being developed one of the authors of the article involves the use of Python.
My immediate thought when seeing the title to the article was "Python is the answer." When some problem or algorithm intrigues me the first thing that happens is that I reach for the Python interpreter.
Python seems to deftly marry precision with looseness. When code is laid out in Python I find it is easier to see what it's trying to do than other languages. It's aesthetic qualities aside, it supports a number of features out of the box which I imagine would be ideal of mathematicians. To list a few, it's treating of lists and tuples as first class objects, support for large integers, complex numbers, it's ability to integrate with C for high-performance work.
I often think of Python as "basic done right" and it's ideal for mathematicians (or anybody) who don't want to think about programming but the problem at hand.
Simon
Why does this keep coming up on ./? What is wrong with PDF? It's undeitable, sure, that's kind of the point. However, the spec is accessible, and there are plenty of open readers, e.g. xpdf and ghostscript.
Really, what is wrong with PDFs and why should they require a warning?
By the way, all scientific papers are disseminated by PDF.
SJW n. One who posts facts.
In other cases, like the proof of the four color theorem, it seems like the source code is important to see, but not essential. Pseudocode should suffice. Providing pseudocode is akin to saying things like "Simplifying expression (1) yields..."; we don't have to provide EVERY step, but with pseudocode you have enough to determine whether the algorithm itself will work. Checking the source code beyond that is akin to checking someone's algebra.
Just because we don't know how the program arrived at the steps it did doesn't mean that we shouldn't use it; we can usually check the steps. After all, the human brain has been a closed-source proof machine for thousands of years, and no one has complained about that :) Just require pseudocode in computer aided proofs, and it should be sufficient.
I'm not going to disagree with the "laid open" part, but the "free of charge" nonsense is just typical marxist university professor hypocrisy.
Let's price some math texts:
Or try a few titles which might be a little more familiar to Slashdotters:
Princeton, which has the finest mathematics department in the world [or at least had the finest mathematics department in the world, before Harold Shapiro & Shirley Tilghman decided they wanted to turn the
The issue is not whether software companies should make their source code open - the real issue is should mathematicians accept proprietary applications as proof of theorums?
As pointed out in the editorial, software developers make mistakes, and this is true regardless of whether that developer is a proprietary software vendor, or a free/open source software project. There is one key difference however, the validity of any given proof can be determined independently when using free/open source code by the very nature of the product (availability of source code). There is no validation for proprietary software beyond the assurances of the company involved.
When mathematic theory becomes applied mathematics (such as the creation of buildings, bridges, aircraft, or thermonuclear devices), which proof would you prefer to hang your life upon - Microsoft's guarantee, or independent verification and peer review? This becomes ever more critical as we create more complex systems that can not be easily verified by hand, yet rushed into applied use by the expediency/efficiencies they deem to provide.
Lodragan Draoidh
The more you explain it, the more I don't understand it. - Mark Twain