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If a programmer locked himself away for 14 years and then emerged and announced he'd written a completely bug free OS, there would be skepticism. Code needs to

If a programmer locked himself away for 14 years and then emerged and announced he'd written a completely bug free OS, there would be skepticism. Code needs to be battle tested by other people to find the bugs. Mathematics is the same, to an extent; one guy working alone for 14 years is likely to have missed ideas and perspectives that could illuminate flaws in his reasoning. Maths bugs. If he's produced hundreds of pages of complex reasoning, on his own, however smart he is I'd say there's a high chance he's missed something. Humans need to collaborate in areas of high complexity. With a single brain, there's too high a chance of bias hiding the problems.

ekianjo 14y ago
I do not think it is fair to compare Software and Abstract Mathematics. Software is mostly an Engineering problem, while Mathematics is mostly Science and Conjecture. And even if they locked themselves for 14 years, there is no "single mind at work" there. Mathematics are built "on the shoulder of giants" through generations of brain dedicated to it. There is no such thing as pure invention - new discoveries lead to new theorems, new leads that other people take on.
- georgeorwell 14y ago
  Proofs are programs. https://www.google.com/search?q=proofs+are+programs https://www.google.com/search?q=proofs+are+programs
  - ekianjo 14y ago
    Let me say it in another way. Abstract Maths is like having a Organic Chemist working on understanding the transformation of food at the molecular level. A Software Programmer is like a cook who knows how to mix and prepare food in order to make a delicious dish out of it.
    - fusiongyro 14y ago
      "Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians."– E. W. Dijkstra
      - tinco 14y ago
        Mr Dijkstra obviously did not code in Ruby.
        jacques_chester 14y ago
        I'm confident he'd look on Ruby as an insult.
        tinco 14y ago
        I am confident people might believe something they don't understand to be an insult..
        jacques_chester 14y ago
        I don't follow you.
        tinco 14y ago
        I was hinting ignorance might be the cause of your confident dismissal of Ruby :) @btilly: it seems as though that would be a correct assertion. @jacques_chester: I did not know that, does he have a piece on programming languages he found disconcerting? Did he prefer Church over Turing? I don't think programming languages can really go beyond being strictly mathematical though..
        jacques_chester 14y ago
        Ruby is probably the language I've written more code in than anything else. I quite like it; I find myself chafing in lots of other languages. My point is that Dijkstra was kinda big on programming-as-strict-mathematics; a loosey-goosey super flexible language like Ruby would not have met with his favour, IMO.
    - konceptz 14y ago
      This is not a good analogy. Many programmers have training in computability theory and understand some very discrete principles. Just because they may become entrenched in UX or some other facet of coding, does not mean they're just "hacking" stuff together in a pleasing way. "A Software Programmer is like a cook who has an undergraduate degree in Organic Chemistry." May be a more apt analogy.
  - jhales 14y ago
    In theory - The reality is there is not a working compiler except for a few special cases.
  - walrus 14y ago
    Not quite. Proofs, in practice, are not programs. They do not contain every detail, nor are they written in completely consistent language.
- codeulike 14y ago
  I agree that Mathematics is usually built "on the shoulder of giants", but the gist of that whole Wired article is that this dude has created a whole new branch of maths, on his own, to prove this theorem. Sounds brilliant, but risky.
  - bradleyjg 14y ago
    It's a branch as mathematicians think of branches, not as laymen do. It isn't a new algebra, calculus, or geometry. Not to minimize the accomplishment at all, but it happens a handful of times a generation.
gizmo686 14y ago
Even if his proof turns out to be flawed, It is likely that the new system he constructed will still provide us a new and usefull way at looking at math. The good thing about working outside of mainstream is that their is far less inertia holding to the old ways. Assuming his work does represent a new branch of math, he has reduced the problem of the rest of us discovering/inventing it from stumbling blindly to making sense of his papers.
zimbatm 14y ago
Agreed but I think there is value in independently-evolving ideas. From my own experience; the more I am connected, the more I share and optimize existing ideas. If left on my own, I will come up with rough but more original ones.
Evbn 14y ago
Wolfram wrote ANKOS in the way you describe.
- codeulike 14y ago
  And ANKOS has been criticised for not being rigorous enough. As a counter example: Time Cube guy came up with Time Cube in the way I describe.
pseut 14y ago
I don't think he's claiming "bug free" -- and if I remember right, people have already found "bugs" and he claims to have a patch that he'll post soon. There's a huge difference between minor errors that invalidate the proof but can be fixed easily once they're noticed and fundamental errors where the proof is just wrong and can't be fixed. So most of the bugs that you're talking about don't really matter (of course, "bugs" that seem trivial at first might turn out to be fundamental irreparable errors, but that's a separate issue).
- codeulike 14y ago
  But a mathematical proof is like a card-pyramid, building steps upon steps to reach a very specific peak. Any bugs anywhere in the structure could be serious indeed, unless they can be patched.
  - shardling 14y ago
    Sure, but each step was probably reached with the aid of intuition -- in other words, the mathematician suspected that it had to be true before they found the particular formal proof employed. So long as the original intuition is actually correct, then any bug will probably be patchable. (Obviously there's no guarantee!)
  - carstimon 14y ago
    This is kind of true, but not quite right. If there's a flaw serious enough to be too hard to patch, it's likely that some problem would have come up later. That is, some serious contradiction would be reached, or something really weird would happen that yells "either this is really unexpected, or you have a problem earlier." To stretch analogies: It seems like you're analogy is saying: My card pyramid is built, but now if I remove a card, it all falls down. The more apt analogy is: When you're building a structure, you might be off a little the first time you build it, but if the overarching design is sound it will still work out and you can fix it and try to be perfect again. If the overarching design is not sound, you won't be able to build it at all. What I'm trying to say is, problems in the more bottom layers are very unlikely.
wging 14y ago
It is worth noting that Andrew Wiles' initial proof of Fermat's Last Theorem also had a bug. This was later fixed, with help. From http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem : However, it soon became apparent that Wiles's initial proof was incorrect. A critical portion of the proof contained an error in a bound on the order of a particular group. The error was caught by several mathematicians refereeing Wiles's manuscript.[112] including Katz, who alerted Wiles on 23 August 1993.[113] Wiles and his former student Richard Taylor spent almost a year trying to repair the proof, without success.[114] On 19 September 1994, Wiles had a flash of insight...
wissler 14y ago
Isaac Newton went away for two years, by himself, to invent Calculus and modern physics.
- yen223 14y ago
  Gottfried Leibniz "invented" calculus around the same time as Newton. Indeed, the dy/dx notations were Leibniz's.
brador 14y ago
A 64 bit operating system built over 7 years from a guy here on HN called losethos: http://www.youtube.com/watch?v=WAr-xYtBFbY http://www.youtube.com/watch?v=WAr-xYtBFbY
- achille 14y ago
  Tragically, the author suffers from a severe mental illness and has been banned from HN, Reddit and others.
tel 14y ago
I think it's more like if a programmer locked himself away for 14 years and then announced he'd written an OS before anyone else. Even if the whole thing is riddled with bugs (and let's not forget this programmer is more on the Bernstein end of things, precision and confidence are high) it's still some place potentially worth exploring. But nobody would quite yet. Instead he announces one more thing, he's used this OS to control a rocket ship and send a satellite to Mars far before anyone else has even come close! Now, assuming he didn't lie there, you really want to figure out what he invented because he just seems to be vastly more powerful than you.

ekianjo 14y ago

I do not think it is fair to compare Software and Abstract Mathematics. Software is mostly an Engineering problem, while Mathematics is mostly Science and Conjecture. And even if they locked themselves for 14 years, there is no "single mind at work" there. Mathematics are built "on the shoulder of giants" through generations of brain dedicated to it. There is no such thing as pure invention - new discoveries lead to new theorems, new leads that other people take on.

georgeorwell 14y ago
Proofs are programs. https://www.google.com/search?q=proofs+are+programs https://www.google.com/search?q=proofs+are+programs
- ekianjo 14y ago
  Let me say it in another way. Abstract Maths is like having a Organic Chemist working on understanding the transformation of food at the molecular level. A Software Programmer is like a cook who knows how to mix and prepare food in order to make a delicious dish out of it.
  - fusiongyro 14y ago
    "Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians."– E. W. Dijkstra
    - tinco 14y ago
      Mr Dijkstra obviously did not code in Ruby.
      - jacques_chester 14y ago
        I'm confident he'd look on Ruby as an insult.
        tinco 14y ago
        I am confident people might believe something they don't understand to be an insult..
        jacques_chester 14y ago
        I don't follow you.
        tinco 14y ago
        I was hinting ignorance might be the cause of your confident dismissal of Ruby :) @btilly: it seems as though that would be a correct assertion. @jacques_chester: I did not know that, does he have a piece on programming languages he found disconcerting? Did he prefer Church over Turing? I don't think programming languages can really go beyond being strictly mathematical though..
        jacques_chester 14y ago
        Ruby is probably the language I've written more code in than anything else. I quite like it; I find myself chafing in lots of other languages. My point is that Dijkstra was kinda big on programming-as-strict-mathematics; a loosey-goosey super flexible language like Ruby would not have met with his favour, IMO.
  - konceptz 14y ago
    This is not a good analogy. Many programmers have training in computability theory and understand some very discrete principles. Just because they may become entrenched in UX or some other facet of coding, does not mean they're just "hacking" stuff together in a pleasing way. "A Software Programmer is like a cook who has an undergraduate degree in Organic Chemistry." May be a more apt analogy.
- jhales 14y ago
  In theory - The reality is there is not a working compiler except for a few special cases.
- walrus 14y ago
  Not quite. Proofs, in practice, are not programs. They do not contain every detail, nor are they written in completely consistent language.
codeulike 14y ago
I agree that Mathematics is usually built "on the shoulder of giants", but the gist of that whole Wired article is that this dude has created a whole new branch of maths, on his own, to prove this theorem. Sounds brilliant, but risky.
- bradleyjg 14y ago
  It's a branch as mathematicians think of branches, not as laymen do. It isn't a new algebra, calculus, or geometry. Not to minimize the accomplishment at all, but it happens a handful of times a generation.

gizmo686 14y ago

Even if his proof turns out to be flawed, It is likely that the new system he constructed will still provide us a new and usefull way at looking at math. The good thing about working outside of mainstream is that their is far less inertia holding to the old ways. Assuming his work does represent a new branch of math, he has reduced the problem of the rest of us discovering/inventing it from stumbling blindly to making sense of his papers.

zimbatm 14y ago

Agreed but I think there is value in independently-evolving ideas. From my own experience; the more I am connected, the more I share and optimize existing ideas. If left on my own, I will come up with rough but more original ones.

Evbn 14y ago

Wolfram wrote ANKOS in the way you describe.

codeulike 14y ago
And ANKOS has been criticised for not being rigorous enough. As a counter example: Time Cube guy came up with Time Cube in the way I describe.

pseut 14y ago

I don't think he's claiming "bug free" -- and if I remember right, people have already found "bugs" and he claims to have a patch that he'll post soon. There's a huge difference between minor errors that invalidate the proof but can be fixed easily once they're noticed and fundamental errors where the proof is just wrong and can't be fixed. So most of the bugs that you're talking about don't really matter (of course, "bugs" that seem trivial at first might turn out to be fundamental irreparable errors, but that's a separate issue).

codeulike 14y ago
But a mathematical proof is like a card-pyramid, building steps upon steps to reach a very specific peak. Any bugs anywhere in the structure could be serious indeed, unless they can be patched.
- shardling 14y ago
  Sure, but each step was probably reached with the aid of intuition -- in other words, the mathematician suspected that it had to be true before they found the particular formal proof employed. So long as the original intuition is actually correct, then any bug will probably be patchable. (Obviously there's no guarantee!)
- carstimon 14y ago
  This is kind of true, but not quite right. If there's a flaw serious enough to be too hard to patch, it's likely that some problem would have come up later. That is, some serious contradiction would be reached, or something really weird would happen that yells "either this is really unexpected, or you have a problem earlier." To stretch analogies: It seems like you're analogy is saying: My card pyramid is built, but now if I remove a card, it all falls down. The more apt analogy is: When you're building a structure, you might be off a little the first time you build it, but if the overarching design is sound it will still work out and you can fix it and try to be perfect again. If the overarching design is not sound, you won't be able to build it at all. What I'm trying to say is, problems in the more bottom layers are very unlikely.

wging 14y ago

It is worth noting that Andrew Wiles' initial proof of Fermat's Last Theorem also had a bug. This was later fixed, with help. From http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem : However, it soon became apparent that Wiles's initial proof was incorrect. A critical portion of the proof contained an error in a bound on the order of a particular group. The error was caught by several mathematicians refereeing Wiles's manuscript.[112] including Katz, who alerted Wiles on 23 August 1993.[113] Wiles and his former student Richard Taylor spent almost a year trying to repair the proof, without success.[114] On 19 September 1994, Wiles had a flash of insight...

wissler 14y ago

Isaac Newton went away for two years, by himself, to invent Calculus and modern physics.

yen223 14y ago
Gottfried Leibniz "invented" calculus around the same time as Newton. Indeed, the dy/dx notations were Leibniz's.

brador 14y ago

A 64 bit operating system built over 7 years from a guy here on HN called losethos: http://www.youtube.com/watch?v=WAr-xYtBFbY http://www.youtube.com/watch?v=WAr-xYtBFbY

achille 14y ago
Tragically, the author suffers from a severe mental illness and has been banned from HN, Reddit and others.

tel 14y ago

I think it's more like if a programmer locked himself away for 14 years and then announced he'd written an OS before anyone else. Even if the whole thing is riddled with bugs (and let's not forget this programmer is more on the Bernstein end of things, precision and confidence are high) it's still some place potentially worth exploring. But nobody would quite yet. Instead he announces one more thing, he's used this OS to control a rocket ship and send a satellite to Mars far before anyone else has even come close! Now, assuming he didn't lie there, you really want to figure out what he invented because he just seems to be vastly more powerful than you.