4 ms·

> None of Zuse, Babbage, Torres y Quevedo, Ludgate, Dickinson, Desch, Atanasoff–Berry, Mauchly / Eckert, nor many of the other pioneers of computing came via Hi

> None of Zuse, Babbage, Torres y Quevedo, Ludgate, Dickinson, Desch, Atanasoff–Berry, Mauchly / Eckert, nor many of the other pioneers of computing came via Hilbert and FOM problems I don't think this is a fair comparison. The modern computer is really distinct from everything that came before. That's because it was built according to the theory of Turing Machines. One of the most important historical papers for the development of modern computers was the Report on the ENIAC by Von Neumann[1]. Von Neumann took the idea's of others working in the field, and was able to apply his understanding of mathematical logic to formulate the principles which led to the first working modern computer, which Von Neumann built in the basement of IAS. At that time, there was a major debate at IAS between Einstein and Von Neumann, which centered around whether or not to only do pure math at IAS, with the idea that building a computer was part of experimental science. [2] > Regarding the arrow of influence: a Fields medalist spent a decade coming up with a new foundation of mathematics (or at least algebraic topology), only to realise that the computer science department already teaches Coq to undergraduates! LOL! That is an interesting and funny story. However, I don't think this example demonstrates that in the future, mathematics will not be the source of improvements to code writing standards. Question: if code writing standards improve, where else will these improvements come from other than pure mathematics? I consider this question to be a problem type similar to maximum compression algorithms, i.e. its a question whose solution can only be verified using the language of pure mathematics. Therefore it seems likely these improvements can also have their roots in pure mathematics as well. At least, I would not say it "seems unlikely" [1] https://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC https://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the... [2] https://www.amazon.com/Turings-Cathedral-Origins-Digital-Universe/dp/1400075998 https://www.amazon.com/Turings-Cathedral-Origins-Digital-Uni...

GregarianChild 6y ago
Regarding your question, I think mathematics and programming about the same: being precise! Programming is much more demanding, much more unforgiving in this regard, because you are talking to a stupid machine, rather than a smart human. The powers automation gives mathematicians (once you've climbed the mountain of initial unfamiliarity), are so spectacular, take the average Joe so much beyond what even Gauss, Newtown, Grothendieck or Archimedes had at their disposal, that I expect that over the next century mathematics will be rewritten to suit computing, rather than vice versa. K. Buzzards's work is one step in this direction, scriptable notebooks like Jupyter or Mathematica are another.
- calhoun137 6y ago
  > I expect that mathematics will be rewritten to suit computing, rather than vice versa I agree with this. I believe pure mathematics is suffering greatly because many mathematicians refuse to fully embrace the computational power of modern technology. My belief is the age of pretty formulas is coming to an end, and that the future of mathematics will be it focuses more and more on computational aspects of the subject, and problem sets in pure math courses will be done using programs that are much more advanced than anything which exists today, and everyone will think nothing more of those programs than we do about calculators. Apologies for the self plug, but this has been my vision with mathinspector[1]. I've been working very hard on that, and this is why I got so interested in your statement. Thank you for clarifying your thinking here. Makes sense to me, and you could be right [1] https://github.com/MathInspector/MathInspector https://github.com/MathInspector/MathInspector
  - GregarianChild 6y ago
    The MathInspector is nice. Reminds me of the "Incredible Proof Machine" [1] which I find to be a neat tool in teaching logic. [1] https://incredible.pm/ https://incredible.pm/
    - calhoun137 6y ago
      Thank you!!! It's so funny that you mentioned "scriptable notebooks like Jupyter or Mathematica" since I have been spending all of my time on mathinspector recently. I think our points of view are actually very strongly aligned. However I believe the next big idea is likely to come from outside of computer science. Personally, I am betting on biology. So many of the most sophisticated techniques are based on biology, e.g. neural nets and genetic algorithms. I have done a lot of work on extending the theory of computation with a new axiom which gives Turing machines a self replicating axiom[1], [2] In many parts of science, there is a cross pollination, where new ways of thinking about subject X come from a new discovery in subject Y. Typically, research will follow a group think pattern until it hits a brick wall, then you need that really big breakthrough idea. This line of reasoning leads to the conclusion, imo, that it's approximately equally likely to come from either pure computer science, or pure mathematics, or somewhere else. [1] https://math.stackexchange.com/questions/3605352/what-is-the-efficiency-of-the-algorithm-which-solves-this-word-problem https://math.stackexchange.com/questions/3605352/what-is-the... [2] https://medium.com/swlh/self-replicating-computer-programs-8136bbbacc60 https://medium.com/swlh/self-replicating-computer-programs-8...

GregarianChild 6y ago

Regarding your question, I think mathematics and programming about the same: being precise! Programming is much more demanding, much more unforgiving in this regard, because you are talking to a stupid machine, rather than a smart human. The powers automation gives mathematicians (once you've climbed the mountain of initial unfamiliarity), are so spectacular, take the average Joe so much beyond what even Gauss, Newtown, Grothendieck or Archimedes had at their disposal, that I expect that over the next century mathematics will be rewritten to suit computing, rather than vice versa. K. Buzzards's work is one step in this direction, scriptable notebooks like Jupyter or Mathematica are another.

calhoun137 6y ago
> I expect that mathematics will be rewritten to suit computing, rather than vice versa I agree with this. I believe pure mathematics is suffering greatly because many mathematicians refuse to fully embrace the computational power of modern technology. My belief is the age of pretty formulas is coming to an end, and that the future of mathematics will be it focuses more and more on computational aspects of the subject, and problem sets in pure math courses will be done using programs that are much more advanced than anything which exists today, and everyone will think nothing more of those programs than we do about calculators. Apologies for the self plug, but this has been my vision with mathinspector[1]. I've been working very hard on that, and this is why I got so interested in your statement. Thank you for clarifying your thinking here. Makes sense to me, and you could be right [1] https://github.com/MathInspector/MathInspector https://github.com/MathInspector/MathInspector
- GregarianChild 6y ago
  The MathInspector is nice. Reminds me of the "Incredible Proof Machine" [1] which I find to be a neat tool in teaching logic. [1] https://incredible.pm/ https://incredible.pm/
  - calhoun137 6y ago
    Thank you!!! It's so funny that you mentioned "scriptable notebooks like Jupyter or Mathematica" since I have been spending all of my time on mathinspector recently. I think our points of view are actually very strongly aligned. However I believe the next big idea is likely to come from outside of computer science. Personally, I am betting on biology. So many of the most sophisticated techniques are based on biology, e.g. neural nets and genetic algorithms. I have done a lot of work on extending the theory of computation with a new axiom which gives Turing machines a self replicating axiom[1], [2] In many parts of science, there is a cross pollination, where new ways of thinking about subject X come from a new discovery in subject Y. Typically, research will follow a group think pattern until it hits a brick wall, then you need that really big breakthrough idea. This line of reasoning leads to the conclusion, imo, that it's approximately equally likely to come from either pure computer science, or pure mathematics, or somewhere else. [1] https://math.stackexchange.com/questions/3605352/what-is-the-efficiency-of-the-algorithm-which-solves-this-word-problem https://math.stackexchange.com/questions/3605352/what-is-the... [2] https://medium.com/swlh/self-replicating-computer-programs-8136bbbacc60 https://medium.com/swlh/self-replicating-computer-programs-8...