The network of mathematics
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The network of mathematics
1–10 of 21 posts
Re: The network of mathematics
#2Not mentioned in the article is that the Stacks Project is on github https://github.com/stacks
I've always thought that math books should in digraph rather than linear form. What would be interesting is to combine this with a wiki. You could have alternate proofs of the same lemma, or even entirely different presentations (starting from different axioms, for instance)
Re: The network of mathematics
#3I remember seeing many years ago a fairly dense one page diagram of how most of the major "bits" of mathematic hang together. I can never for the life of me dig it up again. Anyone know what I'm on about / got any pointers?
Re: The network of mathematics
#4I remember seeing many years ago a fairly dense one page diagram of how most of the major "bits" of mathematic hang together. I can never for the life of me dig it up again. Anyone know what I'm on about / got any pointers?
This may have been what you're thinking of. Sadly I lack a source; it's just been kicking around my miscellaneous images folder.
Re: The network of mathematics
#5I remember seeing many years ago a fairly dense one page diagram of how most of the major "bits" of mathematic hang together. I can never for the life of me dig it up again. Anyone know what I'm on about / got any pointers?
This may have been what you're thinking of. Sadly I lack a source; it's just been kicking around my miscellaneous images folder. http://i.imgur.com/tBgQkxi.jpg
That's from http://arxiv.org/pdf/gr-qc/9704009.pdf
There's some more from the author here: http://space.mit.edu/home/tegmark/crazy.html
Re: The network of mathematics
#6Earlier quoted context omitted.
This may have been what you're thinking of. Sadly I lack a source; it's just been kicking around my miscellaneous images folder. http://i.imgur.com/tBgQkxi.jpg
That's from http://arxiv.org/pdf/gr-qc/9704009.pdf There's some more from the author here: http://space.mit.edu/home/tegmark/crazy.html
Thank you! I love the internet :)
Re: The network of mathematics
#7I remember seeing many years ago a fairly dense one page diagram of how most of the major "bits" of mathematic hang together. I can never for the life of me dig it up again. Anyone know what I'm on about / got any pointers?
This may have been what you're thinking of. Sadly I lack a source; it's just been kicking around my miscellaneous images folder. http://i.imgur.com/tBgQkxi.jpg
That's it! Thanks!
Re: The network of mathematics
#8No, "all math" will not be linked up like this some day, because that is impossible. Not all mathematical truths can be proven to be true.
Re: The network of mathematics
#9I remember seeing many years ago a fairly dense one page diagram of how most of the major "bits" of mathematic hang together. I can never for the life of me dig it up again. Anyone know what I'm on about / got any pointers?
Another good resource is http://www.math.niu.edu/~rusin/known-math/index/tour_div.htm....
Re: The network of mathematics
#10No, "all math" will not be linked up like this some day, because that is impossible. Not all mathematical truths can be proven to be true.
I don't think this is just matter of just unprovable theorems being unreachable.
There isn't an equivalent "no conceptual framework is 'best' for all mathematical inquiries" theorem. Such a claim probably can't be proven. But as you say, that doesn't keep it from being true.
Still, Godel's theorem on the cutting down of proofs via assume unprovable claims is worth considering. http://en.wikipedia.org/wiki/G%C3%B6del%27s_speed-up_theorem