[math-fun] Draft of essay about two proofs of a rectangle tiling theorem
I'm hoping to post the essay "What Proof is Best?" on my blog in a few days; comments are very welcome! The current draft is at http://jamespropp.org/mathenchant/057-draft2.pdf Thanks, Jim
Thanks, Jim! I certainly agree that multiple proofs deserve Bookhood (and some clearly don’t). This is a great example, especially given your comments about how each proof has different power to generalize. I think you should do a column sometime on the Devil’s book — the book of mathematical truths that are easy to state, but which have no proof in God's book. Perhaps the 4-color theorem is one of these… - Cris
On Jan 22, 2020, at 9:11 PM, James Propp <jamespropp@gmail.com> wrote:
I'm hoping to post the essay "What Proof is Best?" on my blog in a few days; comments are very welcome! The current draft is at
http://jamespropp.org/mathenchant/057-draft2.pdf
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I plan to give the Devil his due next month! :-) Jim On Wed, Jan 22, 2020 at 11:53 PM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
Thanks, Jim! I certainly agree that multiple proofs deserve Bookhood (and some clearly don’t). This is a great example, especially given your comments about how each proof has different power to generalize.
I think you should do a column sometime on the Devil’s book — the book of mathematical truths that are easy to state, but which have no proof in God's book. Perhaps the 4-color theorem is one of these…
- Cris
On Jan 22, 2020, at 9:11 PM, James Propp <jamespropp@gmail.com> wrote:
I'm hoping to post the essay "What Proof is Best?" on my blog in a few days; comments are very welcome! The current draft is at
http://jamespropp.org/mathenchant/057-draft2.pdf
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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in return for all intangibles in perpetuity? C p.s. I haven’t found a source for the Devil’s book (or even, more modestly, for the claim the Book exists :-) I don’t think I made it up myself, but who knows...
On Jan 22, 2020, at 10:02 PM, James Propp <jamespropp@gmail.com> wrote:
I plan to give the Devil his due next month! :-)
Jim
On Wed, Jan 22, 2020 at 11:53 PM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
Thanks, Jim! I certainly agree that multiple proofs deserve Bookhood (and some clearly don’t). This is a great example, especially given your comments about how each proof has different power to generalize.
I think you should do a column sometime on the Devil’s book — the book of mathematical truths that are easy to state, but which have no proof in God's book. Perhaps the 4-color theorem is one of these…
- Cris
On Jan 22, 2020, at 9:11 PM, James Propp <jamespropp@gmail.com> wrote:
I'm hoping to post the essay "What Proof is Best?" on my blog in a few days; comments are very welcome! The current draft is at
http://jamespropp.org/mathenchant/057-draft2.pdf
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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It’s a thread on MathOverflow. Jim On Thu, Jan 23, 2020 at 12:05 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
in return for all intangibles in perpetuity?
C
p.s. I haven’t found a source for the Devil’s book (or even, more modestly, for the claim the Book exists :-) I don’t think I made it up myself, but who knows...
On Jan 22, 2020, at 10:02 PM, James Propp <jamespropp@gmail.com> wrote:
I plan to give the Devil his due next month! :-)
Jim
On Wed, Jan 22, 2020 at 11:53 PM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
Thanks, Jim! I certainly agree that multiple proofs deserve Bookhood
(and
some clearly don’t). This is a great example, especially given your comments about how each proof has different power to generalize.
I think you should do a column sometime on the Devil’s book — the book of mathematical truths that are easy to state, but which have no proof in God's book. Perhaps the 4-color theorem is one of these…
- Cris
On Jan 22, 2020, at 9:11 PM, James Propp <jamespropp@gmail.com> wrote:
I'm hoping to post the essay "What Proof is Best?" on my blog in a few days; comments are very welcome! The current draft is at
http://jamespropp.org/mathenchant/057-draft2.pdf
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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What about Devil's sun? https://www.thisiscolossal.com/2020/01/sinister-sunrise-elias-chasiotis/ R.E Boss
-----Oorspronkelijk bericht----- Van: math-fun <math-fun- bounces+bossipm=outlook.com@mailman.xmission.com> Namens James Propp Verzonden: donderdag 23 januari 2020 11:58 Aan: Cris Moore <moore@santafe.edu>; math-fun <math- fun@mailman.xmission.com> Onderwerp: Re: [math-fun] Draft of essay about two proofs of a rectangle tiling theorem Urgentie: Hoog
It’s a thread on MathOverflow.
Jim
On Thu, Jan 23, 2020 at 12:05 AM Cris Moore via math-fun < math- fun@mailman.xmission.com> wrote:
in return for all intangibles in perpetuity?
C
p.s. I haven’t found a source for the Devil’s book (or even, more modestly, for the claim the Book exists :-) I don’t think I made it up myself, but who knows...
On Jan 22, 2020, at 10:02 PM, James Propp <jamespropp@gmail.com>
wrote:
I plan to give the Devil his due next month! :-)
Jim
On Wed, Jan 22, 2020 at 11:53 PM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
Thanks, Jim! I certainly agree that multiple proofs deserve Bookhood
(and
some clearly don’t). This is a great example, especially given your comments about how each proof has different power to generalize.
I think you should do a column sometime on the Devil’s book — the book of mathematical truths that are easy to state, but which have no proof in God's book. Perhaps the 4-color theorem is one of these…
- Cris
On Jan 22, 2020, at 9:11 PM, James Propp <jamespropp@gmail.com> wrote:
I'm hoping to post the essay "What Proof is Best?" on my blog in a few days; comments are very welcome! The current draft is at
http://jamespropp.org/mathenchant/057-draft2.pdf
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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can’t find it under “devil’s book”… link?
On Jan 23, 2020, at 3:58 AM, James Propp <jamespropp@gmail.com> wrote:
It’s a thread on MathOverflow.
Jim
On Thu, Jan 23, 2020 at 12:05 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
in return for all intangibles in perpetuity?
C
p.s. I haven’t found a source for the Devil’s book (or even, more modestly, for the claim the Book exists :-) I don’t think I made it up myself, but who knows...
On Jan 22, 2020, at 10:02 PM, James Propp <jamespropp@gmail.com> wrote:
I plan to give the Devil his due next month! :-)
Jim
On Wed, Jan 22, 2020 at 11:53 PM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
Thanks, Jim! I certainly agree that multiple proofs deserve Bookhood
(and
some clearly don’t). This is a great example, especially given your comments about how each proof has different power to generalize.
I think you should do a column sometime on the Devil’s book — the book of mathematical truths that are easy to state, but which have no proof in God's book. Perhaps the 4-color theorem is one of these…
- Cris
On Jan 22, 2020, at 9:11 PM, James Propp <jamespropp@gmail.com> wrote:
I'm hoping to post the essay "What Proof is Best?" on my blog in a few days; comments are very welcome! The current draft is at
http://jamespropp.org/mathenchant/057-draft2.pdf
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Cristopher Moore Professor, Santa Fe Institute I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
CM: "I haven’t found a source for the Devil’s book ..." In Shalosh B. Ekhad's "A Proof of Morley's Theorem (From The (Devil's) Book)" [mid-1990s] is written: "According to Doron Zeilberger, the devil(SC(?)), also has a notebook, that contains purely routine, albeit often long, proofs of all theorems." https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/morley.html
I would think the Devil's book should contain false proofs whose errors are so subtle that they could go undetected for decades, if not longer. Tom Hans Havermann writes:
CM: "I haven’t found a source for the Devil’s book ..."
In Shalosh B. Ekhad's "A Proof of Morley's Theorem (From The (Devil's) Book)" [mid-1990s] is written: "According to Doron Zeilberger, the devil(SC(?)), also has a notebook, that contains purely routine, albeit often long, proofs of all theorems."
https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/morley.html
And are we all quite certain that it does not also contain one or two correct proofs of false "theorems" ... ?! WFL On 1/23/20, Tom Karzes <karzes@sonic.net> wrote:
I would think the Devil's book should contain false proofs whose errors are so subtle that they could go undetected for decades, if not longer.
Tom
Hans Havermann writes:
CM: "I haven’t found a source for the Devil’s book ..."
In Shalosh B. Ekhad's "A Proof of Morley's Theorem (From The (Devil's) Book)" [mid-1990s] is written: "According to Doron Zeilberger, the devil(SC(?)), also has a notebook, that contains purely routine, albeit often long, proofs of all theorems."
https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/morley.html
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That is Asmodeus’ book. I’m referring to Beelzebub’s. Cris
On Jan 23, 2020, at 6:29 AM, Tom Karzes <karzes@sonic.net> wrote:
I would think the Devil's book should contain false proofs whose errors are so subtle that they could go undetected for decades, if not longer.
Tom
Hans Havermann writes:
CM: "I haven’t found a source for the Devil’s book ..."
In Shalosh B. Ekhad's "A Proof of Morley's Theorem (From The (Devil's) Book)" [mid-1990s] is written: "According to Doron Zeilberger, the devil(SC(?)), also has a notebook, that contains purely routine, albeit often long, proofs of all theorems."
https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/morley.html
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Or, more likely, Satan has succeeded in impersonating God, so in fact, God's book really is Satan's beautiful book of the fruits of the tree of knowledge. I don't think it matters one way or the other. The problem in the essay is an interesting one, and good for you taking a pro-diversity stance. However, since you have lost time on a digression about popular television, I think you are missing an opportunity to talk about the dichotomy of originality and reproducibility. These days it seems that the best proof (or the best science), is whichever seems correct, yet is also the least reproducible. So much so that a fallacy has developed, where reproducibility and originality are mutually exclusive. "If a theorem (or an experiment) is reproducible, then it must have already been done, so it can not be original". This fallacy, I think, is a practical outgrowth of overpopulation relative to resources available, whereby some scientists have to be disrespected, when really they should not be. With big issues like cohomology or climate change, another obscure theorem from the crown of mathematics is not needed as much as we need a larger part of the population to understand basic facts that mathematicians and scientists aren't incentivized to prove again. So, in defence of reproducibility, I think scientists should be considered original when they develop new proofs of old truths, especially as part of an effort to include a wider population in the pursuit of science. (This would involve changing the schedule of who is to be disrespected.) After all, how can you call something "science", when only the smart half of the population claims it as intelligable? --Brad On Wed, Jan 22, 2020 at 10:12 PM James Propp <jamespropp@gmail.com> wrote:
I'm hoping to post the essay "What Proof is Best?" on my blog in a few days; comments are very welcome! The current draft is at
http://jamespropp.org/mathenchant/057-draft2.pdf
Thanks,
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (7)
-
Brad Klee -
Cris Moore -
Fred Lunnon -
Hans Havermann -
James Propp -
R B -
Tom Karzes