November 2014 - mathfun@mailman.xmission.com

[math-fun] Autonomous Weapons meet the Halting Problem
by Henry Baker 19 Nov '14

19 Nov '14

FYI -- Cory Doctorow has been chiding non-computer people for years about their lack of understanding of the logical limitations of computers -- "why can't I tell a computer to only do good stuff?". I would imagine that this misunderstanding problem will continue until undecidability is part of the required curriculum for all high schools. ---- http://arxiv.org/abs/1411.2842 Logical Limitations to Machine Ethics with Consequences to Lethal Autonomous Weapons Matthias Englert, Sandra Siebert, Martin Ziegler (Submitted on 11 Nov 2014) Lethal Autonomous Weapons promise to revolutionize warfare -- and raise a multitude of ethical and legal questions. It has thus been suggested to program values and principles of conduct (such as the Geneva Conventions) into the machines' control, thereby rendering them both physically and morally superior to human combatants. We employ mathematical logic and theoretical computer science to explore fundamental limitations to the moral behaviour of intelligent machines in a series of "Gedankenexperiments": Refining and sharpening variants of the Trolley Problem leads us to construct an (admittedly artificial but) fully deterministic situation where a robot is presented with two choices: one morally clearly preferable over the other -- yet, based on the undecidability of the Halting problem, it provably cannot decide algorithmically which one. Our considerations have surprising implications to the question of responsibility and liability for an autonomous system's actions and lead to specific technical recommendations. Subjects: Computers and Society (cs.CY); Artificial Intelligence (cs.AI) ACM classes: K.4.1; I.2.0 Cite as: arXiv:1411.2842 [cs.CY] (or arXiv:1411.2842v1 [cs.CY] for this version) Submission history From: Martin Ziegler [view email] [v1] Tue, 11 Nov 2014 15:05:01 GMT (22kb)

1 0

[math-fun] The probability that N independent statistical tests fail simultaneously (review)
by Warren D Smith 19 Nov '14

19 Nov '14

>Ch.Greathouse: Let's say that we're testing a coin to see if it's unfairly biased towards heads. The null hypothesis is that it's a fair coin. Test 1 consists of flipping the coin twice and seeing if both times it comes up heads; p = 0.25. Test 2 consists of flipping it once and seeing if it comes up heads; p = 0.5. The chance that a fair coin would fail both tests is 1/8 for a p-value of 0.125. Your formula gives 1/4 * (2*1/2 - 1/4) = 3/16 = 0.1875. Am I missing something? Charles Greathouse Analyst/Programmer Case Western Reserve University --WDS Response: this is two tests labeled by you as "test 1" and "test 2." Say they decided X<0.25 and Y<0.5. However, what I meant by "interchangeable" (and I'm sorry I was not clearer re that) was... Somebody tells you they did 2 tests, and says one of them failed like "X<0.25" and the other failed with "Y<0.5" BUT DOES NOT SAY which X and Y were. You then know that one of these two events happened: I. "X<0.25 and Y<0.5" II. "X<0.5 and Y<0.25" but do not know which. (Or they both could have occurred, since they overlap -- but you do not know whether that happened either.) Given this knowledge (and non-knowledge) by you, the p-level is 3/16. If you look in my preliminary paper, http://rangevoting.org/CombinedTestFail.html at the exact problem statement wording, I hope you will see this is the version I am speaking of. This also happens to be the problem version that is highly relevant to a lot of real life stat-testing applications, i.e. I did not pick it merely because I was evil. Is that ok?

2 2

[math-fun] The probability that N independent statistical tests fail simultaneously (review)
by Warren D Smith 18 Nov '14

18 Nov '14

So my preliminary paper "The chance that N independent statistical tests fail simultaneously" http://rangevoting.org/CombinedTestFail.html has now obtained 5 mathematicians in a row not obtaining the right formula for F2, followed by 2 disputants on the ElectionIntegrity email list who both claimed statistical expertise, disputing it... followed by Paul F. Velleman, an actual professor of statistics at Cornell, telling me that not only was I right, in fact this was a well known literature area that I was probably just rediscovering the wheel about. The magic key words he suggested are "multiple comparison problem." Amazing. Well, Velleman is certainly more right than the others. It turns out there are several entire books on this area of statistics, and the whole "multiple comparison problem" is, at least generally speaking, a well known phenomenon. Evidently, however, it is not well known enough. In particular, at least one election-integrity paper by Josh Mitteldorf and others, is invalidated because he did not know about this effect, and it would not surprise me if every paper on that topic he ever wrote or co-wrote, also is invalidated, plus quite likely some of Mitteldorf's other papers in non-election areas. (His response? He emailed me "I don't have time to continue this discussion." You know what Josh? If a goodly fraction of my life's scientific work had just been invalidated, I'd find the effing time, especially if somebody was very generously and helpfully pointing it out to you.) And Mitteldorf is by no means the only victim -- a large number of medical experimental papers also contain wrong statistical calculations due to their authors not knowing about this effect, which probably means lives have been lost. I would guess thousands of papers are invalidated. QUOTE from Yoav Benjamini & Yosef Hochberg: Controlling the false discovery rate: a practical and powerful approach to multiple testing". J. Royal Statistical Society, Series B 57,1 (1995) 125-133: "Even though MCPs have been in use since the early 1950s and in spite of advocacy for their use (e.g. mandatory for some journals, as well as in institutions like the FDA) researchers have not yet widely adopted these procedures. In medical research for example, Godfrey (1985), Pocock et al (1987) and Smith et al (1987) examined samples of reports of comparative studies from major medical journals. They found that researchers overlook various kinds of multiplicity, and as a result reporting tends to exaggerate treatment differences" Want more? Here's a second QUOTE from the review paper D.A.Berry: The difficult and ubiquitous problems of multiplicities, Pharmaceutical Statistics 6 (2007) 155-160: "Most scientists are oblivious to the problems of multiplicities. Yet they are everywhere. In one or more of its forms, multiplicities are present in every statistical application. They may be out in the open or hidden. And even if they are out in the open, recognizing them is but the first step in a difficult process of inference. Problems of multiplicities are the most difficult that we statisticians face. They threaten the validity of every statistical conclusion." Anybody get the picture yet? So now, I am trying to look into the literature Velleman so helpfully pointed me toward. Books on this topic include: Rupert G. Miller Jr: Simultaneous statistical inference, Springer-Verlag, 2nd ed, 1981. QA276 .M474 Jason C.Hsu: Multiple comparisons: Theory and methods. London, UK: Chapman and Hall 1996. Larry E. Toothaker: Multiple comparisons for researchers, Newbury Park, Calif. : Sage Publications, 1991. Q180.55.M4 T66 Shanti Swarup Gupta & Deng-Yuan Huang: Multiple statistical decision theory :recent developments, New York : Springer-Verlag, c1981. QA279.7 .G87 Peter H.Westfall & S.S.Young: Resampling-based multiple testing: Examples and methods for p-value adjustment. New York, NY: Wiley 1993. There also are several web pages devoted to this area, including wikipedia's and "Beware of multiple comparisons" http://www.graphpad.com/guides/prism/6/statistics/index.htm?beware_of_multi… In addition to those books just on this topic, apparently at least 10 general-purpose statistics guidebooks at least make some mention of the Multiple Comparisons Problem. E.g. Statistics for anthropology (Cambridge U.P.) / Lorena Madrigal 2012 Using statistical methods in social work practice : a complete SPSS guide (Lyceum Books 2006) / Soleman H. Abu-Bader Modern data analysis / edited by Robert L. Launer, Andrew F. Siegel. New York : Academic Press, 1982 Handbook of Biological Statistics / John McDonald Another good magic keyphrase is "false discovery rate." What do I think of all this literature? I'm trying to figure that out... I'll let you know after I read some more of it. A simple and safe idea which many sources recommend is, if you are doing T different tests then your p-level cutoff for statistical significance (e.g. if seeking 99.9% confidence, it would be 0.001) should be divided by T for each test, then proceed. That'll protect you. I already knew that since I was a child, but it is a weak idea. If you want to wring the most confidence from your tests, you need stronger methods, i.e. need a better understanding than just that. A large fraction (in fact virtually all of the ones I looked at so far) of the statistics theory papers on this topic DO NOT GIVE CLEARLY STATED THEOREMS, WITH PROOFS. I think for a topic clearly tricky like this, that is unacceptable behavior. So I will say straight off that the workers in this area have, in the vast majority, done poor work. The allegedly strongest result in one line of work on this is Yosef Hochberg: A Sharper Bonferroni Procedure for Multiple Tests of Significance, Biometrika 75,4 (1988) 800-802 which is available electronically: http://www-stat.wharton.upenn.edu/~steele/Courses/956/Resource/MultipleComp… and http://svn.donarmstrong.com/don/trunk/projects/research/linkage/papers/mult… and it seems to me still to be a quite weak result. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

3 2

[math-fun] Unfair Games
by James Propp 18 Nov '14

18 Nov '14

Does anyone have handy a copy of Martin Baxter's article "Unfair Games", Eureka, 50 (1990), 60-68? If so, and if I'm right in suspecting that it's about games like Brussels Sprouts in which the winner is predetermined, could someone list for me the games of this kind that Baxter discusses? Thanks, Jim Propp

5 5

Re: [math-fun] about Grothendieck
by Axel Vogt 17 Nov '14

17 Nov '14

On 16.11.2014 23:27, math-fun-request(a)mailman.xmission.com wrote: > Send math-fun mailing list submissions to > math-fun(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > or, via email, send a message with subject or body 'help' to > math-fun-request(a)mailman.xmission.com > > You can reach the person managing the list at > math-fun-owner(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of math-fun digest..." > > > Today's Topics: > > 1. Re: Grothendieck (rcs(a)xmission.com) > 2. Greatest 3 mathematicians of the 20th century? (Warren D Smith) > 3. Re: Greatest 3 mathematicians of the 20th century? > (Whitfield Diffie) > 4. Re: Greatest 3 mathematicians of the 20th century? > (Gustavus Simmons) > 5. Re: about Grothendieck (Axel Vogt) > 6. Re: about Grothendieck (Simon Plouffe) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sun, 16 Nov 2014 13:25:07 -0700 > From: rcs(a)xmission.com > To: math-fun(a)mailman.xmission.com > Cc: rcs(a)xmission.com > Subject: Re: [math-fun] Grothendieck > Message-ID: > <20141116132507.9q2ab6valccwg884(a)webmail-backup.xmission.com> > Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; > format="flowed" > > re Applications of Grothendieck, some possible links. > > There's a not-yet-comprehended K-page proof of the ABC conjecture > by Mochizuki. > He might understand Grothendieck's work better than anyone else. > Based only on superficial verbal similarity (I don't understand this > stuff at all), M's Inter-Universal_Teichmuller_Theory appears to be > descended from G. > Mochizuki has announced a seminar for next Spring. > Chen has a decent summary. > > Jeff Lagarias told me a long story about trying to find reviewers > for the proof, and failing. > > http://projectwordsworth.com/the-paradox-of-the-proof/ Caroline Chen > http://en.wikipedia.org/wiki/Abc_conjecture > http://en.wikipedia.org/wiki/Shinichi_Mochizuki > http://www.kurims.kyoto-u.ac.jp/~motizuki/top-english.html M's web page > http://en.wikipedia.org/wiki/Inter-universal_Teichm%C3%BCller_theory > > One obvious approach is to try to force the proof through a computer > proof checking program. This seems too hard. > > A recent success (August 2014) is Hales' computer check of the > 1998 Ferguson-Hales proof of the Kepler Conjecture -- there's no > denser way to pack spheres than the usual "one". > https://code.google.com/p/flyspeck/wiki/AnnouncingCompletion > The Flyspeck project team is a couple of dozen people, working for > a few years. The final product includes a special version of the > proof checker. One contrast with the ABC work is that the Kepler > proof has no particular conceptual mountain to climb-- it's a > boatload of linear & non-linear programming problems. The final > computer check needs only 5K compute-hours. The real cost here is > the effort of the project team. > > Rich > > ---------- > Quoting Warren D Smith <warren.wds(a)gmail.com>: > >> http://en.wikipedia.org/wiki/Weil_conjectures >> >> is something that Grothendieck contributed to, which seems amazing >> and whose statement can actually be comprehended. >> Does it have any applications, or does it just seem amazing? >> Well, I actually am aware of a few applications of the Weil conjectures, but >> I think most or all of those applications were later also accomplished >> in far simpler ways without needing to go anywhere near said >> conjectures. >> >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> > > > > > > ------------------------------ > > Message: 2 > Date: Sun, 16 Nov 2014 15:38:27 -0500 > From: Warren D Smith <warren.wds(a)gmail.com> > To: math-fun(a)mailman.xmission.com > Subject: [math-fun] Greatest 3 mathematicians of the 20th century? > Message-ID: > <CAAJP7Y140oz1N8X8moLwrpcokkGifDn5BBkbS_a+ADs0v6e1ew(a)mail.gmail.com> > Content-Type: text/plain; charset=ISO-8859-1 > > Well, since Plouffe started down that road, you know you all want to > submit your votes too. Here, these ones seem pretty good to me: > > Albert Einstein > John von Neumann > Pal Erdos > > Not a fields medalist among them, though -- that's evidently the kiss > of death :) > > > > ------------------------------ > > Message: 3 > Date: Sun, 16 Nov 2014 12:45:56 -0800 > From: Whitfield Diffie <whitfield.diffie(a)gmail.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: Re: [math-fun] Greatest 3 mathematicians of the 20th century? > Message-ID: > <CAF+O-CVscUYP0N_DTzc24+3Fqad4Km6SvyP8LvnzqOdq2ZO1+Q(a)mail.gmail.com> > Content-Type: text/plain; charset=ISO-8859-1 > >> Well, since Plouffe started down that road, you know you all want to >> submit your votes too. > > Sure. I suggest > > Emmy Noether > John von Neumann > Andre Weil > > > Whit > > > > ------------------------------ > > Message: 4 > Date: Sun, 16 Nov 2014 13:53:28 -0700 > From: "Gustavus Simmons" <gsimmons30(a)comcast.net> > To: "math-fun" <math-fun(a)mailman.xmission.com> > Subject: Re: [math-fun] Greatest 3 mathematicians of the 20th century? > Message-ID: <D9353768BA33412CB208731553AEC92C@oldmachine> > Content-Type: text/plain; format=flowed; charset="iso-8859-1"; > reply-type=original > > To follow up on Warren's comment about the Field's medal, Arno Penzias -- > himself a Nobel laureate for having discovered the background radiation > consistent with the Big Bang theory -- was fond of saying: "The Nobel prize > has ruined many an otherwise promising career in physics". > > ----- Original Message ----- > From: "Warren D Smith" <warren.wds(a)gmail.com> > To: <math-fun(a)mailman.xmission.com> > Sent: Sunday, November 16, 2014 1:38 PM > Subject: [math-fun] Greatest 3 mathematicians of the 20th century? > > >> Well, since Plouffe started down that road, you know you all want to >> submit your votes too. Here, these ones seem pretty good to me: >> >> Albert Einstein >> John von Neumann >> Pal Erdos >> >> Not a fields medalist among them, though -- that's evidently the kiss >> of death :) >> >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> >> __________ Information from ESET Smart Security, version of virus >> signature database 10733 (20141116) __________ >> >> The message was checked by ESET Smart Security. >> >> http://www.eset.com >> >> >> > > > __________ Information from ESET Smart Security, version of virus signature database 10733 (20141116) __________ > > The message was checked by ESET Smart Security. > > http://www.eset.com > > > > > > > ------------------------------ > > Message: 5 > Date: Sun, 16 Nov 2014 22:59:39 +0100 > From: Axel Vogt <mail(a)axelvogt.de> > To: math-fun(a)mailman.xmission.com > Subject: Re: [math-fun] about Grothendieck > Message-ID: <54691E4B.1090601(a)axelvogt.de> > Content-Type: text/plain; charset=windows-1252; format=flowed > >> From: Simon Plouffe >> To: math-fun(a)mailman.xmission.com >> Subject: [math-fun] about Grothendieck > ... > > I am not aware of Bourbaki-style in reading Grothendieck. > > > > ------------------------------ > > Message: 6 > Date: Sun, 16 Nov 2014 23:26:55 +0100 > From: Simon Plouffe <simon.plouffe(a)gmail.com> > To: math-fun(a)mailman.xmission.com > Subject: Re: [math-fun] about Grothendieck > Message-ID: <546924AF.7070805(a)gmail.com> > Content-Type: text/plain; charset=ISO-8859-1; format=flowed > > hello, > > Alexander Grothendieck was a member of Bourbaki for > years. From 1957 to 1962 at the least. > > reference : > http://en.wikipedia.org/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9brique > > and here : > http://www.numdam.org/numdam-bin/search?h=aur&aur=Grothendieck,+Alexander&f… > > for example this document : > http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1963__17_/PMIHES_1963__17__… > > which is from 1963, from what I can see this is the purest Bourbaki style of > mathematics. > > ... A.G. is a great master of higher mathematics. > > 2 things could happen, in 200 years this will look like > trivial or something else will come out in a complete different > direction ? What will prevail is the principle of l'?conomie > de pens?e, i.e. the shortest and simplest way to explain things. > Maybe that guy was 400 years ahead of his time ? Well, this was > 50 years ago and as far as I can tell, there is no simplification > that came out. > > I had a personal friend (Pierre Bouchard) in Montr?al, recently > deceased, he was a specialist of Grothendieck's work, we (some friends > and I) asked him many times, how come this is interesting ?, tell us! > please!, > He could hardly give any example. We all stumbled on the first > books of Bourbaki (he had them all). That example of the definition > of the empty set was a subject of discussion, lots of it, nothing > came out of all this. > > Maybe as they say in the 'le monde' article that the subconscious > of mathematicians is haunted by that guy and what he did, I am > not certain of this. This is my personal opinion. > > Best regards, > Simon Plouffe Just about the last link: This still is not Bourbaki, it is EGA. In my own very sloppy words for that 2 chapters: The first "translates" methods of (usual) Topology to Algebra, allowing to switch if needed. And extends it to singular 'spaces'. The 2nd tells when the above behaves well. I can understand inhibitions, but suggest to have a look at Dieudonne "The historical development of Algebraic Geometry", AMS 1972, which completely avoids 'abstract nonsense'. A Bourbakist and the co-Author for EGA, just have a look.

1 0

Re: [math-fun] About Grothendieck and Bourbaki
by Axel Vogt 17 Nov '14

17 Nov '14

> From: Olivier Gerard <olivier.gerard(a)gmail.com> > Subject: [math-fun] About Grothendieck and Bourbaki ... > Simon is right that A. Grothendieck mathematical writings > was very much influenced > by the Bourbaki style. He was in early direct contact with several > important members such as Henri Cartan, Jean Dieudonn?, > Laurent Schwartz and joined the group later for a few years. > > Another related point is that Jean Dieudonn?, who had a strong > role in the final editorial stages of many Bourbaki volumes > decided to become a kind of assistant and co-author of the > younger Grothendieck for the hundreds of pages of the E.G.A. volumes > (= Elements of Algebraic Geometry). > > But both Grothendieck and Dieudonn? had their own special > voices, interest and projects and diverged on many points. > Other important members of the Bourbaki group such as > Andr? Weil, Ehresmann, ... did not write their own books > in the manner of the Bourbaki volumes. It would not have > made sense anyway. But they used many of its conventions > and notations. ... Especially EGA is not Bourbaki style at all, for my taste.

1 0

[math-fun] About Grothendieck and Bourbaki
by Olivier Gerard 17 Nov '14

17 Nov '14

The main cause of trouble in all this is that we are all guilty of propagating bad journalism methods and angles - Who is the best mathematician of the century, the three most important theorems of all time ? - Who will win ? Who is right ? Bourbaki-style abstract nonsense with their species-loving crypto allies who never take an empty set for granted or down-to-earth no-nonsense experimental mathematicians who know how to count the leaves on a tree when they see one ? I suggest that keen amateurs and professional of mathematics would be better off leaving this kind of sensationalism to people magazines. Simon is right that A. Grothendieck mathematical writings was very much influenced by the Bourbaki style. He was in early direct contact with several important members such as Henri Cartan, Jean Dieudonné, Laurent Schwartz and joined the group later for a few years. Another related point is that Jean Dieudonné, who had a strong role in the final editorial stages of many Bourbaki volumes decided to become a kind of assistant and co-author of the younger Grothendieck for the hundreds of pages of the E.G.A. volumes (= Elements of Algebraic Geometry). But both Grothendieck and Dieudonné had their own special voices, interest and projects and diverged on many points. Other important members of the Bourbaki group such as André Weil, Ehresmann, ... did not write their own books in the manner of the Bourbaki volumes. It would not have made sense anyway. But they used many of its conventions and notations. The Bourbaki style was a collective, the results of relentless criticism between members of the intermediate or alternate redactions of sections and chapters. The goals have changed over the course of the group's life, but the starting point was to write down what the members saw as the core of mathematics, allowing others to elaborate on say, functional analysis. It is also really wrong to use Bourbaki as a scapegoat for some of the mathematical viewpoints one has had no chance to really practice and appreciate. I would like to write about the mutual interest and strong relevance of all this for combinatorics among other things, but this will be another time. Bourbaki's treaty by itself is not hegemonic on mathematics. I except Bourbaki historical notes, often written by Dieudonné, that I find very partial. But some of the most vocal members such as André Weil and Jean Dieudonné made very strong, sometimes provocative, statements and were very influential in the professional world. Their personal tastes were as biased and as subjective as anyone but their position made that these were not easily dismissed as tastes and opinions but took a programmatic turn and motivated frightful epigons. One can appreciate Bourbaki treatises but have widely different opinions from the well-known members. Most things that Simon alludes to are not Bourbaki's. Most of the times Bourbaki's treaty is collecting, ordering and systematizing important past research, proposing new names and notations of which many have become standard now, starting with the most basic (such as set theory or rings) but most ideas come from people such as Frege, Russel, Peano, Zermelo, Hilbert, Hasse, Noether, Artin, Van der Waerden, Borel, Banach, von Neumann, etc. Those ones are the authors and the inspirators. Simon was amused by some parts of Book I about set theory I guess, of perhaps the "fascicule" preprint. I wonder what he would think of Russel and Whitehead's Principia Mathematica and many other works by logicians, including to this day. But there are fascinating things going on on this front. Not very readable for the uninitiated, I agree. Bourbaki books are very close to an encyclopedic dictionary with no special interest in being original but the most general possible, even if this requires tremendous work, knowledge and ingenuity. One can read them with the same kind of pleasure you read the entries for important words in a large dictionary such as the O.E.D., not for the spelling and the main definition but for all the meanings you would not have listed yourself even if you could grasp them easily enough when reading widely. It expands the mind to consider uses of langage you have not been exposed to. You are free to steal them or reject them. You are free to invent something else as a result. The fact that Simon (and countless others) attributes to Bourbaki what has been the outcome of heated debates and a fantastic renovation of mathematics in the 1890s to the 1940s by many great logicians and mathematicians is a bit ironic. They just wanted to be an easy and homogenous reference for all this. They strived for unity in mathematics. You may think it is a bit naïve. Grothendieck's mathematical style has evolved a lot and is quite in contrast with his litterary or epistolary style. In mathematics, it was a mixture of large-scale engineering, akin to building tunnels and bridges across oceans instead of rivers, and search for harmony, generality and security in a way most people would find insecure : by removing special cases, historical examples and concepts. What is common between his mathematics and his other writings is the energy, the will to encompass, to settle as much of the Universe as possible, a longing for the absolute, a rejection for compromise, a certain view of civilisation which finds no human being worthy of being called civilized and wants to start again and again. Olivier Gérard

4 4

[math-fun] Bourbaki
by Warren D Smith 17 Nov '14

17 Nov '14

I always hated Bourbaki. They had the attitude they were going to be self contained and derive everything from foundations, which sucked because, they could not do that in 1 book, and you want links to all the other literature, which makes your book worth 100X more, and they were not providing. The resulting books were then pretty useless and horrible compared to something which did not take their attitude. Probably Russell+Whitehead was even more horrible than Bourbaki. I wasn't going to read either. However, in the case of their book on Lie theory, Bourbaki wasn't so bad for me, it did actually help me learn. And I suppose you might argue that the recent drive toward computer-verified proofs, is somehow a vindication of Bourbaki, sort of?

1 0

Re: [math-fun] about Grothendieck
by Axel Vogt 16 Nov '14

16 Nov '14

> From: Simon Plouffe > To: math-fun(a)mailman.xmission.com > Subject: [math-fun] about Grothendieck ... I am not aware of Bourbaki-style in reading Grothendieck.

4 4

[math-fun] Greatest 3 mathematicians of the 20th century?
by Warren D Smith 16 Nov '14

16 Nov '14

Well, since Plouffe started down that road, you know you all want to submit your votes too. Here, these ones seem pretty good to me: Albert Einstein John von Neumann Pal Erdos Not a fields medalist among them, though -- that's evidently the kiss of death :)

3 2