HDTenEightyP/NetNews huggingface dataset:
From: wilson@glitch.cs.jhu.edu (Dwight Wilson)
Subject: Re: Fermat's Last Theorem
Summary: Just adding to the noise
Organization: The Johns Hopkins University CS Department
Date: Fri, 10 Apr 1992 02:14:30 GMT

In article <1992Apr10.013258.4518@augean.eleceng.adelaide.edu.AU> dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>
>OK Bob here's a little general knowledge quiz for you. Who are the greatest
>pros of the 20th century in the following sports:
>
>a) Cricket
>b) Baseball
>c) Golf
>d) Atheletics
>e) Gymnastics
>f) Ice skating
>h) Bungee jumping
>i) Tiddly Winks
>j) Female mud wrestling
>k) Barefoot boxing
>l) Fartlek
>

Does Bob participate in any groups that discuss these sports?  If not,
this is irrelevant.  It would be more appropriate to ask him who
the top contemporary bridge players are (which I'm sure he
can answer).

-Dwight
Newsgroups: sci.math,sci.physics
From: markh@csd4.csd.uwm.edu (Mark William Hopkins)
Subject: Re: Mathematical intuition (was: New Mersenne Prime)
Organization: Computing Services Division, University of Wisconsin - Milwaukee
Distribution: na
Date: Wed, 15 Apr 1992 04:38:54 GMT

>>In article <1992Apr1.070901.29914@augean.eleceng.adelaide.edu.AU>, dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes...
>>> 
>>>I would expect to not come accross as many counter-intuitive examples
>>>in maths as in physics.
>>> 
>>>Physics models the real world, which we have no control over, and so springs
>>>lots of surprises at us.
>>> 
>>
In article <22425@dog.ee.lbl.gov> sichase@csa1.lbl.gov writes:
>Of course, as a physicist, I have always held the opposite point of view.
>Everywhere continuous but nowhere differentiable functions just don't crop up
>much in physics, you know...

Brownian motion is continuous and nowhere differentiable.
Newsgroups: sci.math
From:  (Brad Hards)
Subject: Re: wavelet code?
Organization: Australian Defence Force Academy, Canberra, Australia
Date: Wed, 15 Apr 1992 11:34:57 GMT

tomas		(tomas@cats.ucsc.edu) wrote:
>       Hi, can anyone tell me where I could find code (preferably in C)
> to determine the wavelet analysis and wavelet synthesis (reconstruction)
> of a time series.

Get a copy of an April 1992 issue of Doctor Dobbs Journal (QA 76.5 in most
libraries in US) and check out the code there. Note that DDJ code is also
available on SIMTEL mirrors in the ddjmag directory, and that april 1992
is in ddj9204.zip. 

Brad Hards
From: sichase@csa2.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: On knowing who's who (was: Fermat's Last Theorem)
Date: 9 Apr 92 19:07:22 GMT
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
Distribution: na
Reply-To: sichase@csa2.lbl.gov
NNTP-Posting-Host: 128.3.254.197
News-Software: VAX/VMS VNEWS 1.3-4   

In article <a_rubin.702838383@dn66>, a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes...
>In <COLUMBUS.92Apr9091341@strident.think.com> columbus@strident.think.com (Michael Weiss) writes:
> 
>>	<STROMME.92Apr6130830@jeeves.math.utah.edu> <3660@tuegate.tue.nl>
>>	<1992Apr9.021905.20917@linus.mitre.org>
>>NNTP-Posting-Host: strident.think.com
>>In-reply-to: bs@gauss.mitre.org's message of Thu, 9 Apr 1992 02:19:05 GMT
> 
>>Our story so far:
> 
>>   Derek Abbott: "Who is this Erdos dude?"
>>   Robert D. Silverman: "You're kidding, right? How could you not know one
>>    	of the foremost mathematicians of this century?"  (approximate
>>    	quotation)
>>   Various posters: give the guy a break.
>>   Other posters: give *us* a break.
> 
>>In an interview in Scientific American a few months back, then Chief of
>>Staff John Sununu did not know (or professed not to know) who Leon Lederman
>>is.  I leave it for the reader to decide which side of the debate (if
>>either) this factlet supports.
> 
>OK, who IS Leon Lederman?
> 

Leon Lederman is probably the most famous and most uncannily successful
experimental particle physicist of our generation.  He has so many big
discoveries to his name that when he was awarded the Nobel Prize a few years
ago he wasn't sure at first what it was for.

He discovered the Upsilon particle, which is equivalent to discovering the 
b quark.

He discovered that the muon neutrino was distinct from the electron neutrino,
thereby proving that there were distinct "families" of subatomic particles.

He did several other important things which I can't remember right now.

He (at least until very recently) was director of Fermilab.

Nota bene:  Modern experimental particle physics is a collaborative effort.
Nothing Lederman did was done alone, although he was a driving force.  He
shared the Nobel prize for the "families" discovery with two others.

Conclusion:  Lederman is as luminary a figure as Erdos, if not moreso in his
respective field.   Derek probably didn't know who he is either. :)
But jeez, guys.  I lament the fact that more people don't know who Erdos, or
Lederman, or Weinberg, etc., are.  But most people don't even know who
Euler, Gauss, Maxwell, Faraday, Boltzmann, Bernoulli, Fermat, Laplace,
Lagrange, and so forth... are.  

So I think that if someone asks, we who know are obliged to put on the best
smile possible (no condescending allowed) and teach them.  Don't you want them
to learn?
From: gsmith@concour.cs.concordia.ca (Gene Ward Smith)
Newsgroups: sci.math
Subject: Re: factoid about new prime
Date: 10 Apr 92 20:06:56 GMT
Organization: Centre Interuniversitaire en Calcul Mathematique Algebrique

Your computation is open to objection also--2^216091 - 1 was not the
previous record prime, it was the previous record Mersenne prime.


--
     Gene Ward Smith/Brahms Gang/CICMA/Concordia University 
                  gsmith@concour.cs.concordia.ca
From: torbenm@diku.dk (Torben AEgidius Mogensen)
Newsgroups: sci.math
Subject: Re: polyominoes, anyone?
Date: 14 Apr 92 14:31:55 GMT
Organization: Department of Computer Science, U of Copenhagen

holerbch@phoenix.Princeton.EDU (Uwe Hollerbach) writes:

>G'day, folks!
>	Since pentominoes have come up recently in one or two threads
>in this newsgroup, I thought I'd ask a question which I have been
>wondering about for some time. Is there a formula for the number of
>n-ominoes, for general n, other than enumerating all possible n-ominoes,
>then counting how many you have? I have done just that up to 10 (not by
>hand; you think I'm crazy!?); see the table below. But something more
>general would be nice; that table is starting to get quite difficult
>to extend...

>1  2  3  4  5   6   7    8    9     10
>1  1  2  5  12  35  108  369  1285  4655

>Failing an exact formula, is anything known about the asymptotics?

>regards, Uwe

What were your requirements for polyominism: did you allow enclosed
areas or not? For example, did you allow these?

	XXX	XXX
	X X	X X
	XXX	XX

This is interesting only from the point of view of tiling: you
obviously cannot tile a finite/infinite plane if any of the tiles
contain enclosed ares (unless these can be filled by other tiles).

I don't think a closed form formula exist, as it would be impossible
to account for non-overlapping and mirroring. Judging from your
numbers, I would guess the P(n+1) to approach C*P(n) in the limit, C
being about 4.

A related question is how many polyominoids (3D polyominoes) there are
for a given n. The beginning of the list is:

1  2  3  4  5
1  1  2  8  27 (as far as I recall)

I have counted mirror images as distinct polyominoids, unless you can
rotate them to be equal using 3-space. Using a similar rule for
polyominoes (rotation in 2-space) increase the number of different
polyominoes, so you e.g. have 18 pentanominoes. Maybe it is easier to
find a formula for the number of these?
 
The question of enclosed volumes becomes interesting, as the two
examples above do not preclude "tiling" a finite or infinite volume
(assuming that there are other polyominoids that have "taps" to fill
the gaps).

	Torben Mogensen (torbenm@diku.dk)
From: dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott)
Newsgroups: sci.math
Subject: Re: Fermat's Last TheorumREAD/NEW
Date: 6 Apr 92 05:39:45 GMT
Organization: Electrical and Electronic Eng., University of Adelaide

In article <22900.29d9ca24@amherst.edu> mkrogers@amherst.edu writes:
>In article <1992Mar30.052412.7245@augean.eleceng.adelaide.edu.AU>, dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>> Is it true that there is a monetary prize awaiting the person who can
>> prove Fermat's Last Theorum?
>>
>> If so: how much, who decides, who keeps the money and is it
>> protected against inflation?
>
>Not planning of solving this one right away, huh? :)

Anything is possible, if they pay me enough.


Derek :-)
From: wsadjw@rw7.urc.tue.nl (Jan Willem Nienhuys)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 9 Apr 92 11:28:03 GMT
Reply-To: wsadjw@urc.tue.nl
Organization: Eindhoven University of Technology, The Netherlands

In article <1992Apr9.081944.6101@cunixf.cc.columbia.edu> gd1@cunixa.cc.columbia.edu (Gautam Dalmia) writes:
>                                             The net is not an
>appropriate place to hammer into people the fact that one has achieved
>the position of an expert in something.

But not either a place to hammer into people that one is ignorant
(`who is Erdos') and proud of it too (`this Erdos DUDE'); the original
poster who started this thread has been doing this repeatedly (`hammer').

Moron
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Re: Zero, "Arabic" numerals, etc.
Date: 9 Apr 92 13:10:26 GMT
Article-I.D.: mentor.44588
Organization: Purdue University Statistics Department

In article <1992Apr8.102143.8360@midway.uchicago.edu> trivedi@curie.uchicago.edu (Anil Trivedi) writes:

>The following discussion took place in soc.culture.arabic; I thought
>it may be of interest to some here as well.


>In article <1992Apr8.032426.11816@noose.ecn.purdue.edu> souissi@ei.ecn.purdue.edu (Ridha Souissi) writes:
>>In article <1992Apr8.000731.29997@midway.uchicago.edu> trivedi@rabi.uchicago.edu (Anil Trivedi) writes:
>>>In article <1992Apr07.073012.30344@slate.mines.colorado.edu> imustafa@slate.mines.colorado.edu (MUSTAFA IBRAHIM ) writes:

>MI:
>>>>		" Zero was introduced by the Arabs...

>AT:
>>>No it wasn't, except to Eurocentric minds. It has long been known and
>>>accepted that zero was invented by Indians; modern scholarship suggests
>>>that Mayans and Babylonians may have independently arrived at it also.
>>>Europeans learnt about it from the Arabs.

I believe that there is little question but that the Babylonians had it
first.  In a sense, it was somewhat forced by their method of writing
numbers, using base 60.  They also had terminating sexagessimal fractions,
similar to our terminating decimals.  The Ptolemaic school had tables of
trigonometric functions, using base 60, with fractions given in minutes,
seconds, thirds, etc., 

What is being discussed is not the notion of zero, but a SYMBOL for 
zero.  The mathematics done by the Egyptians and Greeks with different
symbols for the digits in different places was not that much different
from the later versions using the same symbol in each place, and the
zero symbol used to separate places.  
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
Newsgroups: sci.math
From: delliott@cec1.wustl.edu (Dave Elliott)
Subject: Re: On knowing who's who (was: Fermat's Last Theorem)
Organization: Washington University, St. Louis Mo.
	What has Paul done for us lately, well:
Date: Mon, 13 Apr 1992 20:47:57 GMT

"The Probabilistic Method" by Noga Alon, Joel Spencer and Paul Erdos (Erd\"{o}s)Wiley-Interscience, 1991. 
"The first complete guide to the theory and vast applications of the 
probabilistic method. ... with applications to discrete math, theoretical
computer science, circuit complexity, coding theory, and computational
geometry."
...
... so if you have written a paper with Alon or Spencer, you are Erdos2.

David




                                David L. Elliott
				Dept. of Systems Science and Mathematics
                                Washington University, St. Louis, MO 63130
				delliott@CEC2.WUSTL.EDU
Newsgroups: sci.math
From: hbe@sonia.math.ucla.edu (H. Enderton)
Subject: Re: Does Goedel's work apply to number theory?
Organization: UCLA Mathematics Department
Distribution: usa
Date: Thu, 9 Apr 92 22:04:42 GMT

In article <1992Apr9.213653.965@aero.org> sinclair@aero.org
(William S. Sinclair) writes:
>A colleague where I work insists that Goedel's work shows that there
>can be unprovable statements in the field of number theory. Even if they
>exist, are the any KNOWN unprovable statements in this field?

One needs to be careful about the term "unprovable."  That is, to get
a mathematical result, one has to give an exact meaning to the term.
But the answer to your question is Yes.

>Has there 
>been much conjecuture about the prvability of conjectures such as Fermat's
>theorem, or Goldbach's conjecture?

Conjectures, yes.  Non-trivial theorems, no.

--Herb Enderton    (hbe@math.ucla.edu)

Newsgroups: sci.math,comp.theory
From: kym@bingvaxu.cc.binghamton.edu (R. Kym Horsell)
Subject: Re: factorial function
Organization: State University of New York at Binghamton
Distribution: usa
Date: Sat, 11 Apr 1992 03:53:28 GMT

In article <1992Apr11.005805.12761@linus.mitre.org> bs@faron.mitre.org (Robert D. Silverman) writes:
>In article <1992Apr10.201515.14401@ringer.cs.utsa.edu> djimenez@ringer.cs.utsa.edu (Daniel Jimenez) writes:
>:What I'd really like would be a simple O(log n) algorithm
>:for n!, but I suspect there isn't one out there.
> 
>It's easy to show that an O(log n) algorithm is impossible.
>n! is about (n/e)^n so log(n!) is about n log n. It takes just
>this long to merely write down the answer.

I'm not sure whether the original poster had in mind O(log n) ARITHMETIC
operations or BIT operations.

-kym
From: rh@smds.UUCP (Richard Harter)
Newsgroups: sci.math
Subject: Re: factoid about new prime
Date: 8 Apr 92 07:34:09 GMT
Organization: SMDS Inc., Concord, MA

In article <1992Apr7.150455.22306@news.eng.convex.com>, dodson@convex.COM (Dave Dodson) writes:

> I thought the original posting was supposed to be humor:  If the previous
> largest known Mersenne prime was P, CNN was saying that the new one is 4P,
> which obviously has 4 as a factor, and therefore is not prime.

Well, you know how the old saying goes -- you can tell a horse's ass a
joke but you can't make him laugh.

:-)
-- 
Richard Harter: SMDS Inc.  Net address: rh@smds.com Phone: 508-369-7398 
US Mail: SMDS Inc., PO Box 555, Concord MA 01742.    Fax: 508-369-8272
In the fields of Hell where the grass grows high
Are the graves of dreams allowed to die.
Xref: sparky sci.math:5892 alt.irc:1344
From: jk87377@cc.tut.fi (Juhana Kouhia)
Newsgroups: sci.math,alt.irc
Subject: Re: electronic math seminar?
Date: 10 Apr 92 13:56:25 GMT
Distribution: sci
Organization: Tampere University of Technology



I have crossposted this to alt.irc, this discussion is from the
sci.math. This discussion is on the serious conferencing via Net.
(So there's more wanted from the program than for the normal
IRC discussions.)

In article <ARA.92Apr8130344@camelot.ai.mit.edu> ara@zurich.ai.mit.edu
(Allan Adler) writes:
>
>PHONE

Phone is not good at all.

>There are a few problems with this idea, though.
>(1) You want to make it open to the "public", i.e. anyone wanting to attend
>    the seminar should be able to log in to do so.
>(2) You don't want an arbitrary time limit on the meeting.
>(3) It would be nice to be able to save a transcript of the seminar.
>(4) It would be nice to be able to feed previously prepared files into
>    the discussion.
>(5) One should be able to control the scrolling of stuff as it goes by,
>    so it doesn't go by too quickly.

How IRC (Internet Relay Chat?) works for this?
What problems we have with IRC?

(1) -- Transcript may be available via mail servers and FTP places,
       also many people can attempt at once. In phone every person
       takes one part of the screen, in IRC that is not the case.
(2) -- This is ok, also you can go to lunch and continue discussion later.
       (And read the missed discussions from the transcript.)
(3) -- Have I told this before? transcript is available somehow.
(4) -- Is this possible?
(5) -- I have tested IRC a bit, I wasn't able to control the text
       at all -- it just floated away..

Also, IRC doesn't call you as does phone and talk programs, so we have
to announce the meeting time and maybe program in this group.

What I would like to get to IRC is that I'm able to pick up
others sentences (this could be possible if there's numbering system
for each sentence, personal numbering system; starting from the
beginning of the session). Also, there should be real text editor for
typing and editing my own sentences (cursor editing system like emacs,
vi, etc.) and then after I have edited the text, I can point out the
region which I would like to send out (this allows that the editing
file could be full of the notes, like mathematical equations which are
hard to type in everytime, and I don't have to clean the editing
area all of the time).

Juhana Kouhia
From: msp@dcs.warwick.ac.uk (Mike Paterson)
Newsgroups: sci.math
Subject: Re: Anyone seen one of these before?
Date: 7 Apr 92 10:13:28 GMT
Organization: Department of Computer Science, Warwick University, England

Perhaps my PDE is more readable in the form:

        d/dx exp(dV/dx) + d/dy exp(dV/dy) = 0 ?
Mike

-- 
 Internet,EARN/BITNET,UUCP: msp@dcs.warwick.ac.uk | Mike Paterson 
 JANET: msp@uk.ac.warwick.dcs                     | Dept. of Computer Science
 PHONE: +44 203 523194                            | University of Warwick     
 FAX:   +44 203 525714                            | Coventry, CV4 7AL, ENGLAND
From: pcmoan@solan.unit.no (Per Christian Moan)
Newsgroups: sci.math
Subject: More on primes
Date: 13 Apr 92 21:07:02 GMT
Organization: Norwegian Institue of Technology


Let P3(n) be the # of primes < n of the form a^2+b^2+c^2 where a,b,c are integers.
Let P2(n)              --"--                 a^2+b^2            -"-

Has it been proved that :
      
     lim   P3(n)/P(n) ~> 3/4 and lim    P2(n)/P(n) ~> 1/2
     n->oo                       n->oo

P(n) denoting the number of primes less than n.


Just asking...
Per Christian.
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: New Proof checking and NP approximations
Keywords: Logic Computer Science Fields Medal Wagner Conjecture
Date: 8 Apr 92 20:43:39 GMT
Organization: Renaissance Technologies Corp., Setuket, NY


There was an article in the April 7 NY Times on a new proof checking
trick that allows one to rule out fast approximation of NP problems.

From the article, one gets the idea that one can check whether two
integer sequences have a high probability of being identical without
checking all the integers. It's easy to see that the method presented
would do this, and I presume the application to proofs is via some
Godel numbering. OK, but it seems that you need to have a good proof
to compare to as far as the article goes, and this can't be really 
the point...

I would also like a bit more on how this prevents you from getting
fast approximate solutions to hard problems.

Can someone who knows about this stuff be prevailed upon to make
some intelligent remarks?

It would seem that these guys have a Fields Medal coming. Is this likely?

A few years back, a couple of guys proved the Wagner Conjecture. (I forget
their names, and of course it's now rightly their theore,...) This was
used in a lot of cases to show nonconstructive existence of DP algorithms
for problems which even today no polynomial solutions are known. Is
there any way in which this new technology relates to this kind of situation?

Later,
Andrew Mullhaupt
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: On knowing who's who (was: Fermat's Last Theorem)
Date: 9 Apr 92 09:13:41
Organization: Thinking Machines Corporation, Cambridge MA, USA
	<STROMME.92Apr6130830@jeeves.math.utah.edu> <3660@tuegate.tue.nl>
	<1992Apr9.021905.20917@linus.mitre.org>
NNTP-Posting-Host: strident.think.com
In-reply-to: bs@gauss.mitre.org's message of Thu, 9 Apr 1992 02:19:05 GMT

Our story so far:

   Derek Abbott: "Who is this Erdos dude?"
   Robert D. Silverman: "You're kidding, right? How could you not know one
    	of the foremost mathematicians of this century?"  (approximate
    	quotation)
   Various posters: give the guy a break.
   Other posters: give *us* a break.

In an interview in Scientific American a few months back, then Chief of
Staff John Sununu did not know (or professed not to know) who Leon Lederman
is.  I leave it for the reader to decide which side of the debate (if
either) this factlet supports.
Newsgroups: sci.math,sci.crypt
From: oliver@rhea.math.ucla.edu (Mike Oliver)
Subject: Re: Mathematical intuition (was: New Mersenne Prime)
Organization: UCLA Mathematics Department
Date: Mon, 6 Apr 92 09:10:10 GMT

In article <01010064.06jdsg@titipu.meta.com> ed@titipu.meta.com (Edward Reid) writes:

>Has anything been proven undecidable?  Is this
>possible?

Very.  But you need to be careful what you mean.  A sentence's undecidability
is only meaningful with respect to a specific theory; for example
if S is a sentence, then S is undecidable in theory T if T proves
neither S nor (not S).  But S will always be decidable in *some*
theory, for example if you take S as an axiom.

> I know that for certain problems, such as the Fermat conjecture,
>it's impossible because a proof of undecidability would be equivalent to a
>proof of the conjecture.

Well, sort of.  It's true that you can prove that if FLT is undecidable
in (say) Peano Arithmetic, then FLT is true, since if it were false
the counterexample would provide a proof of (not FLT) from PA.

However, you have no hope of proving *in PA itself* that FLT is
undecidable in PA, since that would imply that PA is consistent,
which is not provable from PA (assuming that PA is in fact consistent).
But it might conceivably be possible to prove in some stronger
theory, say PA+Con(PA), that FLT is undecidable in PA.
(Con(PA) is the formalization of the assertion "PA is consistent")

Now if you had a proof from PA+Con(PA) that FLT is undecidable in
PA, then you would have a proof from PA+Con(PA) of FLT.  But you
would not have such a proof from PA, so FLT would still be undecidable
in PA.

Of course a proof from PA+Con(PA) would settle the issue in practically
everyone's mind.  But that wouldn't change the fact that there still
would be no proof from PA.

> Does this generalize?

Not completely.  The particular arguments here apply only to
\Pi^0_1 sentences; roughly speaking, a sentence is \Pi^0_1 if
it asserts that a particular computer program will never halt.
(In this case, for example, a program searching for a counterexample
to FLT.)

So for example the Continuum Hypothesis, which asserts that there
are no sets of intermediate cardinality between that of the integers
and that of the reals, has been proved undecidable in ZFC (assuming
ZFC is consistent).  But that does *not* lead to a proof of
CH from ZFC+Con(ZFC), because CH is not \Pi^0_1.

--
------------------------------------------------------------------
Mike Oliver 
UUCP:...!{ucbvax,{hao!cepu}}!ucla-cs!math.ucla.edu!oliver
ARPA: oliver@math.ucla.edu
From: cwalker@client10.bucknell.edu (carleton walker `93)
Newsgroups: sci.math
Subject: Art Gallery Problem
Date: 15 Apr 92 20:20:37 GMT
Organization: Bucknell University, Lewisburg, Pa.


	I'm looking for information on the art gallery problem. I more
interested in books than papers on the subject, but any help is
appreciated.

Thanks,
Carl Walker
--
Carl Walker				"Hectic days ahead of us,
Bucknell University			 Rotten ones behind,
Lewisburg, PA				 Keeping plastics in our pockets,
					 Children never mind." - K, S, & W