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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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<P>Servers for rsync are available at rsync.metamath.org and
cn.metamath.org.
<!--, and uk.metamath.org.--> To check availability, use the
command "rsync rsync.metamath.org::" or "rsync cn.metamath.org::",
<!-- or
"rsync uk.metamath.org::" -->
which should respond with "metamath
metamath". See the <A TARGET="_top"
HREF="http://us.metamath.org/mirror.txt">mirror.txt</A> file for more
information. Note that rsync.metamath.org may be throttled to
reduce network load on the development site. If you just want to get a
local copy of the site for off-line viewing, the cn.metamath.org
<!-- and
uk.metamath.org -->
rsync server is much faster.
<!--
<P><FONT SIZE=-1> <A NAME="footnote1"></A> <SUP><A
HREF="#cite1">1</A></SUP>HTTP will automatically redirect to HTTPS when
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not yet have HTTPS installed, causing HTTPS links to fail. While we
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is safest to use HTTP to publish a link to a us.metamath.org page. This
means that "https://" may have to be manually changed to "http://" after
pasting from a browser's "Copy Link" function.</FONT>
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<HR NOSHADE SIZE=1>
<!--
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mirror site link into the Address bar. <I>To fix this problem</I>
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this. If you do, let me know. Fortunately, this is the only web page
on this site with this problem.)</FONT>
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<HR NOSHADE SIZE=1>
<P> <CENTER><SPAN CLASS=sm>Some comments about this site found on the
web (see HTML source for references)</SPAN></CENTER> <DIV> <DL>
<!--
<DT>Profound.
<DD> - Ryan Scott (The Assayer) (<A TARGET="_top"
HREF="http://www.theassayer.org/cgi-bin/asbook.cgi?book=794">review</A>)
<!!- http://www.theassayer.org/cgi-bin/asuser.cgi?login=Ryanov 18-Jan-04 -->
<!--
<DT>Metamath. Brain full.
<DD> - Dan Sanderson (BrainLog Archives)
<!!- http://www.dansanderson.com/blog/archives.php3?year=2001&month=05 23-Nov-02 -->
<DT><A TARGET="_top"
HREF="http://us.metamath.org/mpeuni/mmset.html#trivia">2+2=4</A>
- ever wondered why?
<DD> - Maria Schwartz
<!-- http://www.reddusk.de/favlinx.htm 11/25/02 -->
<P><DT>A modern <I class=dti>Principia Mathematica</I> on the web.
<DD> - Josh Purinton
<!-- http://www.kuro5hin.org/story/2001/1/5/102820/2289 11/25/02 -->
<P><DT>Metamath.org - Giving math its proper treatment.
<DD> - Tempus Dictum, Inc.
<!-- http://www.tempusdictum.com/tdlinks.html 10/3/04 -->
<!--
<P><DT>[GIF Images for Math Symbols] ...not great, but not too bad...
<DD> - Prof. William J. Rapaport (U. at Buffalo, SUNY)
<!!- The State University of New York -->
<!-- http://www.cse.buffalo.edu/~rapaport/663/F03/logic.html 12-Sep-03 -->
<!--
<P><DT>What you get when you run mathematics through a disassembler.
<DD> - Michael Schaeffer
<!!- http://www.mschaef.com/links.html 23-Nov-02 -->
<!--
<P><DT>GIF Images for Math Symbols - Works in ALL Browsers I have tried!
<DD> - Ian G. Clark, Ph.D. (University of Newcastle-upon-Tyne)
<!!- http://www.users.totalise.co.uk/~ian.g.clark/comp.html 23-Nov-02 -->
<!--
<P><DT>This site is not for the fainthearted, even among professional logicians.
<DD> - AK Dewdney
-->
<!-- http://www.math.uwaterloo.ca/navigation/ideas/reviews/metamath.shtml 22-Feb-03 -->
<!--
(author, <SPAN CLASS=sm>The Turing Omnibus</SPAN>) (<A TARGET="_top"
HREF="http://www.math.uwaterloo.ca/navigation/ideas/reviews/metamath.shtml"
>review</A>)
-->
<!--
<P><DT>Metamath -
nice but too basic (and I don't like the way they ignore
alpha conversion).
<DD> - Freek Wiedijk (Mizar Forum)
-->
<!-- http://mizar.uwb.edu.pl/forum/archive/0401/msg00023.html 28-Nov-04 -->
<P><DT> Metamath Music Page - Proofs you can listen to in MIDI format. Fun
<I>and</I> edjemacational!
<DD> - Haddon Kime (composer,
<A TARGET="_top"
HREF="http://web.archive.org/web/20110725123937/http://www.haddongivenskime.com/theater/proof/">music
score</A> for the play <SPAN CLASS=sm><A TARGET="_top"
HREF="https://en.wikipedia.org/wiki/Proof_(play)">Proof</A></SPAN>) <!--
http://www.haddongivenskime.com/theater/proof/ 18-Aug-2006 --> <!--
http://haddonkime.com/theater_html/proof.html 12-Dec-04 -->
<!--
<P><DT>Now a Mizar to Metamath compiler, that would be a very
interesting and very useless thing :-)
<DD> - Freek Wiedijk (Mizar Forum)
<!!- http://mizar.uwb.edu.pl/forum/archive/0311/msg00022.html 13-Dec-03 -->
<!--
<P><DT>Metamath - Exploring proofs of mathematics, quantum logic, and Hilbert
Space for fun and, er, whatever.
<DD> - Dethe Elza
<!!- http://delza.alliances.org/hotlist/ 14-Nov-03 -->
<!--
<P><DT>I've burned a ton of wee morning hours lately poking around in this.
Even listened to a bunch of the proofs-as-music... Cool shit.
<DD> - Jeff Bone (FoRK Archive)
<!!- http://www.xent.com/FoRK-archive/2001.05/0132.html 23-Nov-02 -->
<!-- http://www.xent.com/pipermail/fork/2003-July/023218.html 12-Oct-02 -->
<!--
<P><DT>Say you're a meta-mathematics geek and you really like playing with
proofs. Did you know you can make music with proofs? Nerdalicious!
<DD> - Cody Clark (crossimpact.net)
<!!-
http://crossimpact.net/archives/2002/06/24/nothin-rocks-like-banach-tarski/
4-Dec-04 -->
<P><DT>Seriously, folks, this site is one of the coolest things I've seen in a
long time. If you enjoy formal systems, this site will make you very
happy.
<DD> - John Bethencourt, <A TARGET="_top"
HREF="http://web.archive.org/web/20080218050000/http://www.upl.cs.wisc.edu/~bethenco/metamath.html">"Principia
Mathematica Revisited"</A>
<!-- http://www.upl.cs.wisc.edu/~bethenco/metamath.html 13-Dec-03 -->
<!--
Principia Mathematica Revisited
"What you get when you run mathematics through a disassembler." -
Michael Schaeffer
I recently ran across a really cool website: metamath.org. Here's the
site's description of itself:
Metamath is a tiny language that can express theorems in abstract
mathematics, accompanied by proofs that can be verified by a computer
program. This site has a collection of web pages generated from those
proofs and lets you see mathematics developed formally from first
principles with absolute rigor. Hopefully it will amuse you, amaze you,
and possibly enlighten you in its own special way.
The `symbol-pushing' part of mathematics has always appealed to me.
I've often fantasized about deriving definitions from an absolutely
minimal core and then creating an enormous database of theorems, all of
which can be reduced to a sequence of typographic manipulations of
axioms. That's exactly what this site does. The only fundamental
symbols in the language of Metamath are the following:
* (arrow): implies
* (sideways backwards L): not
* (upside down A): for all
* (equals sign): equals
* (stylized epsilon): is an element of
* and (left and right parentheses)
All other symbols are simply shorthand notation for these. At the site,
you can explore a database of thousands of theorems that result from
various sets of axioms: propositional calculus, predicate calculus, and
Zermelo-Fraenkel set theory with the axiom of choice.
What really makes Norman Megill (the creator) such a great guy is the
fact that you can download the GPL'd source for the software used to
build and verify the proofs in the Metamath language. Also available
are a complete tarball of the entire site and a GFDL'd book about
meta-mathematics and the Metamath software (with TeX source).
Seriously, folks, this site is one of the coolest things I've seen in a
long time. If you enjoy formal systems, this site will make you very
happy. On a random note, the website also has a page about converting
the proofs to musical compositions.
posted on 05 Dec, 2003 | rss | permanent link to this entry
-->
<!--
<P><DT>Most philosophers agree that contemplation of Reality is the highest
form of happiness. So, if you want happiness, play Metamath Solitaire
all by yourself.
<DD> - Kannan Nambiar (Former Professor and Dean, School of Computer Science,
Jawaharlal Nehru University)
(<A TARGET="_top"
HREF="http://www.merlot.org/search/UserCommentList.po?aOid=1000000000000001863"
>review</A>)
<!!- http://www.merlot.org/search/UserCommentList.po?aOid=1000000000000001863 18-Jan-04 -->
<!--
<P><DT>Metamath has an archive of mathematical proofs, cross-references, for
you to explore. And a very odd section dedicated to translating those
proofs into music.
<DD> - Matt Webb (interconnected.org)
<!!- http://interconnected.org/home/2001_04_22_archive.shtml 23-Nov-02 -->
<!--
<P><DT>If set theory (or quantum logic) is more your style, Metamath should be
sufficient to keep you for a while, although it can get hard to follow
due to lack of prose. (Gotta love the <A TARGET="_top"
HREF="http://us.metamath.org/mpeuni/equid.html">proof that
x=x</A>.)
<DD> - Casey Schneider-Mizell (MetaFilter)
<!!- http://www.metafilter.com/comments.mefi/21286 23-Nov-02 -->
<!--
<P><DT>I would consider the Metamath format slightly low-level, with adhoc
handling of bound variable scopes; lambda calculus provides a more
abstract and clean notion of variable binding and substitution.
<DD> - Makarius Wenzel
<!!-
https://lists.cam.ac.uk/pipermail/cl-isabelle-users/2006-January/msg00022.html
14-Jan-2006 -->
<!--
<P><DT>Wff'n'Proof Rides Again - Ever have that urge to go back and regain the
old Wff'n'Proof star? If you grew up with this game you're probably right
there with me. Well it may not be the game but the Metamath site sure
does take it to new limits.
<DD> - Tom Higgins (WSMF Web Thing)
<!!- http://wsmf.blogspot.com/2001_04_01_wsmf_archive.html 23-Nov-02 -->
<!--
<P><DT>Math is the "universal language" and Metamath is a site dedicated to
helping non-mathemeticians learn mathematical proofs. It is not
non-complicated (your Euclidean high school geometry class it is not) but it
is also well explained and contains the oft-missing inner details.
<DD> - "atrox" (screaming-penguin.com)
<!!- http://screaming-penguin.com/main.php?storyid=1666&PHPSESSID=3Dedbb=46 23-Nov-02 -->
<!--
<P><DT>Care for some mathematical proofs? How about 3000 interconnected proofs
in logic and set theory, building from simple axioms. They're all here,
hyperlinked up the wazoo. Also available: proof-generation programs,
the entire database behind the site, and curiously interesting music
generated from the structure of selected proofs.
<DD> - Mike Gunderloy (Mike's Weblog)
<!!- http://www.larkfarm.com/weblog_item.asp?LogID=1155 23-Nov-02 -->
<!--
<P><DT>Metamath - this is something I always wanted to do myself - a relational
database of mathematical knowledge together with a proof assistant that
doesn't let you make any mistakes in the proof.
<DD> - Michael Milirud
-->
<!-- http://micweb.net/education/Mathematics/ -->
<!--
<P><DT>The Metamath system maybe should not be counted as an "industrial
strength" system: it only has one user. However, the system is
beautifully executed and differs in many respects from the other
systems. For one thing it is very fast: it can check its full
(non-trivial) library in only a few seconds. Also it really makes the
logical structure of the mathematics completely transparent.
<DD> - Freek Wiedijk, "Comparing mathematical provers"
<!!- http://www.cs.kun.nl/~freek/notes/diffs.ps.gz 23-Nov-02 -->
<P><DT>I feel I understand Metamath reasonably well now. It has some issues,
but its overwhelming strength is that it's simple. For example, I
believe that a fully functional proof verifier could be done in about
<A TARGET="_top" HREF="http://us.metamath.org/index.html#langverify">300
lines of Python</A>. I wonder how many lines of Python a corresponding
verifier for HOL would be; I'd guess around an order of magnitude
larger. That kind of difference has profound implications. <!-- Norm Megill
is certainly to be commended for the "simplicity engineering" he's put
into Metamath. -->
<DD> - Raph Levien (advogato.org)
<!-- http://www.advogato.org/person/raph/diary.html?start=267 23-Nov-02 -->
<!--
<DT>[See faq#3 on the Metamath
Home Page for the Python program. - <I>nm</I>]<DD>
-->
<P><DT>...let's look at why mathematical
proofs are so difficult to understand for most people...any
realistic mathematical proof will leave out a great many
steps, which are considered to be the "required background knowledge"
for anyone who wants to understand the proof. By the way, a very
interesting project called the Metamath project is trying to create an
online archive of mathematical proofs which are specified all the way to
the bottom, starting from set theory. But this is a very rare exception
to the general rule.
<DD> - Mike Vanier, "Why I love computer science"
<!-- http://www.cs.caltech.edu/~mvanier/hacking/rants/computer_science.html 23-Nov-02 -->
</DL>
</DIV>
<!--
<HR NOSHADE SIZE=1>
<CENTER><IMG SRC="debyrinth.jpg" WIDTH=640 HEIGHT=465 ALT="Debyrinth">
<BR><I>...deeper and deeper into the labyrinth until axioms will ultimately be found at the bottom...</I></CENTER>
--><P>
<FONT SIZE=-2 FACE=sans-serif><A
HREF="http://us.metamath.org/symbols/searchindex.html"
STYLE="color: white">.</A></FONT> <!-- temporary -->
<HR NOSHADE SIZE=1>
<A TARGET="_top"
HREF="http://validator.w3.org/check/referer"><IMG BORDER="0"
SRC="valid-html401.png" ALT="Valid HTML 4.01!" HEIGHT="31"
WIDTH="88" ALIGN=right></A>
<CENTER><I><FONT SIZE=-1>Updated on
2-Nov-2021 by N. Megill.</FONT></I></CENTER>
<CENTER><I><FONT SIZE=-1>Updated on
30-Jan-2017 by David A. Wheeler.</FONT></I></CENTER>
<CENTER><FONT FACE="ARIAL" SIZE=-2>Your
comments are welcome:
Norman Megill <A HREF="http://us2.metamath.org:88/email.html"><IMG BORDER=0
SRC="_nmemail.gif" ALIGN=TOP
ALT="nm at alum dot mit dot edu"
TITLE="nm at alum dot mit dot edu"
WIDTH=90 HEIGHT=13></A></FONT></CENTER>
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