A Hyperwelcome


This is a (very limited) wiki on proofs. I've always been interested in proofs, since they seem both precise and vague, obvious and enigmatic at the same time.

I started out rewriting proofs I've read, including proofs of why the square root of 2 is irrational and why the number of primes is infinite. Another proof looks at the Fundamental Theorem of Arithmetic.

Standard condensed proofs are difficult to read, so I've expanded upon them using a kind of statement–challenge approach. Someone claims X and the demand rings out: “Why?” The chain of Whys continues for a while (but not forever!).

For my exposition of the Fundamental Theorem of Algebra I used a conclusion-first kind of explanation as I worked through some equations, but the general explanation used a more start-to-finish point-form structure on two levels: a quick overview and a somewhat more detailed one.

Latest proof is a rewrite of a proof I read about linearly independent automorphisms in Galois theory, and that old chestnut, the Pythagorean theorem (new rewrite uses a chain of Becauses).

I also tried out a proof calculator Jape a while ago.

Remember… I'm not an expert. I have no math degree. Take all this with a grain (or bucket) of salt. If this (sometimes sloppy) reordering of proof steps is helpful while you have a standard proof beside you, then I'm happy.

The Image

The pictures show two pages from a 19th-century edition of the first six books of Euclid's Elements. A copy of the book was digitized by the University of British Columbia's Digital Mathematics Archive. As the site notes,

An unusual and attractive edition of Euclid was published in 1847 in England, edited by an otherwise unknown mathematician named Oliver Byrne. It covers the first 6 books of Euclid, which range through most of elementary plane geometry and the theory of proportions. What distinguishes Byrne's edition is that he attempts to present Euclid's proofs in terms of pictures, using as little text - and in particular as few labels - as possible. What makes the book especially striking is his use of colour.

The theorem proved on the two pages is I.47, the Pythagorean Theorem.

New articles

Here's a list of the most recently created new pages:

Latest revisions

Here's a list of the latest revised pages:

Article list

You can look at a separate page with a system-generated list and various options, but the following list eliminates some of the more mundane system-related pages:

A Hyperwelcome nullsetnullset rev. 53 08 Feb 2010 18:53
Add A Page nullsetnullset rev. 0 23 Feb 2009 20:02
Articles nullsetnullset rev. 8 28 Feb 2009 06:37
Automated deduction nullsetnullset rev. 9 17 Jan 2009 04:38
Cauchy Integral Theorem nullsetnullset rev. 9 13 Sep 2007 21:31
Contact nullsetnullset rev. 3 23 Feb 2009 19:32
Craig Silverstein nullsetnullset rev. 4 23 Feb 2009 19:34
Drafts nullsetnullset rev. 30 02 Mar 2009 14:20
End Material nullsetnullset rev. 7 23 Feb 2009 19:37
Euclid nullsetnullset rev. 0 11 Jun 2008 16:57
Even square implies even number nullsetnullset rev. 4 27 Feb 2009 05:56
Fundamental Theorem Of Algebra nullsetnullset rev. 7 14 Feb 2010 18:42
Fundamental Theorem Of Arithmetic nullsetnullset rev. 3 09 Feb 2010 17:12
How To Edit Pages - Quickstart nullsetnullset rev. 0 01 Aug 2007 18:18
Inverse nullsetnullset rev. 1 23 Feb 2009 20:24
Jape nullsetnullset rev. 7 11 Mar 2009 21:22
Jape Notes nullsetnullset rev. 14 24 Feb 2009 20:38
LaTeX nullsetnullset rev. 8 26 Feb 2009 15:42
Linearly Independent Automorphisms nullsetnullset rev. 1 19 Nov 2012 10:01
Math Sites nullsetnullset rev. 7 23 Feb 2009 20:29
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Please note that I am not a mathematician and so the presentation of proofs that I make may be deeply flawed. I'm using this writing process to figure out what I'm reading. Please consult more authoritative sources as well.

Feel free to contact me by leaving a comment or sending me a private message.

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