Theorem of the Day  

Welcome to a gallery whose exhibits are the crowning achievements of mathematics: her theorems. Each day offers a different theorem (or lemma, law, formula or identity), each one worthy of adorning the walls of a mathematical Alte Pinakothek, Guggenheim, Louvre, Tate, Uffizi or Zach Feuer. Each theorem has been presented so as to be appreciated by as wide an audience as possible. If you can have a go at a Sudoku puzzle (certainly a mathematical creature even though not an arithmetic one) then you can have a go at today's theorem. By 'have a go' I mean admire it; turn it over in your mind; try to follow the example, if one is given; if you are studying it online, follow the web link, which will provide a pictorial interpretation, a proof or even a clever animation. Click on the 'further reading' link. It will usually take you to the amazon.co.uk page for the book. O! naked commercialism — if you then buy the book I get a referral fee! I have the gravest doubts upon this subject, but I intend to crush them; it seems the neatest way to provide full bibliographic details. Each theorem is as selfcontained as possible. Whilst online, the button will take you to a Glossary page where there is a brief explanation of some parts of mathematical language; the arrow will take you to a related but usually less sophisticated theorem which may shed light on today's; the arrow may point to a theorem which leads on from today's or takes you deeper into its subject. For some theorems are deeper than others; some use more technical language than others; some are just harder to understand than others. Some days are harder than others. I hope even the most difficult days offer something of wonder. 
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Theorem of the Day is maintained by Robin Whitty. Comments or suggestions are welcomed by me.
All text and images and associated .pdf files © Robin Whitty, 2005–2009, except where otherwise acknowledged. See FAQ for more.