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Today's Theorem on Monday 16 February, 2026
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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 Abattoirs, Baltic, Duniya, Guggenheim, Louvre, Mind's Eye, Staatliche Museen, Tate, Uffizi or Zach Feuer.
Each
theorem has been presented so as to be appreciated by as wide an audience
as possible. If the statement of the theorem appears obscure, pass on to the illustration and its accompanying explanation. If it still seems hard it is probably because it is hard. But no more than O'Keeffe's Blue and Green Music, say, is a 'hard' painting or Hepworth's Two Figures is a 'hard' sculpture. It is there for you to engage with on your own terms.
By 'engage' I mean: admire it, turn it over in your mind, try to follow the example,
if one is given; if you are studying it on-line, follow the web link,
which will provide a pictorial interpretation, a proof or perhaps a clever
animation.
Click on the 'further
reading' link. It will take you to the appropriate bibliography entry, often accompanied by links to insightful reviews of the recommended book. A link to the amazon.co.uk page for the book provides full bibliographical details and often, a preview of its contents.
Each theorem is
as self-contained as possible; when viewing a theorem on-line, the  button, top-right, links to supplementary notes. The  links to a Glossary page where there is a brief explanation
of some parts of mathematical language; At the bottom of the page, the  button will take you to the theorem's entry in the complete theorem list, where you may find additional versions: printable poster, additional languages, non-colour-sensitive, etc. The  arrow will take you to a related but usually less sophisticated theorem
which may shed light on today's; and 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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