248-dimension maths puzzle solved^c 19. March 2007 What's attractive about studying E8 is that it's as complicated as symmetry can get. Mathematics can almost always offer another example that's harder than the one you're looking at now, but for Lie groups, E8 is the hardest one. ... Each of the 205,263,363,600 entries on the matrix is far more complicated than a straightforward number; some are complex equations.

Advanced geometry of Islamic art 23. February 2007

On teaching mathematics by V.I. Arnold Excellent about the need for re-unification of mathematics and geometry, and physics. ... Also: Jacobi noted, as mathematics' most fascinating property, that in it one and the same function controls both the presentations of a whole number as a sum of four squares and the real movement of a pendulum. These discoveries of connections between heterogeneous mathematical objects can be compared with the discovery of the connection between electricity and magnetism in physics or with the discovery of the similarity between the east coast of America and the west coast of Africa in geology. The emotional significance of such discoveries for teaching is difficult to overestimate. It is they who teach us to search and find such wonderful phenomena of harmony of the Universe.

Plus Magazine Plus magazine opens a window to the world of maths, with all its beauty and applications, by providing articles from the top mathematicians and science writers on topics as diverse as art, medicine, cosmology and sport.

Český objev zvyšuje bezpečnost elektronického podpisu 8. November 2006

Maths genius declines top prize 22. August 2006 Grigory Perelman, the Russian who seems to have solved one of the hardest problems in mathematics, has declined one of the discipline's top awards. ... The Poincare Conjecture says that a three-dimensional sphere is the only enclosed three-dimensional space with no holes.

Mother tongue may determine maths skills 27. June 2006

The On-Line Encyclopedia of Integer Sequences

Math That Makes You Go Wow A Multi-Disciplinary Exploration of Non-Orientable Surfaces

Chaos:
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Classification of Mathematical Sculpture

Great Math Programs

Wikipedia: Mersenne primeⁱ

Cryptography^e

Wikipedia - Mathematicsⁱ

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Historic maths problem 'cracked' 27. November 2003

Clay Mathematics Institute: 7 Millennium Problems
• Great maths puzzle 'solved' 7. May 2003 "The Poincare Conjecture says that a three-dimensional sphere is the only enclosed three-dimensional space with no holes. But the proof of the conjecture has eluded mathematicians." "If Perelman has solved Thurston's problem then experts say it would be possible to produce a catalogue of all possible three-dimensional shapes in the Universe, meaning that we could ultimately describe the actual shape of the cosmos itself."

Mathematicians crack big puzzle 19. November 1999

The secret of squares revealed 3. March 2000 We count in sets of ten. This seems natural to us because we have ten fingers. However the ancient Babylonians used different units, which is why we measure time in units of 60 minutes and clock-faces have 12 hours. We need not use sets of ten, any number would do. Mathematicians call this modular arithmetic. So we count in modulus ten. When perfect squares and modular arithmetic are combined strange and unexpected things happen. A question mathematicians have wanted to answer for hundreds of year is this: when is a number a perfect square when units are counted in a prime number modulus? (A prime is a special number that can only be divided by 1 and itself, e.g. 2, 3, 5, 7, 11 and so on.) It turns out that the relationship between a number and its square when the counting units are a prime is so surprising that mathematicians have been trying to decide what it means for hundreds of years.

Prime number breakthrough 4. April 2003 A curious observation is that primes occur in twins with a surprising regularity. For example: 11 and 13; 17 and 19; 29 and 31; 41 and 43; 59 and 61. Just as with single primes, the frequency of twin primes decreases as one gets to larger numbers. But do they completely fizzle out beyond some very large number? That is the big question. Around a trillion, for instance, only about one in every 28 numbers is a prime.

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