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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...


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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.


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It is called the Shimura-Taniyama-Weil (STW) conjecture, and it has baffled and defeated some of the greatest minds in maths over the last 40 years. The STW conjecture links two seemingly unrelated areas of mathematics: the theory of numbers and the theory of shapes or, as mathematicians prefer to call them, elliptic curves and modular forms. For decades, mathematicians have studied these subjects realising that there are deep connections...


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Benoit Mandelbrot, who discovered mathematical shapes known as fractals, has died of cancer at the age of 85. Mandelbrot, who had joint French and US nationality, developed fractals as a mathematical way of understanding the infinite complexity of nature.


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Researchers have developed a simple technique that adds evidence to the theory that the Universe is flat. Moreover, the method - developed by revisiting a 30-year-old idea - confirms that "dark energy" makes up nearly three-quarters of the Universe. The research, published in Nature, uses existing data and relies on fewer assumptions than current approaches.


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 dark matter universe philosophy geometry gravity cosmology


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