Reducing redundant information to find simplifying patterns in data sets and complex networks is a scientific challenge in many knowledge fields. Moreover, detecting the dimensionality of the data is ...

Margaret Wertheim gave a talk for the Australian Mathematical Sciences Institute at their 2016 annual Summer School. We have built a world of largely straight lines – the houses we live in, the ...

Complex geometry investigates the properties and structures inherent in complex manifolds, while hyperbolicity imposes stringent restrictions on the behaviour of holomorphic maps. Together, these ...

Mathematicians often comment on the beauty of their chosen discipline. For the non-mathematicians among us, that can be hard to visualise. But in Prof Caroline Series’s field of hyperbolic geometry, ...

In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is rejected. The parallel postulate in Euclidean geometry states, for two ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don’t apply: angles of a triangle add up to less than 180 degrees and Euclid’s parallel postulate, ...

American Journal of Mathematics, Vol. 118, No. 3 (Jun., 1996), pp. 611-620 (10 pages) Let C be a very generic smooth curve of degree d in the complex projective plane. In this paper, we show that for ...

Atomic interactions in everyday solids and liquids are so complex that some of these materials’ properties continue to elude physicists’ understanding. Solving the problems mathematically is beyond ...

Coral reefs can be crocheted. The atmosphere can be knit. And a stop sign can be folded into a pair of pants. Welcome to the intersection of math and handicraft. Unexpectedly, handicraft in general, ...