Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

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The Abhyankar-Sathaye Problem asks whether any biregular embedding $\varphi \colon {\Bbb C}^{k}\hookrightarrow {\Bbb C}^{n}$ can be rectified, that is, whether there exists an automorphism α ∈ Aut Cn ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...

When you buy through links on our articles, Future and its syndication partners may earn a commission. Mathematicians have solved a longstanding algebra problem, providing a general solution for ...