The basic principle behind Sistine is simple. Surfaces viewed from an angle tend to look shiny, and you can tell if a finger is touching the surface by checking if it’s touching its own reflection.

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

Abstract: This paper is about Jacobi’s triple product identity and Euler’s pentagonal number theorem. To be specific, it gives the proofs of Jacobi’s triple product identity via Gaussian polynomials ...

Of all the endless questions children and mathematicians have asked about infinity, one of the biggest has to do with its size. Whether it’s on the playground or at bedtime, children encounter the ...

Simple mathematical concepts such as counting appear to be firmly anchored in the natural process of thinking. Studies have shown that even very young children and animals possess such skills to a ...

In the early 1980s, it was discovered that alternating sign matrices (ASMs), which are also commonly encountered in statistical mechanics, are counted by the same numbers as two classes of plane ...

1 Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Kuantan, Malaysia. 2 Department of Computer Science, Faculty of ICT, ...

Last time, I described the Legendre-Fenchel transform. For a real vector space V V, the transform gives a bijection between the convex functions on V V and the convex functions on its dual V # V^{#}.