Recently a preprint was posted on the arXiv ( arXiv:1904.12720 ) claiming to have constructed the first examples of compact orientable hyperbolic non-spin manifolds (in every dimension at least 4). I was a bit surprised by this, since I thought that such examples should be already known. Apparently not … One reason why constructing such … Continue reading "Compact hyperbolic non-spin manifolds"

The classical algorithm, that everyone knows from elementary school, for multiplying two n-digit integers runs in \(O(n^2)\)-time. Recently, there was a preprint posted on HAL (link) in which the authors provide an algorithm which runs in \(O(n\log(n))\)-time. A nice article about this discovery may be found at the QuantaMagazine: link. Further, it was also recently proven in another preprint … Continue reading "Multiplying integers"