I am a research mathematician at a university in the United States. My training is in pure mathematics (geometry). However, for the past couple of months, I have been supervising some computer scie...| MathOverflow
The $X^{s,b}$ spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel's theorem and duality, these estimates reduce to estimating a weighted convolution integral in terms of the $L^2$ norms of the component functions. In this paper we systematically study weig...| arXiv.org
I analyse differences in style between traditional prose mathematics writing and computer-formalised mathematics writing, presenting five case studies. I note two aspects where good style seems to differ between the two: in their incorporation of computation and of abstraction. I argue that this reflects a different mathematical aesthetic for formalised mathematics.| arXiv.org
This post was inspired by some recent discussions with Bjoern Bringmann. Symbolic math software packages are highly developed for many mathematical tasks in areas such as algebra, calculus, and num…| What's new
