A math mystery that has baffled geniuses since 1932 has finally been solved.
April 17, 2026
Original Paper
Mazur's Separable Quotient Problem for Nonseparable Bourgain-Pisier L∞-Spaces
arXiv · 2604.11832
The Takeaway
Back in the 1930s, the legendary mathematician Stefan Mazur asked a fundamental question about the structure of infinite-dimensional spaces that has remained unanswered for nearly a century. This paper finally provides an affirmative answer for a specific, notoriously difficult class of these spaces known as nonseparable Bourgain-Pisier spaces. While this sounds abstract, it deals with the very scaffolding of how we map out infinite possibilities in physics and engineering. For 92 years, we didn't know if these complex spaces could always be simplified into a more manageable 'quotient' form. This proof settles the debate, closing a major chapter in the history of functional analysis. It’s a powerful reminder that even the most 'unsolvable' problems of the past are eventually within our reach.
From the abstract
Mazur's separable quotient problem, open since 1932, asks whether every infinite-dimensional Banach space admits an infinite-dimensional separable quotient. We prove that any $\mathscr{L}_\infty$-space $Y$ containing a subspace $X$ such that $Y/X$ is infinite-dimensional with the Schur property admits $c_0$ as a quotient. The natural class to which this criterion applies is the nonseparable $\mathscr{L}_\infty$-spaces constructed via the Lopez-Abad extension method, the nonseparable analogue of