Quantum mechanics: knocking at the gates of mathematical foundations

TL;DR

This paper explores the foundational aspects of quantum mechanics and their intriguing links to mathematical foundations, highlighting the clash with classical intuition and the need for new conceptual frameworks.

Contribution

It surveys key issues in quantum foundations and discusses novel connections with the mathematical underpinnings of quantum theory.

Findings

Quantum features challenge classical concepts

Connections between quantum foundations and mathematics are explored

Highlights the need for new conceptual frameworks in quantum theory

Abstract

The Weltanschauung emerging from quantum theory clashes profoundly with our classical concepts. Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our everyday intuition. In this article I survey some aspects of quantum foundations and discuss intriguing connections with the foundations of mathematics.