Abel Prize 2009 as a necessitation to discussion on geometry, or physicist versus geometers

TL;DR

This paper discusses the limitations of current geometric knowledge, emphasizing its impact on physics and advocating for acknowledgment of nonaxomatizable geometries to improve scientific understanding.

Contribution

It highlights the neglect of nonaxomatizable geometries among geometers and argues for their importance in advancing the understanding of geometry in physics.

Findings

Contemporary geometers overlook nonaxomatizable geometries.

Poor geometric knowledge influences physicists to adopt quantum paradigms.

Recognizing nonaxomatizable geometries could enhance physical theories.

Abstract

Contemporary geometers do not acknowledge nonaxomatizable geometries. This fact means that our knowledge of geometry is poor. A perfect knowledge of geometry is important for "consumers of geometry" (physicists dealing with geometry of microcosm), because poor knowledge of geometry forces physicists to refuse from the orthodox geometrical paradigm and to use the quantum paradigm, which is a simple fitting, compensating our imperfect knowledge of geometry.