TL;DR
This paper reviews recent developments in noncommutative geometry, focusing on incorporating gravity into models of space-time and exploring its role as an ultraviolet regulator, supported by an extensive bibliography.
Contribution
It provides a comprehensive historical overview of noncommutative geometry, highlighting efforts to integrate gravity and regulate ultraviolet divergences in space-time models.
Findings
Noncommutative geometry offers promising approaches to quantum gravity.
Gravity can be incorporated into noncommutative models of space-time.
Noncommutative models may serve as ultraviolet regulators.
Abstract
A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An extensive bibliography has been added containing reference to recent review articles as well as to part of the original literature.
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