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Updated: Jun 16, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Geometry and physics
Michael Atiyah1, Robbert Dijkgraaf, Nigel Hitchin
1School of Mathematics, University of Edinburgh, , Edinburgh EH9 3JZ, UK.
Summary
Mathematics and quantum physics have seen fruitful interactions, leading to advancements in geometry and topology. This review highlights key trends and examples of these interdisciplinary connections.
Area of Science:
- Quantum physics
- Mathematics
- Theoretical physics
- Mathematical physics
Background:
- The intersection of mathematics and quantum physics has a rich history.
- Recent decades have seen a surge in fruitful collaborations and discoveries.
- Understanding these connections is crucial for advancing both fields.
Purpose of the Study:
- To review the significant interactions between mathematics and quantum physics over the past decades.
- To identify and discuss general trends in this interdisciplinary area.
- To highlight specific examples of successful mathematical applications in quantum physics.
Main Methods:
- Literature review of seminal works and recent publications.
- Analysis of interdisciplinary trends and conceptual bridges.
- Case studies focusing on specific mathematical areas and their quantum physics counterparts.
Main Results:
- Identification of key mathematical concepts driving quantum physics research.
- Examples include the counting of curves in algebraic geometry.
- Demonstration of the utility of knot invariants and four-dimensional topology in quantum field theory.
Conclusions:
- The synergy between mathematics and quantum physics continues to yield profound insights.
- Future research directions are likely to emerge from further integration of advanced mathematical tools.
- These interactions are fundamental to the progress of theoretical physics.
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