The Role of Mathematics in Physical Sciences — Interdisciplinary and Philosophical Aspects -- Mathematics and Physics: Reflecting on the Historical Role of Mathematics -- Oliver Heaviside’s “Dinner” -- Quantum Physics and Mathematical Debates Concerning the Problem of the Ontological Priority between Continuous Quantity and Discrete Quantity -- John von Neumann on Mathematical and Axiomatic Physics -- Classical Indian Mathematical Thought in the Context of the Theories of Matter and Mind -- Mathematics and Physics: Reflecting on Their Interaction -- The Role of Mathematics in Physical Sciences and Dirac’s Methodological Revolution -- Algorithmic Representation of Astrophysical Structures -- The Flexibility of Mathematics -- The Laws of Nature and the Effectiveness of Mathematics -- Some Mathematical Aspects of Modern Science and Their Relevant Physical Implications -- Theoretical Explanations in Mathematical Physics -- Mathematics, Physics and Music -- Theoretical Mathematics -- Final Remarks -- Mathematics and Physics -- Values and Meaning in the Quantum Universe.Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.