Mathematical physicists and cosmologists discuss the truth and beauty of mathematics, exploring topics such as the rigor of mathematical proofs, the cultural relativity of mathematics, the interplay of truth and beauty in mathematics, and the role of beauty in physics and as a clue to scientific validity.
Mathematics can be true even if not all true facts in mathematics are provable.
Beauty in mathematics is subjective and can vary depending on individual perspectives and preferences.
Deep dives
The Nature of Truth in Mathematics
Mathematics is considered true because it provides a rigorous path to construct facts and theorems through a logical sequence of steps. However, mathematicians also acknowledge that not all true facts in mathematics are provable. The assumptions of mathematics are crucial, as history has shown that wrong assumptions have been taken as self-evident. Different mathematical universes can be built based on different starting points, leading to questions about the right mathematical universe and the potential bias of physicists who believe in a preferred mathematical universe.
Beauty and Simplicity in Mathematics
Mathematics claims two transcendent attributes: truth and beauty. Beauty in mathematics is often associated with simplicity and elegance. Certain equations and mathematical structures, such as the sphere or the Mandelbrot fractal, are admired for their perfection and the ability to capture complexity with simplicity. However, beauty is subjective and can vary depending on individual perspectives and preferences.
The Debate on Beauty and Truth in Physics
In physics, the idea that beauty is a guide to truth is debated. Some physicists argue that seeking simple and elegant theories is crucial for understanding the laws of nature, while others believe that this approach can be misleading and hinder scientific progress. The belief in the deep association between the structure of the physical world and idealized mathematics can lead to cherry-picking examples that support preconceived notions of beauty. It is important to maintain a scientific methodology and follow the evidence rather than relying solely on aesthetic arguments.
Does mathematics have two transcendent attributes: truth and beauty? What makes math true? What makes math beautiful? Are there different kinds of mathematical existence? How can math combine idealized perfection and explanatory simplicity?
Featuring interviews with Robbert Dijkgraaf, Edward Witten, Max Tegmark, Sabine Hossenfelder, and Jim Holt.
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