Education and the search for truth

Good morning, colleagues and students.I have been teaching Math and History of Education for several years. I would like to present a topic that is fundamental in the training and development of students in today's world.

Can mathematical beauty ruin us?

Since the publication of Principles of Infinitesimal Calculus, in 1946, René Guénon opened the doors to a necessary debate about the real purpose of mathematics and its foundations, which, in fact, has only been growing. In the book Lost in Math: How Beauty Leads Physics Astray, Sabine Hossenfelder raises a series of questions about the possible mistakes made your colleagues in the physics community.

She argues that modern physics theories have no empirical basis and, in some ways, only continue to be discussed because they sound good mathematically. Hossenfelder notes that the number of scientists who determine whether a theory is true or not simply by its apparent aesthetic beauty is increasing. According to she, mathematics can never be proven as a true description of nature, because in the end mathematics only hides probable truths about mathematical structures. The claim that these structures correspond to physical reality is a separate claim that must always be tested and confirmed by experience.

In contrast, Cornell University's 1979 Nobel Prize in Physics, Steven Weinberg, claims that our sense of beauty has changed. And... The beauty we seek now, not in art, not in home decoration – or in horse breeding – but the beauty we seek in physical theories is a beauty of rigidity. We would like theories that, as far as possible, could not be varied without leading to impossibilities, such as mathematical inconsistencies. Hossenfelder ended up joining a group of scholars very concerned about what they call the "orthodox" direction that has been taking place in the field of mathematical physics.

Lee Smolin states his concern in the 2006 book The Trouble With Physics as follows: "We physicists need to deal with the crisis we face. A scientific theory (string theory, multiverse) that makes no predictions and therefore is not subject to experiment can never fail, but such a theory can never succeed as long as science represents knowledge gained from arguments supported by evidence. There needs to be an honest assessment of the wisdom of maintaining a failed research program after decades of finding a basis in experimental results or a precise mathematical formulation. String theorists must face the possibility that they have been shown to be wrong and others have been shown to be correct."

Starting from the Quranic concepts of Al-Haqq (الْحَق), which means The Truth and Al-Adl (ٱلْعَدْلُ), The Justice, I believe that Mathematics taken as a tool or practical device for a certain science is not the most appropriate path, as reflected for years, it has seemed more correct to define Mathematics as: the ability to socially express forms, quantities and patterns in meditation on the world. However, something in this discussion seems to have escaped the hands of scholars, whether from the aesthetic or methodical group, who, due to their own rigidity, end up losing balance and ontological humility. The search for truth must be the key point of any investigation; even if from observer A's point of view it looks like X and from observer B it looks like Y. True beauty is found, in truth, and there is no greater honor than serving it.

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