05/28/2021
Due to the COVID-19 crisis, the political and economic structures of the world have been abruptly thrust into a massive transformation. Ironically, what had been a burden to every nation—COVID-19—has, under the guise of disease control, become a problem-solver for issues such as climate crisis, war, famine, and ecological collapse. In particular, because of the peculiar nature of this illness—united we fall, divided we survive—the role of the military and the concept of the “enemy” have shifted from external to internal. Amid the spectacle of disorder that had been emerging in developing countries and spreading worldwide, a new order without war is taking shape. Observing this, one cannot help but feel that COVID-19, standing before the future vision of sustainability, has ironically averted a world war. Perhaps that is why, in South Korea, despite the inconvenience of having to wear masks at all times, people have, in a curious display of collective patience, taken a step back and endured.
However, the COVID-19 pandemic has ushered in an era in which applied mathematics is rapidly gaining prominence—whether in mathematical epidemiological modeling, climate modeling, mathematical security methodologies in information warfare, or artificial intelligence built upon mathematical models of complex systems—alongside the growth of programming. In this context, physics, together with applied mathematics—particularly starting from the domain of mathematical physics—needs to reestablish the intellectual foundations of theoretical physics. This includes promoting deep interactions between physics and mathematics in such areas as string theory and Calabi–Yau space research; quantum field theory and algebraic geometry; and general relativity and differential geometry. Such collaboration would help narrow the wide gap between mathematics and physics, as illustrated in [Figure 1], and foster active communication.
At a time when intuitionism is becoming outdated, I wish to call for its replacement with theoretical pragmatism—a framework that could serve as a platform for accelerating the accumulation of intellectual heritage in mathematics and physics in this era of low growth. This could mark the beginning of The Second Hilbert’s Program, and I sincerely hope that, if such a program unfolds successfully, the talented individuals in mathematics and physics will be able to realize their own aspirations.
[Figure 1] Field Arranged By Purity (Source: Purity, https://xkcd.com/435/)
[Reference List]
- “The Great Power of Abstract Thinking” – Jeong-il Park, Gimmyoung Publishers
2. “Philosophy of Mathematics: Understanding and Critique of Logicism, Formalism, and Intuitionism” – Stephan Körner (translated by Hyun-bae Choi), Nanam Publishing
3. Purity, https://xkcd.com/435/
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