A SERIOUS PROBLEM IN EDUCATION: THE DUALITY OF THE "INDEFINITE INTEGRAL"

Summary. A Hidden Crisis in Education: Are We Teaching Foolishness? Serhii G. Kokhan. System analyst, psychologist, educator, publicist, researcher. Olexander S. Kokhan. Linguist.Ukraine. Kyiv.Warning! You can understand the gist of this article even without any understanding of mathematics, just skip the mathematical constructions. Discussions with gpt chat in this case you can just read the last 25%. Imagine a world where the very foundations of science, taught in prestigious universities for over two centuries, are built on fundamental errors. This compelling article exposes a shocking educational tragedy, particularly in the realm of mathematics, that has silently crippled generations of bright minds and severely impacted national development. At its core lies the unassuming "indefinite integral"—a concept critical for engineers and scientists, yet often taught with a "duality in definitions" so absurd it renders 99% of its practical applications invalid. The authors, drawing on decades of personal struggle and research, reveal how this "unnoticed error collapses education," driving talented students away from STEM fields as they grapple with contradictory teachings. But the problem isn't just academic; it's deeply human. Discover why confronting this truth unleashes a "universal educational tragedy" that challenges the self-respect of accomplished professionals and forces educators to grapple with a lifetime of unknowingly perpetuating flawed knowledge. The article also unveils the unexpected role of artificial intelligence as a potential ally in this battle for intellectual honesty. This isn't merely a critique; it's an urgent "open appeal and call" to governments, educational bodies, and concerned citizens worldwide to correct these "terribly consequential errors" and liberate future generations from "absurd, foolish, meaningless torment" in learning. Will the long-standing "resistance to truth" finally yield to reason, or will the "crippling of minds and destinies" continue unnoticed? Dive into this article to uncover a hidden crisis that impacts us all and learn what it truly takes to mend the broken foundations of modern education. The article also includes examples of real dialogues with artificial intelligence, where the artificial intelligence first naively tries to relay generally accepted definitions. Then it tries to wriggle out of it several times with academic fog, and then finally admits that the definition is absolutely wrong. License: CC BY-NC.- Free use is permitted for non-commercial purposes with mention of the authors.- For commercial purposes, permission from Serhii G. Kokhan is required. Ukraine. Kyiv, 07.2025.