"To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be"
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Euler is doing something quietly subversive here: puncturing the metaphysical aura around infinitesimals by treating them as bookkeeping, not ghostly substances. In the 18th century, calculus still carried a faint smell of heresy. Newton and Leibniz had built a spectacular engine, but its parts included these suspicious "infinitely small" quantities that seemed too convenient to be real. Critics (Berkeley famously) mocked infinitesimals as logical sleight of hand. Euler, the era's most prolific mathematical pragmatist, answers with a shrug that’s also a strategy: the infinitesimal is "actually zero."
That line reads like simplification, but it’s really a declaration of method. Euler is telling readers to stop asking what an infinitesimal is in the metaphysical sense and start asking what it does in calculation. The subtext is: the power of calculus doesn’t depend on smuggling in mystical entities; it depends on a controlled procedure where terms that vanish in the limit can be treated as zero at the decisive moment. He’s normalizing a practice that, in his hands, produced correct answers with astonishing reliability, even when the foundations were still shaky by modern standards.
"Hence there are not so many mysteries" is a cultural move as much as a mathematical one. Euler positions the working mathematician against the armchair skeptic: less awe, fewer anxieties, more results. It’s a confidence statement from a period when mathematics was racing ahead of its own philosophical explanations, and Euler is choosing momentum over mysticism.
That line reads like simplification, but it’s really a declaration of method. Euler is telling readers to stop asking what an infinitesimal is in the metaphysical sense and start asking what it does in calculation. The subtext is: the power of calculus doesn’t depend on smuggling in mystical entities; it depends on a controlled procedure where terms that vanish in the limit can be treated as zero at the decisive moment. He’s normalizing a practice that, in his hands, produced correct answers with astonishing reliability, even when the foundations were still shaky by modern standards.
"Hence there are not so many mysteries" is a cultural move as much as a mathematical one. Euler positions the working mathematician against the armchair skeptic: less awe, fewer anxieties, more results. It’s a confidence statement from a period when mathematics was racing ahead of its own philosophical explanations, and Euler is choosing momentum over mysticism.
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| Topic | Reason & Logic |
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