Aging & Wisdom Quote by Henri Poincare

Poincare is doing something sly here: flattering the past while warning his own era against mathematical vanity. The line lands because it’s half nostalgia, half jab. “In the old days” isn’t just a date stamp; it’s a moral category. It conjures an imagined time when invention had a tether to necessity, when new functions weren’t minted like fashionable nouns but forged to solve stubborn problems in mechanics, astronomy, heat, fluids. By contrast, “invented a new function” hints at a growing culture of abstraction for abstraction’s sake, a late-19th-century boom in formalism, special functions, and symbol-heavy generalization that could start to feel like a self-contained industry.

The subtext isn’t anti-theory. Poincare himself helped create entire landscapes of “pure” mathematics. The sting is directed at motivation and accountability: are you extending the world’s descriptive power, or just extending a notation system? “Something useful in mind” is also a claim about how ideas mature: usefulness may be delayed, but it’s the pressure of real questions that gives a concept shape. Without that pressure, novelty risks becoming decorative.

Context matters: Poincare lived amid a shifting map of mathematics, where rigor was tightening, set theory was unsettling foundations, and physics was about to be rewritten. His quip defends a particular kind of creativity - the kind that starts from contact with reality, then earns its abstraction. It’s a reminder that “new” isn’t a synonym for “necessary,” and that the best inventions, even in math, feel like answers rather than accessories.