"Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics"
About this Quote
The key word is technique. Hardy isn’t praising pure math as a museum of elegant theorems; he’s selling it as the gym where minds learn the habits that later look like innovation: abstraction, generalization, proof, the ability to move symbols without handrails. Applied problems are often narrow and time-bound, tied to today’s technologies and constraints. Pure mathematics, precisely because it’s freed from a particular job-to-be-done, trains transferable power. It teaches you to build tools, not just use them.
There’s also a lightly barbed institutional subtext: universities and funders love “impact,” but impact is downstream. Hardy is staking out intellectual autonomy as a long-term public good. Historically, he’s writing in an era when mathematics was professionalizing and modernizing, and when war and industry were demanding calculable returns. His claim resists that pressure while still playing the same game: usefulness. He just insists the real utility is patience, depth, and a discipline of thinking that can’t be rushed into a deliverable.
Quote Details
| Topic | Teaching |
|---|---|
| Source | G. H. Hardy, A Mathematician's Apology (1940) — passage on the usefulness of pure mathematics (commonly cited from Hardy's essay on mathematical utility). |
| Cite |
Citation Formats
APA Style (7th ed.)
Hardy, G. H. (2026, January 16). Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. FixQuotes. https://fixquotes.com/quotes/pure-mathematics-is-on-the-whole-distinctly-more-104789/
Chicago Style
Hardy, G. H. "Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics." FixQuotes. January 16, 2026. https://fixquotes.com/quotes/pure-mathematics-is-on-the-whole-distinctly-more-104789/.
MLA Style (9th ed.)
"Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics." FixQuotes, 16 Jan. 2026, https://fixquotes.com/quotes/pure-mathematics-is-on-the-whole-distinctly-more-104789/. Accessed 12 Feb. 2026.





