Discovered or invented? · Scope
Why does mathematics developed for its own sake so often turn out to be useful?
In 1960 the physicist Eugene Wigner wrote about the 'unreasonable effectiveness' of mathematics in the natural sciences. Ideas pursued for curiosity have repeatedly become the language of later science and technology. This question asks whether that is luck, design, selection or something deeper.
Claims
- Mathematics studies patterns and structure in general, so it is not surprising that the patterns it describes reappear in nature and technology.
- Usefulness is evidence that mathematics captures something true about the world rather than being a human game.
Counterclaims
- We remember the pure mathematics that became useful and forget the large amount that did not, so the effect may be exaggerated by selection.
- Scientists often choose the mathematics that fits, adjusting models until they work, so the effectiveness is partly built in by the people applying it.
Real-life situations from mathematics
Number theory and online security
In A Mathematician's Apology (1940) G. H. Hardy took pride in number theory having no practical use. In 1977 Rivest, Shamir and Adleman published RSA encryption, based on prime numbers, which now helps protect online payments.
Curved geometry and gravity
Bernhard Riemann developed the geometry of curved spaces in 1854 as pure mathematics. About sixty years later Einstein used it as the language of general relativity (1915), his theory of gravity.
Check dates and figures in a reliable source before you use them, and cite that source.
Use this in your TOK work
Essay. Fits titles about the value of knowledge, or about the relationship between areas of knowledge. Compare with the natural sciences.
Exhibition. A padlock icon from a web browser, with a note on RSA, makes an everyday object for a prompt about the value or usefulness of knowledge.
Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.
Themes and study heading
Knowledge and technology Scope
What mathematics is about, and where its edges lie.