Discovered or invented? · Perspectives
Is mathematics a language, and if so, what does it describe?
Galileo described the book of nature as written in mathematics. Mathematics has symbols, grammar and conventions, and people talk of 'reading' an equation. This question asks whether the comparison with language helps or misleads, and what mathematical sentences are about.
Claims
- Mathematics behaves like a language: it has a vocabulary of symbols and rules for combining them, and it lets people communicate precisely across national languages.
- Good notation, like good language, makes some thoughts easier to have, which is why changes in notation have changed what mathematicians could do.
Counterclaims
- Unlike a language, mathematics has results that are true or false regardless of how they are written; changing notation does not change the theorem.
- Mathematics also involves pictures, intuition and physical models that are not language-like at all.
Real-life situations from mathematics
The equals sign
Robert Recorde introduced the symbol = in The Whetstone of Witte (1557), choosing two parallel lines because no two things could be more equal. Before that, equality was written out in words.
Newton's dots and Leibniz's d
Newton and Leibniz developed calculus with different notations. British mathematicians largely kept Newton's notation, and some historians argue this slowed their progress until the Analytical Society promoted Leibniz's dy/dx in Cambridge from 1812.
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 language and knowledge, or about how representations shape knowledge.
Exhibition. A page of mathematics in an unfamiliar script that you can still partly read because of its symbols is a strong object for a language prompt.
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 language Perspectives
Different views of what mathematics is and whose it is.