Calculus is called “analysis” because 19th-century mathematicians analysed heuristic methods to find out why they worked
Sir, The methods of calculus (letters, Oct 4 & 5) were discovered in the 17th century before the discovery of the mathematical notion of a limit, on which a rigorous treatment depends. That is why advanced calculus is called “analysis”: 19th-century mathematicians analysed heuristic methods to find out why they worked. Traditionally British schools have taught the heuristic methods.
Another tradition, followed until recently on the Continent and in the US, avoids a heuristic approach and postpones the teaching of calculus until students can understand analysis. However, US schools have recently come to see the advantages of the British approach.