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Current Commentary: Doing away with variables

Posted on 3. May, 2018.

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In primary school we do our sums, and these involve much more than just addition: there is also subtraction, ultiplication, and long division to be reckoned with. But it is always a numbers game, until a friendly teenager shows us their homework, in which the sums involve letters. 

Those letters, the nec plus ultra (and near-synonym) of the Humanities, have somehow managed to infiltrate the austere realm of sums, which suddenly appear riddled with occurrences of not only x, y, z, but also a, b, c and perhaps even p, q, r. If anything is clear from this, it is that mathematicians do not seem to be able to make their minds up about where to start the alphabet. ‘But how do you know what x is?’ we ask, intrigued. ‘That’s just the thing, no one ever knows and you have to find out’, they wail. Pressing the point somewhat, we are informed that x becomes something new every time it is worked out, and you have to start over again. Small wonder our teenage Sisyphus seems angst-ridden.

The good news is that variables do not really exist. The bad news is that we will still need to use them all the time.

Read the full article in Science Progress, Volume 101, Number 1, March 2018, pp. 76-82(7).

DOI: https://doi.org/10.3184/003685018X15154174791851

Author: Hugo A.Van De Berg
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
E-mail: hugo@maths.warwick.ac.uk


Image: In this example, the equation ‘to be solved’ is sin x = 0, but we decide to regard x as a set index.