don't mention fried ants

(More from T W Körner, The Pleasures of Counting - a passage which makes the end of the book, on which a post currently waits in the drafts folder, all the more inexplicable)

The study of algorithms is part of the constant search for better ways of doing things just like the search for ways of preventing cholera or submarines. But the task does not end there. Having found a better way you must persuade others to adopt it. Learning how to do this can only come from long and painful experience. ... Until the reader has experienced the shock of having her well thought-out and carefully argued proposal thrown out for the most fatuous of reasons, she will not understand why I write this section or why, before any difficult committee meeting, it is important to recite the two phrases: 'You can only resign once' and 'Those who fight too long with dragons become dragons themselves.'

When a government committee was set up in 1978 to consider mathematics teaching in English and Welsh schools, their first step was to set up a survey to find out the opinions and mathematical needs of a representative sample of adults. However, the survey ran into an unexpected difficulty when many of those approached refused to be interviewed.

Both direct and indirect approaches were tried, the word 'mathematics' was replaced by 'arithmetic' or 'everyday use of numbers', but it was clear that the refusal for people's refusal to be interviewed was simply that the subject was mathematics.... Several personal contacts pursued by the enquiry officer were also adamant in their refusals. Evidently there were some painful associations which they feared might be uncovered. This apparently widespread perception amongst adults of mathematics as a daunting subject pervaded a great deal of the sample selection; half of the people approached as being appropriate for inclusion in the sample declined to take part.

Even among those who agreed to take part,

The extent to which the need to undertake even an apparently simple and straightforward piece of mathematics could induce feelings of anxiety, helplessness, fear and even guilt in some of those interviewed was, perhaps, the most striking feature of the study.

There did not appear to be any connection between mathematical competence and occupation group. However,

The feelings of guilt to which we referred earlier appeared to be especially marked among those whose academic qualifications were high and who, in consequence of this, felt they ought to have a confident understanding of mathematics, even though this was not the case.

In view of this, it is clear that mathematicians should not refer to mathematics in advocating a given course of action. By itself this is not a great disadvantage. Darwin's On the Origin of Species is a marvellous example of sustained book-length argument without any recourse to mathematics. Unfortunately, most people are also unwilling to follow sustained argument.