Jerome Bruner said somewhere that an educated man must not be dazzled by the myth that advanced knowledge is the result of wizardry. Unfortunately, mathematicians and educators conspire to maintain this myth for mathematics. Students don’t want to understand why it works: they only want to know how to use it. Mathematicians don’t want to make the effort to explain their field to laymen; they are content to do their research and talk to other experts. The result, predictably, is a public perception of mathematics as inexplicable and arcane.
In alchemy, the arcane represented a profound secret of nature. Indeed, in this age, most profound secrets of nature are expressed in mathematical terms. Because the alchemists always associated great mystery with the arcane, it soon came to symbolize as well an elixir, a type of marvelous remedy. The same thing has happened in this age: many scientists, especially social scientists, find that the best remedy for an ailing theory is a mysterious dose of numbers and statistics. Mathematics provides for soft science what one mathematician described as “mystification, intimidation and an impression of precision and profundity.” Mathematics is the elixir of the scientific age.
Despite the significance of the mathematical sciences in our technological society, the distance between the research frontier and public understanding is probably greater in mathematics than in any other field of human endeavor. In virtually all other areas of science, the educated public is aware in a rudimentary fashion of major twentieth century contributions: most people have at least a vague understanding of black holes, genetic engineering, and microprocessors, even though they neither understand nor care to understand such things in detail.
In contrast, public vocabulary concerning mathematics is quite primitive: it is not a decade, not a century, but a millennium out of date. Explaining what is actually happening in contemporary mathematical science to the average layman is like explaining artificial satellites to a citizen of the Roman Empire who believed that the earth was flat.
The typical public attitude towards mathematics is an anomalous mixture of disinterest and awe. Although the average citizen speaks in wondering tones about his genius nephew who scored 800 on his mathematical aptitude test, he appears proud of his own ignorance of things mathematical: “I never did understand percentages.” Even well-educated people who wouldn’t dare admit in public that they have never heard of Keynesian economics will brag of their lack of understanding of statistics or calculus. By and large non-mathematicians do not value mathematical knowledge enough to regret their ignorance of it. For the most part, the average citizen is content to leave its arcane workings to an inner sanctum of wizards.

Extracted from Mathematics: Our Invisible Culture (pdf) by Lynn Arthur Steen, St. Olaf College, Sept. 1985