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Mathematics and art are generally viewed as very different disciplines – one devoted to abstract thought, the other to feeling. But sometimes the parallels between the two are uncanny. From Islamic tiling to the chaotic patterns of Jackson Pollock, we can see remarkable similarities between art and the mathematical research that follows it. The two modes of thinking are not exactly the same, but, in interesting ways, often one seems to foreshadow the other. Does art sometimes spur mathematical discovery? There’s no simple answer to this question, but in some instances it seems very likely.

“News of Boston public schools’ decision to go with the Peters projection has gone viral over the past week, and my teeth have not stopped itching,” Jonathan Crowe writes on his blog, The Map Room. “It is incredibly short-sighted and narrow-minded to say it should be one or the other,” says Mark Monmonier, author of Rhumb Lines and Map Wars: A Social History of the Mercator Projection. Even Ronald Grim, curator of the norman B. Leventhal Map Center at the Boston Public Library, had concerns: “In my mind, both the Mercator and the Peters are controversial projections,” he says in a phone interview. “But we were not asked to be part of the decision.” Choosing between map projections is a necessarily difficult task. The Earth is resolutely three-dimensional, and any attempts to smooth it out are going to add a certain amount of warping. It’s a balancing act: the more accurate you make the continents’ relative area, the more you have to distort their shapes, and vice versa. The art of cartography lies in choosing to privilege one or another of these accuracies—or finding a sweet spot between them that serves your particular purpose.

As the doctor Mark Tonelli has argued, distinct forms of knowledge can’t be judged by the same standards: what a patient prefers on the basis of personal experience; what a doctor thinks on the basis of clinical experience; and what clinical research has discovered — each of these is valuable in its own way. While scientists concur that randomized trials are ideal for evaluating the average effects of treatments, such precision isn’t necessary when the benefits are obvious or clear from other data.

Distrusting expertise makes it easy to confuse an absence of randomized evaluations with an absence of knowledge. And this leads to the false belief that knowledge of what works in social policy, education or fighting terrorism can come only from randomized evaluations. But by that logic (as a spoof scientific article claimed), we don’t know if parachutes really work because we have no randomized controlled trials of them.

Experiments, of course, are invaluable and have, in the past, shown the consensus opinion of experts to be wrong. But those who fetishize this methodology, as the flossing example shows, can also impair progress toward the truth. A strong demand for evidence is a good thing. But nurturing a more nuanced view of expertise should be part of that demand.

No one prepared me for the heartbreak of losing my first language.