The importance of naming

A common concept in history is that knowing the name of something or someone gives one power over that thing or person. This concept occurs in many different forms, in numerous cultures"in ancient and primitive tribes, as well as in Islamic, Jewish, Egyptian, Vedic, Hindu, and Christian traditions. The strength of this belief varies, and there are certainly exceptions to it. Nonetheless, the persistence and historical continuity of the linking of naming and power are unmistakable. Some scholars find it embedded in the first verses of Genesis, probably written over three thousand years ago; others believe it to be an intrinsic characteristic of classical Greek religion; still others find it a central feature in magic and folklore; and modern feminists often see it as the reason that a woman in marriage is traditionally asked to take the name of her new husband. In all these cases, naming something or someone is seen as the exertion of dominion over that thing or person. Several twentieth-century mathematicians gave naming a peculiar twist that reflected their deep religious mysticism and influenced their creativity.

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In modern mathematics, the naming theme emerges in different ways. The great Russian-French mathematician Alexander Grothendieck"still alive but no longer active as a mathematician"put a heavy emphasis on naming as a way to gain cognitive power over objects even before they have been understood. One observer of Grothendieck's work wrote, "Grothendieck had a flair for choosing striking, evocative names for new concepts; indeed, he saw the act of naming mathematical objects as an integral part of their discovery, as a way to grasp them even before they have been entirely understood." Mathematicians often observe that, on the basis of intuition, they sometimes develop concepts that are at first ineffable and resist definition. These concepts must be named before they can be brought under control and properly enter the mathematical world. Naming can be the path toward that control.

In the late nineteenth and early twentieth centuries, this topic became critical when mathematicians developed whole classes of "mathematical objects" of which no one had earlier conceived. Being totally unknown, they arrived unnamed. There was even serious doubt that they truly "existed." Maybe they did not deserve names.

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