by Loren Graham, MIT and Harvard University

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.

In Genesis we hear in the first verses that "God said 'Let there be Light' and there was light." Think about that statement logically. God named the thing before he created it; the naming seems a necessary first step toward creation. Then, according to Genesis, God gave Man the right to name all the animals and, at the same time, the right of dominion over them. Here again the act of naming carries with it a sense of power, of hegemony. The Egyptian god Ptah allegedly had the power to create anything he could name. The ancient Egyptians similarly believed that one gained power over a god if one knew his name. According to the Jewish religion, the name of God was so holy that it was not to be said out loud. A likely reason for this prohibition was that naming God might be seen as an attempt to assert dominion over him, to duplicate illegitimately a power that God uniquely possessed.

A specific use of naming to bring religious power is that of the "The Jesus Prayer." The practice of this prayer dates back to at least the fifth century, when certain Christian "desert fathers" in Egypt and the Middle East promoted the view that the ceaseless repetition of the names "Jesus" and "God" brings the worshipper not only to a state of religious ecstasy but also to profound insight on the world. These "hesychasts" took a different position from that of many Jews, who considered the name of God to be too holy or powerful to be enunciated. The desert fathers agreed that the names of God and his son are powerful, but they believed they could transfer some of that power back on themselves, thereby gaining knowledge of the world. The practice of the Jesus Prayer has continued down to the present day, but after the split between the eastern and western forms of Catholicism, it was much stronger in Orthodoxy, especially Russian Orthodoxy, than it was in the Roman Catholic Church. Several of the most important Russian mathematicians of the twentieth century were practitioners of the Jesus Prayer, and maintained that it has relevance to mathematics.

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.

Georg Cantor initiated this discussion when he promoted the view that there is more than one type of infinity. Until his time, most mathematicians and philosophers had accepted Aristotle's view that infinity is a potentiality, a single abstraction, and not an actuality. Cantor radically broke with the Aristotelian tradition by suggesting that infinity is an actuality, not a potentiality, and that it can exist in multiple forms. His first distinction was between countable and uncountable infinities. An example of the first is all the integers; an example of the second is the points on a line segment. But are these two infinities of the same type if one is countable and the other is not? Not at all, said Cantor. So if these infinities are different should they be given different names? Cantor's answer was in the affirmative, and he began the process of naming different infinities by different "Aleph numbers." Now the door was open to the creation, and the naming, of a whole gamut of infinities—an infinity of infinities, in fact. A new world of transfinite numbers was being created.

Particularly valuable work in this new field of set theory was done by Russian mathematicians, especially Dmitri Egorov and Nikolai Luzin. Both of them were under the heavy influence of a religious sect of the Russian Orthodox Church called Name Worshippers, whose members put a heavy emphasis on the power of naming. Intellectually and religiously, Egorov and Luzin were descendants of the desert fathers of the fifth century, who had such a strong influence in the Russian Orthodox Church. Egorov and Luzin believed that if they named God, they assured his existence, and similarly they thought that by naming the new sets, they could make them real. God could not be defined, but he could be named. The new sets also resisted definition, but they too could be named. The Russians returned to Moscow and created one of the most powerful mathematical schools of the twentieth century. The story of what they did, and how religious thought motivated them, is told in the recent book Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity, written by Jean-Michel Kantor and me.

This paper was commissioned by the Philoctetes Center as part of a grant from The John Templeton Foundation. This and three other commissioned pieces are featured in a special issue of Dialog, the newsletter of the Philoctetes Center.