One of the values of the philosophy of Alfred North Whitehead is that it can help us appreciate many forms of mysticism -- at least eight of them. (See Eight Forms of Mysticism.) These eight forms have been experienced by countless people throughout the world, within and outside of religious contexts. Each entails a deeply intuitive awakening to one of the following: (1) the absolute interconnectedness and mutual becoming of all things in the universe, (2) the warmth and togetherness of local community in the context of family, friends, and neighbors, (3) a creative energy pervading the cosmos of which all things are expressions, (4) divine archetypes -- mathematical and emotional -- within the mind of God, (5) the tender and inclusive embrace of divine love, (6) the collective unconcious of humanity, (7) various realms of shamanic journeying, and (8) the sacrament of ordinary life in the here-and-now.
Often these forms are blended within a single mystical experience, but they can also be experienced separately, each with its own beauty. The fourth form of mysticism, awakening to divine archetypes in the mind of God, includes mathematical mysticism or, to be more precise, imaginative receptivity to the realm of pure potentialities and abstract patterns that inhabit what Whitehead calls the primordial nature of God. Mathematical mysticism is not about the world of mutual inter-becoming per se, but rather about a timeless realm of pure potentialities -- Whitehead calls them “eternal objects” -- which may or may not be embodied in the universe. In Whitehead's words, it is attention to "ideal relationships in abstraction from reference to the passage of brute fact."
Mathematical mysticism is an exploration of the realm of eternal objects, combined with a sense of being inspired by its revelations.
Let Srinivasa Ramanujan be an example, a man whom Whitehead expressed deep admiration in Whitehead's book Modes of Thought. A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess. "An equation for me has no meaning," he once said, "unless it expresses a thought of God."
Film Review by Mary Ann and Frederic Brussat
Growing up in South India, Srinivasa Ramanujan (Dev Patel) shows an immense fascination with mathematics, even though he has no formal training in the subject. He fills notebooks with equations and formulas. In order to support his wife Janaki (Devika Bhise) and mother (Arundathi Nag), this earnest and self-confident young man lands a lowly job as a clerk in a British firm. With great enthusiasm, Ramanujan explains to his bride that there are beautiful patterns in everything and mathematics is like painting without colors. She does not understand but an Indian mentor at the firm recognizes him as a math genius and encourages him to share his work with the world.
In 1913, Ramanujan sends some of his theorems to G. M. Hardy (Jeremy Irons), the leading British mathematician at Cambridge in England. He recognizes that that this young Indian possesses vast intellectual powers that must be tapped. He invites Ramanujan to England and along with his longtime collaborator John Littlewood (Toby Jones) tries to convince his protégé that formal proofs must be added to his mathematical adventures. Otherwise, they can never be published. It is very edifying to witness the friendship that slowly blooms between these two mathematicians: Hardy, a pragmatist and atheist, and Ramanujan, a Hindu believer who claims that every math equation expresses a "thought of God." Both of these tireless explorers are viewed as outsiders. Hardy is seen by his colleagues as a workaholic unwilling to waste his precious time with human beings. More than once, Ramanujan is scorned by Indian-hating academicians who treat him without respect. These slights and humiliations conspire against this scientific pioneer who is initially denied a fellowship at Cambridge, despite his achievements. Trying to maintain his vegetarian diet during World War I rationing, combined with the constant work and his longing for Janaki and India, he begins to suffer health problems. But when he is diagnosed with tuberculosis, he doesn't tell his mentor and friend. When Hardy visits him in the hospital, he is a burnt-out shell of the once ardent and passionate Indian mathematician aglow with new projects.
The Man Who Knew Infinity has been written and directed by Matthew Brown based on a 1991 book by Robert Kanigel. This heart-affecting biodrama stands shoulder-to-shoulder with other top-drawer films about mathematicians and theoretical physicists — A Beautiful Mind, Proof, and The Theory of Everything. While many in the audience may not understand the talk about infinite series, prime numbers, and partitions, they will sense in their bones the passion and the thrills that accompany Ramanujan's math discoveries and triumphs.
Dev Patel, who was so marvelous in Slumdog Millionaire, effectively depicts Ramanujan's Hindu zeal, his passion for mathematics, and his reverence for its beauty. In another richly detailed and nuanced performance, Jeremy Irons reveals the admirable efforts of a cerebral scholar who finds the courage to stand up for the mind-blowing work of his friend in the face of steep opposition and racial prejudice. Both men would no doubt agree with Henry David Thoreau who said: "The language of friendship is not words but meanings."
The First Hundred Integers as Personal Friends
Alfred North Whitehead on Ramanujan
"It is true that nothing is finally understood until its reference to process has been made evident. And yet, there is the understanding of ideal relationships in abstraction from reference to the passage of brute fact. In the notion of such relationships there is no transition. For example, throughout mathematics, in one sense, transition does not enter. The interconnections are displayed in their timeless eternity. It is true that the notions of time, and of approach, and of approximation, occur in mathematical discourse. But as used in the science, the timefulness of time and the motion of approach are abstracted from. In mathematics, as understood, the ideal fact stands out self-evident.
There is very little large-scale understanding, even among mathematicians. There are snippets of understanding, and there are snippets of connections between these snippets. These details of connection are also understood. But these fragments of intelligence succeed each other. They do not stand together as one large self-evident co�rdination. At the best, there is a vague memory of details which have recently been attended to. This succession of details of self-evidence is termed 'proof'. But the large self-evidence of mathematical science is denied to humans. To give an example, the snippet of knowledge that the addition of 1 and 4 produces the same multiplicity as the addition of 1 and 3, seems to me self-evident. It is a humble bit of knowledge; but, unless I deceive myself, it stands before me with a clarity of insight. I hesitate to claim any, such self-evidence when larger numbers are involved. I have recourse to the indignity of proof. Other people have wider powers. For example, consider Ramanujan, the great Indian mathematician, whose early death was a loss to science analogous to that of Galois. It was said of him that each of the first hundred integers was his personal friend. In other words, his insights of self-evidence, and his delight in such insights, were of the same character as most of us feel for the integers up to the number 5. Personally, I cannot claim intimate friendship beyond that group. Also the restriction of the group somewhat, in my own case, hinders the growth of that feeling of delight which Ramanujan enjoyed."