In that same year Whitehead made a radical change in his life. He had been given a ten-year appointment by Trinity College in 1903, and in 1910 this still had three years to run. But Whitehead was impatient and frustrated with his work at Cambridge. If he resigned his teaching position, he would still have a small income as a fellow of the college. He proposed to Mrs. Whitehead that they move to London and take their chances. She agreed.
She was right. In the modern phrase, Whitehead’s career took off after the move. He was appointed to the staff of the University of London in 1911 and in 1914 he became professor of mathematics at the Imperial College. He published important books, notably The Concept of Nature (1920), and by the early 1920s he had become the most distinguished philosopher of science writing in English. He was invited to Harvard to teach philosophy in 1924 and again he decided to move. His years in the United States were his most productive. He taught at Harvard until 1937 and died in Cambridge, Massachusetts, in 1947.
During his first year in London, Whitehead had time on his hands and accepted an invitation from a publisher of popular scientific books to produce a small volume on mathematics. This appeared the next year (1911) under the title Introduction to Mathematics. It is one of the best such books.
Whitehead was a great mathematician, but his and Russell’s Principia Mathematica had been a very difficult book to read and understand. Whitehead’s later books were also sometimes so difficult as to be almost unintelligible. But during that one year of 1910, at least, he possessed the genius of simplicity. Introduction to Mathematics is so clear, simple, and direct, with so many good examples and so few mathematical symbols, that almost anyone who will devote the slightest effort can read it. The astonishing thing is that the book is also rigorous and authoritative. It is good mathematics as well as being easy to read and understand.
Whitehead explains why at the very beginning of the book. “The study of mathematics,” he concedes, “is apt to commence in disappointment.” Great expectations are built up in students, but these are not satisfied.
The reason for this failure of the science to live up to its reputation is that its fundamental ideas are not explained to the student disentangled from the technical procedure that has been invented to facilitate their exact presentation in particular instances. Accordingly, the unfortunate learner finds himself struggling to acquire a knowledge of a mass of details that are not illuminated by any general conception.
Perhaps all beginning students of mathematics, at least mathematics beyond the level of arithmetic or simple geometry and algebra, have become aware of that failing—unless they had an excellent teacher. Alfred North Whitehead was an excellent teacher. He makes the ideas clear.
Introduction to Mathematics is not, he insists, designed to teach mathematics. Perhaps not, but much mathematics can be learned from it. And all mathematics becomes easier to do as well as to understand when one grasps the basic ideas and concepts underlying the operations. Thus the book helps anyone to be a better mathematician than he or she otherwise would.
Is that important? It seems to me that it certainly is. For mathematics is not only extremely useful, it is also extremely beautiful. But its beauty is not grasped if one cannot “do the math,” at least a little.
WILLIAM BUTLER YEATS
1865–1939
Selected Poems
William Butler Yeats was born in Dublin in 1865. He studied art as a young man but decided on a literary career when he was twenty-one. Although a Protestant and a member of the Anglo-Irish ruling class, Yeats was deeply interested in the old Ireland. He helped to found an Irish Literary Society in London and another in Dublin. He also worked to create an Irish national theater, joining with others to acquire the Abbey Theatre in Dublin, which has been the home of the Irish Players for nearly a hundred years. Several of his own plays were produced during those early years, and Yeats throughout his life wished to be known as a playwright.
He was a much better poet than playwright, however, and it is as probably the greatest English poet of the last century that he is known today.
He deserves that honor because, almost alone among poets of the twentieth century, he never ceased to grow, to become better and more interesting, as long as he lived. Most poets run out of steam or reach a plateau beyond which they cannot go—often early in their careers. This never happened to Yeats. He never stopped reaching out, experimenting with new ways of saying new things. Thus his last poems are among his best. Last Poems, which appeared in 1940, the year after his death, contains some of his finest, strangest work.
Yeats loved the misty mysteriousness of the Irish past, and as a young man he wrote the kind of ditties we think of as “Irish.” Politics, the convoluted, tormented politics of Irish independence, obsessed him during his middle years. This was a greater theme than the misty past of Ireland, and Yeats rose to it. Some of the poems he wrote about it are very famous, like “Easter 1916,” about the execution of some Irish nationalists on that day, with its mournful, lamenting cry: “A terrible beauty was born!”
This was the beauty of the martyr, a terrible beauty indeed, and perhaps we can understand that Yeats himself came to know the real meaning of freedom when he saw these men, his friends, hanged for seeking it.
Yeats the politician sat in the Senate of the newly founded Irish Free State during the 1920s, but poetry was by now his main business and he continued to write, getting better and better, more and more profound, more and more disturbing in what he had to say.
Finally, what he had to say was mostly about growing old and not wanting to. He was sixty in 1925, and in that year he wrote “Among School Children,” not his most famous single poem but perhaps his greatest. He mingles among the girls in a school, “A sixty-year-old smiling public man,” and, looking into their eyes, is overcome by wonder at what has occurred. All these years have come and gone, but where did they go? What have they produced? Were they “A compensation for the pang of his birth/Or the uncertainty of his setting forth?”
As he became older he worked all the harder, inventing a character named Crazy Jane who rebels against the formality and politeness of the world. Crazy Jane and the Bishop fight it out over the great questions of life. These poems, “Words for Music Perhaps” as Yeats called them, are not quite songs but have the earthiness, the directness, and the catch in the rhythms that good songs have. Nothing better was written in the twentieth century.
Finally even the heart of Yeats grew old and tired:
O who could have foretold
That the heart grows old?
But this occurred only when Yeats was near death. He died of a broken heart, broken over the human condition, which is summed up in the one terrible word: Mortality. He never gave in; he never accepted it. We remember “Sailing to Byzantium”: Byzantium, where the poet dreams of golden birds that sing forever because they are not alive. Are they the spirit of poetry itself or are they the spirit of this poet who refused to concede that he was merely human?