As a full professor of mathematics for over 30 years, I have been engaged in research and teaching. Research can be difficult to describe to non-experts, but some important advances in mathematics can be explained to an interested public without the need for specialist knowledge, as I have done.
I wrote
Symmetry and the Monster: One of the Greatest Quests of Mathematics
It provides an engaging description of the work that went into proving a famous result, first mentioned by the French mathematician Pierre de Fermat in the margin of a book.
The question was whether a sum of two nth powers of whole numbers could be the nth power of a whole number. It is certainly true for n = 2 but was not known for any n greater than 2. Fermat thought he had a proof that this was the case but later wrote proofs when n was 3 or 4, so his earlier claim was not taken seriously.
The general result turned out to be much harder than anyone imagined, and 350 years later, its truth was implied by another conjecture that was finally proved by Andrew Wiles, as this book explains. I admire the fact that the author distills some essential points from what turned out to be a very sophisticated modern proof.
'I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.'
It was with these words, written in the 1630s, that Pierre de Fermat intrigued and infuriated the mathematics community. For over 350 years, proving Fermat's Last Theorem was the most notorious unsolved mathematical problem, a puzzle whose basics most children could grasp but whose solution eluded the greatest minds in the world. In 1993, after years of secret toil, Englishman Andrew Wiles announced to an astounded audience that he had cracked Fermat's Last Theorem. He had no idea of the nightmare that lay…
This unique book presents stories about mathematics, such as The Young Archimedes by Aldous Huxley and Peter Learns Arithmetic by H. G. Wells. It and its sequel are a mine of fascinating short stories.
It's well worth keeping and rereading. I found both it and its sequel fun to read.
Clifton Fadiman's classic collection of mathematical stories, essays and anecdotes is now once again available. Ranging from the poignant to the comical via the simply surreal, these selections include writing by Aldous Huxley, Martin Gardner, H.G. Wells, George Gamow, G.H. Hardy, Robert Heinlein, Arthur C. Clarke, and many others. Humorous, mysterious, and always entertaining, this collection is sure to bring a smile to the faces of mathematicians and non-mathematicians alike.
This book presents excerpts from original contributions to mathematics by scholars of the past. It includes principal developments from Neolithic times, from Mesopotamia, and from the ancient Greeks, right up to the modern world.
The extensive and well-chosen quotations make this a unique book. I found the excerpts from original sources rendered it a mine of valuable information for me or anyone else interested in the long history of mathematics.
In 1922 Barnes Wallis, who later invented the bouncing bomb immortalized in the movie The Dam Busters, fell in love for the first and last time, aged 35. The object of his affection, Molly Bloxam, was 17 and setting off to study science at University College London. Her father decreed that the two could correspond only if Barnes taught Molly mathematics in his letters.
Mathematics with Love presents, for the first time, the result of this curious dictat: a series of witty, tender and totally accessible introductions to calculus, trigonometry and electrostatic induction that remarkably, wooed and won the girl.…
Hermann Weyl was one of the most influential mathematicians in the twentieth century. Born in North Germany, he worked for many years in Zürich and later moved to the Institute of Advanced Study in Princeton.
He was a colleague of Einstein in both places, and his book on Symmetry is a classic. This slim volume was a stimulus to me when I wrote my book.
Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.
Frenkel came from the Soviet Union, where discrimination against Jews made it impossible for him to get into Moscow State University. During the oral exam they sent two graduate students to question him, pick holes in his responses, and ensure he failed. He turned to an informal network of Soviet mathematicians for help.
Like him, they were denied serious employment in the field, but after the 'cold war' against the Soviet Union, Harvard invited him to take a fellowship that later turned into a permanent job. Years later, when his old tormentor from Moscow State arrives to give a talk, he confronts the man in a lecture room with first-hand evidence of allegations against the system. Faced with a victim, the Russian mathematician's denials rang hollow.
This book reaches beyond mathematics to anyone of independent thought in an environment where it is not permitted to step out of line or, indeed, to be associated with an ethnic group (in this case, people of Jewish heritage) that is discriminated against. I found it spoke from the heart.
A New York Times Science BestsellerWhat if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.In Love and Math , renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel…
My book describes one of the great quests of mathematics: to find all the basic building blocks for symmetry. In other words, all groups of symmetries that cannot be deconstructed into simpler groups.
Symmetry groups first came into use in the mid-nineteenth century to decide which equations could be solved using a formula. They later found applications to physics and chemistry and, more recently, to quantum physics.
I come by my interest in history and the years before, during, and after the Second World War honestly. For one thing, both my father and my father-in-law served as pilots in the war, my father a P-38 pilot in North Africa and my father-in-law a B-17 bomber pilot in England. Their histories connect me with a period I think we can still almost reach with our fingertips and one that has had a momentous impact on our lives today. I have taken that interest and passion to discover and write true life stories of the war—focusing on the untold and unheard stories often of the “Average Joe.”
October 24, 1944, is not a day of national remembrance. Yet, more Americans serving in World War II perished on that day than on any other single day of the war.
The narrative of No Average Day proceeds hour by hour and incident by incident while focusing its attention on ordinary individuals—clerks, radio operators, cooks, sailors, machinist mates, riflemen, and pilots and their air crews. All were men who chose to serve their country and soon found themselves in a terrifying and otherworldly place.
No Average Day reveals the vastness of the war as it reaches past the beaches in…
October 24, 1944, is not a day of national remembrance. Yet, more Americans serving in World War II perished on that day than on December 7, 1941, when the Japanese attacked Pearl Harbor, or on June 6, 1944, when the Allies stormed the beaches of Normandy, or on any other single day of the war. In its telling of the events of October 24, No Average Day proceeds hour by hour and incident by incident. The book begins with Army Private First-Class Paul Miller's pre-dawn demise in the Sendai #6B Japanese prisoner of war camp. It concludes with the death…
