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David Fowler
Times obituary
Elucidating the Internal Structure of Ancient Greek Mathematics
The mathematician David Fowler was one of the leading authorities on the history of mathematics in ancient Greece. What distinguishes the modern world.
from the medieval world most clearly is science, and mathematics is, broadly, the common core of all science. The first cultures to produce serious mathematics were the Egyptian (witness the superb standard of the surveying of the pyramids) and the Mesopotamian (from whom we inherit counting in 60s, for seconds and minutes). But it was the Greeks who first began to apply logical reasoning to mathematics systematically and to use mathematical proof. Proof is the essence of mathematics, and hence the underpinning of science.
By the 6th century BC, the Greeks were doing mathematics that survives to this day. Pythagoras' theorem, for marking out right angles, dates from this time. In particular, if we take a right-angled triangle with two sides of length 1, the theorem tells us that the long side—the hypotenuse—has length √2, the square root of two. This number, as the Greeks proved, is irrational: it cannot be represented as a ratio of whole numbers.
This discovery put Greek mathematicians into a quandary. They knew a great deal about rational numbers (the fractions of our school arithmetic). They knew a great deal about geometry and the lengths of geometric objects. And they valued logical, rigorous proof very highly. But they could not put all this together: the mathematical machinery needed to handle such "real" numbers was not developed until 1872
So the authors of Greek maths books had fearsome problems. In Alexandria around 300 BC, Euclid wrote his Elements of Mathematics, in 12 books. It was to dominate the subject for nearly two thousand years—there have been more than 2,000 editions, and it remains one of the two most famous math books ever written (with Newton's Principia of 1687). Yet the ordering of the material in Euclid seems very strange to a modern eye. It was dictated by the unsolved problems. David Fowler's principal contribution to intellectual life was a systematic study of the internal structure of Greek math, with all this in mind. In Euclid, for example, most of what is said stands the test of time. But it is what is not said, and why, that really counts here The crux is Euclid's Book V, on the theory of proportion, and Book X, on irrationals and "incommensurables" pairs of numbers having irrational ratios.
The key institution in all this was Plato's Academy in Athens, in the 4th century BC. Plato's friend Theaetetus worked on proportion, and this led Eudoxus, a pupil of Plato, to develop his theory of proportion, on which Euclid's Book V is based. We take real numbers and division for granted. The Greeks, in effect, developed a theory of ratio without either of these, using a technical procedure known as anthyphairesis. David Fowler's study of all this, The Mathematics of Plato's Academy: A New Reconstruction, was published by Oxford University Press in 1987, and is his lasting memorial.
Fowler's career was spent at Warwick University, which was founded in 1965 and which rapidly built up one of the four best mathematics departments in the country. When the Nuffield Foundation gave Warwick the money to found its Mathematics Research Centre in 1967, Professor E. C. (now Sir Christopher) Zeeman, who had taught Fowler at Cambridge, appointed him as its director. Fowler led the research centre with distinction for more than 20 years. The many visitors to the centre remember the devotion with which he and his small staff made them welcome and helped to solve their problems. The success of Warwick mathematics owes much to Fowler's admirable leadership.
David Herbert Fowler was born in Blackburn. At 13, while at Russell School, near Morecambe Bay, he designed and built his own television set. He entered Gonville and Caius College, Cambridge, in 1955, and was taught there by Zeeman. This was the beginning of a lifelong friendship.
After a first and two more years at Cambridge as a research student in mathematical analysis, he began his career as a lecturer at Manchester University in 1961. Analysis remained his principal interest for some years after the move to Warwick, but a switch to the history of mathematics in general, and ancient Greek mathematics in particular, was signaled by his papers from 1979 on.
He became one of the leading members of the British Society for the History of Mathematics. He commanded respect among both the mathematical and historical communities. He will long be known by the scholarly world for his book and other writings, but he will be remembered for his human qualities by those lucky enough to have known him. His tact, genius, and dedication were apparent at Warwick and the Mathematics Research Centre, at the British Society for the History of Mathematics, and wherever he went.
Fowler had broad cultural interests, and like many mathematicians, he was musical: he played the clavichord and indeed made one for himself.
He is survived by his wife Denise and their children Stephan and Magali.
David Fowler, mathematician, was born on April 28, 1937. He died on April 13, 2004, aged 66
Elucidating the Internal Structure of Ancient Greek Mathematics
The mathematician David Fowler was one of the leading authorities on the history of mathematics in ancient Greece. What distinguishes the modern world.
from the medieval world most clearly is science, and mathematics is, broadly, the common core of all science. The first cultures to produce serious mathematics were the Egyptian (witness the superb standard of the surveying of the pyramids) and the Mesopotamian (from whom we inherit counting in 60s, for seconds and minutes). But it was the Greeks who first began to apply logical reasoning to mathematics systematically and to use mathematical proof. Proof is the essence of mathematics, and hence the underpinning of science.
By the 6th century BC, the Greeks were doing mathematics that survives to this day. Pythagoras' theorem, for marking out right angles, dates from this time. In particular, if we take a right-angled triangle with two sides of length 1, the theorem tells us that the long side—the hypotenuse—has length √2, the square root of two. This number, as the Greeks proved, is irrational: it cannot be represented as a ratio of whole numbers.
This discovery put Greek mathematicians into a quandary. They knew a great deal about rational numbers (the fractions of our school arithmetic). They knew a great deal about geometry and the lengths of geometric objects. And they valued logical, rigorous proof very highly. But they could not put all this together: the mathematical machinery needed to handle such "real" numbers was not developed until 1872
So the authors of Greek maths books had fearsome problems. In Alexandria around 300 BC, Euclid wrote his Elements of Mathematics, in 12 books. It was to dominate the subject for nearly two thousand years—there have been more than 2,000 editions, and it remains one of the two most famous math books ever written (with Newton's Principia of 1687). Yet the ordering of the material in Euclid seems very strange to a modern eye. It was dictated by the unsolved problems. David Fowler's principal contribution to intellectual life was a systematic study of the internal structure of Greek math, with all this in mind. In Euclid, for example, most of what is said stands the test of time. But it is what is not said, and why, that really counts here The crux is Euclid's Book V, on the theory of proportion, and Book X, on irrationals and "incommensurables" pairs of numbers having irrational ratios.
The key institution in all this was Plato's Academy in Athens, in the 4th century BC. Plato's friend Theaetetus worked on proportion, and this led Eudoxus, a pupil of Plato, to develop his theory of proportion, on which Euclid's Book V is based. We take real numbers and division for granted. The Greeks, in effect, developed a theory of ratio without either of these, using a technical procedure known as anthyphairesis. David Fowler's study of all this, The Mathematics of Plato's Academy: A New Reconstruction, was published by Oxford University Press in 1987, and is his lasting memorial.
Fowler's career was spent at Warwick University, which was founded in 1965 and which rapidly built up one of the four best mathematics departments in the country. When the Nuffield Foundation gave Warwick the money to found its Mathematics Research Centre in 1967, Professor E. C. (now Sir Christopher) Zeeman, who had taught Fowler at Cambridge, appointed him as its director. Fowler led the research centre with distinction for more than 20 years. The many visitors to the centre remember the devotion with which he and his small staff made them welcome and helped to solve their problems. The success of Warwick mathematics owes much to Fowler's admirable leadership.
David Herbert Fowler was born in Blackburn. At 13, while at Russell School, near Morecambe Bay, he designed and built his own television set. He entered Gonville and Caius College, Cambridge, in 1955, and was taught there by Zeeman. This was the beginning of a lifelong friendship.
After a first and two more years at Cambridge as a research student in mathematical analysis, he began his career as a lecturer at Manchester University in 1961. Analysis remained his principal interest for some years after the move to Warwick, but a switch to the history of mathematics in general, and ancient Greek mathematics in particular, was signaled by his papers from 1979 on.
He became one of the leading members of the British Society for the History of Mathematics. He commanded respect among both the mathematical and historical communities. He will long be known by the scholarly world for his book and other writings, but he will be remembered for his human qualities by those lucky enough to have known him. His tact, genius, and dedication were apparent at Warwick and the Mathematics Research Centre, at the British Society for the History of Mathematics, and wherever he went.
Fowler had broad cultural interests, and like many mathematicians, he was musical: he played the clavichord and indeed made one for himself.
He is survived by his wife Denise and their children Stephan and Magali.
David Fowler, mathematician, was born on April 28, 1937. He died on April 13, 2004, aged 66
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