definition, religion was a game of infinite excitement and one worth playing, because multiplying an infinite prize by a finite probability results in infinity.
As well as sharing the parentage of probability theory, Fermat was deeply involved in the founding of another area of mathematics, calculus. Calculus is the ability to calculate the rate of change, known as the derivative, of one quantity with respect to another. For example, the rate of change of distance with respect to time is better known simply as velocity. For mathematicians the quantities tend to be abstract and intangible but the consequences of Fermatâs work were to revolutionise science. Fermatâs mathematics enabled scientists to better understand the concept of velocity and its relation to other fundamental quantities such as acceleration â the rate of change of velocity with respect to time.
Economics is a subject heavily influenced by calculus. Inflation is the rate of change of price, known as the derivative of price, and furthermore economists are often interested in the rate of change of inflation, known as the second derivative of price. These terms are frequently used by politicians and the mathematician Hugo Rossi once observed the following: âIn the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used a third derivative to advance his case for re-election.â
For centuries Isaac Newton was thought to have discovered calculusindependently and without any knowledge of Fermatâs work, but in 1934 Louis Trenchard Moore discovered a note which set the record straight and gave Fermat the credit he deserves. Newton wrote that he developed his calculus based on âMonsieur Fermatâs method of drawing tangentsâ. Ever since the seventeenth century calculus has been used to describe Newtonâs law of gravity and his laws of mechanics, which depend on distance, velocity and acceleration.
The discovery of calculus and probability theory would have been more than enough to earn Fermat a place in the mathematiciansâ hall of fame, but his greatest achievement was in yet another branch of mathematics. While calculus has since been used to send rockets to the moon, and while probability theory has been used for risk assessment by insurance companies, Fermatâs greatest love was for a subject which is largely useless â the theory of numbers. Fermat was driven by an obsession to understand the properties of and the relationships between numbers. This is the purest and most ancient form of mathematics and Fermat was building on a body of knowledge that had been handed down to him from Pythagoras.
The Evolution of Number Theory
After Pythagorasâ death the concept of mathematical proof rapidly spread across the civilised world, and two centuries after his School was burnt to the ground the hub of mathematical study had moved from Croton to the city of Alexandria. In 332 BC , having conquered Greece, Asia Minor and Egypt, Alexander the Great decided that he would build a capital city that would be the most magnificent in the world. Alexandria was indeed a spectacularmetropolis but not immediately a centre of learning. It was only when Alexander died and his half-brother Ptolemy I ascended the throne of Egypt that Alexandria became home to the worldâs first-ever university. Mathematicians and other intellectuals flocked to Ptolemyâs city of culture, and although they were certainly drawn by the reputation of the university, the main attraction was the Alexandrian Library.
The Library was the idea of Demetrius Phalaerus, an unpopular orator who had been forced to flee Athens, and who eventually found sanctuary in Alexandria. He persuaded Ptolemy to gather together all the great books, assuring him that the great minds would follow. Once the tomes of Egypt and Greece had been installed, agents scoured Europe and
As well as sharing the parentage of probability theory, Fermat was deeply involved in the founding of another area of mathematics, calculus. Calculus is the ability to calculate the rate of change, known as the derivative, of one quantity with respect to another. For example, the rate of change of distance with respect to time is better known simply as velocity. For mathematicians the quantities tend to be abstract and intangible but the consequences of Fermatâs work were to revolutionise science. Fermatâs mathematics enabled scientists to better understand the concept of velocity and its relation to other fundamental quantities such as acceleration â the rate of change of velocity with respect to time.
Economics is a subject heavily influenced by calculus. Inflation is the rate of change of price, known as the derivative of price, and furthermore economists are often interested in the rate of change of inflation, known as the second derivative of price. These terms are frequently used by politicians and the mathematician Hugo Rossi once observed the following: âIn the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used a third derivative to advance his case for re-election.â
For centuries Isaac Newton was thought to have discovered calculusindependently and without any knowledge of Fermatâs work, but in 1934 Louis Trenchard Moore discovered a note which set the record straight and gave Fermat the credit he deserves. Newton wrote that he developed his calculus based on âMonsieur Fermatâs method of drawing tangentsâ. Ever since the seventeenth century calculus has been used to describe Newtonâs law of gravity and his laws of mechanics, which depend on distance, velocity and acceleration.
The discovery of calculus and probability theory would have been more than enough to earn Fermat a place in the mathematiciansâ hall of fame, but his greatest achievement was in yet another branch of mathematics. While calculus has since been used to send rockets to the moon, and while probability theory has been used for risk assessment by insurance companies, Fermatâs greatest love was for a subject which is largely useless â the theory of numbers. Fermat was driven by an obsession to understand the properties of and the relationships between numbers. This is the purest and most ancient form of mathematics and Fermat was building on a body of knowledge that had been handed down to him from Pythagoras.
The Evolution of Number Theory
After Pythagorasâ death the concept of mathematical proof rapidly spread across the civilised world, and two centuries after his School was burnt to the ground the hub of mathematical study had moved from Croton to the city of Alexandria. In 332 BC , having conquered Greece, Asia Minor and Egypt, Alexander the Great decided that he would build a capital city that would be the most magnificent in the world. Alexandria was indeed a spectacularmetropolis but not immediately a centre of learning. It was only when Alexander died and his half-brother Ptolemy I ascended the throne of Egypt that Alexandria became home to the worldâs first-ever university. Mathematicians and other intellectuals flocked to Ptolemyâs city of culture, and although they were certainly drawn by the reputation of the university, the main attraction was the Alexandrian Library.
The Library was the idea of Demetrius Phalaerus, an unpopular orator who had been forced to flee Athens, and who eventually found sanctuary in Alexandria. He persuaded Ptolemy to gather together all the great books, assuring him that the great minds would follow. Once the tomes of Egypt and Greece had been installed, agents scoured Europe and
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