Introduction Mathematics today is the fruit of centuries of brilliant insights by men and women whose personalities and life experiences were often as extraordinary as their mathematical achievements. When we study mathematics, we learn about ideas and concepts that were developed over the past centuries. Very often these topics are built upon one another. But who has done the building? We know the names of the many famous mathematicians and in many cases their discoveries and developments carry their name, such as the Pythagorean Theorem or the Fermat''s Last Theorem. But who were these brilliant developers of this ubiquitous subject? Were they merely average folks who had a penchant for mathematics, or were they brilliant beyond description, with an intelligence that allowed them to make these noteworthy discoveries? This book is intended to shed light on the personalities of fifty famous mathematicians who flourished over the several centuries and who made significant contributions to the field. There were times when their supreme intelligence set them apart from others and isolated them socially. Other times their brilliance allowed them to function in a way that gave them a path to discoveries, which were well beyond what the norm could accomplish. There were also times when their supreme brilliance cost them their lives.

This book will focus on these mathematicians'' lives, personalities, and unusual experiences. We will highlight their brilliant discoveries in a fashion intelligible to the general reader, and hopefully motivate further pursuit of these topics. Our goal here is to entertain the reader with these unusual elements of brilliance, which reflects itself very nicely in their personalities. In many cases these brilliant mathematicians have had very unusual experiences in their life; some have evolved out of severe poverty, while others may have flourished in a wealthy environment. Some of them had unusual experiences in their schooling, while others educated themselves. In any case, these unusually-gifted individuals can provide a refreshing view of the history of mathematics from a more personal standpoint. --------------------------------- From Chapter 5 - Archimedes Archimedes is probably most famous for proclaiming "Eureka! Eureka!" ("I''ve found it! I''ve found it") after he had stepped into a bath and suddenly noticed that the amount by which the water level rose is a measure of the volume of the part of his body he had submerged. The background story is that the local Tyrant Hiero of Syracus (c.

308 BCE-215 BCE) contracted Archimedes to find a method by which the purity of a golden crown can be assessed (without destroying it). This stems from the notion that Hiero suspected his goldsmiths of having replaced some of the gold he had given them with silver. Archimedes was able to solve the problem because gold weighs more than silver. A crown mixed with silver would have to be bulkier than a purely golden crown of the same weight. Consequently, it would also displace more water. However, the oldest source for this story is a book on architecture by the Roman writer Vitruvius, which appeared approximately two hundred years after the episode, and it is very likely that the story has been substantially modified and embellished, even though there may be some truth in it. Galileo Galilei (1564-1642) pointed out that Archimedes could have achieved a much more accurate measurement by using a different method relying on his own law of buoyancy, now known as "Archimedes'' principle." Archimedes is also remembered as an ingenious inventor of mechanical devices, such as Archimedes'' screw for lifting water .

and various "super weapons" of the ancient world. Perhaps less well known is the fact that Archimedes is generally considered the greatest mathematician of classical antiquity. His mathematical achievements go well beyond the work of other ancient Greek mathematicians, in particular, he anticipated modern calculus when he used closely related concepts to prove geometrical theorems. Unfortunately, almost nothing is known about Archimedes'' life, except a few anecdotes and some biographical information he mentioned in his writings. Archimedes was born in the city of Syracuse on the island of Sicily in 287 BCE. It is believed that he studied in the city of Alexandria in Egypt, which was an intellectual center of the ancient world. His father was an astronomer named Phidias, of whom nothing else is known. However, two of Archimedes'' works have introductions addressed to Eratosthenes (c.

276 BCE - c. 195 BCE), who was in charge of the legendary Library of Alexandria, a place where the greatest scholars of the ancient world would meet. Eratosthenes is famous for calculating the circumference of the Earth by measuring the Sun''s angle of elevation at noon in Alexandria and in a city that was a known north-south distance away from Alexandria. Considering the extremely primitive measuring tools Eratosthenes had to use, he obtained a remarkably accurate result. Archimedes was killed in 212 BCE during the capture of Syracuse by Roman forces under General Marcus Claudius Marcellus in the Second Punic War. Plutarch recounts three slightly-different versions of his killing; the most popular one is that where Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus, but Archimedes declined, saying that he had to finish working on the problem. The famous last words attributed to Archimedes are "Do not disturb my circles," a reference to the circles in the mathematical drawing that he was supposedly studying.

------------------------------------------ From Chapter 24 - Maria Gaetana Agnesi When one looks at the history of mathematics, it is overloaded with male mathematicians. One wonders who the first female mathematician in the Western world was to receive an international reputation. Most people would consider Maria Gaetana Agnesi to fit that role. She was born on May 16, 1718 in Milan, which then was a part of the Austro-Hungarian Empire, and is now a city in Italy. She grew up in a wealthy household as the oldest child of a wealthy silk merchant, who fathered twenty-one children. The first signs of her prodigy appeared at age 5, when she spoke Italian and French. By age 9, she further demonstrated her talent by mastering several modern languages as well as Latin, Greek, and Hebrew. Within the next few years she mastered mathematics.

Recognizing her talents, her father would invite friends and have her perform by displaying her vast intelligence. Interestingly, in 1738 when she was twenty years old, a series of essays were published titled Propositiones Philosophiae (Propositions of Philosophy), which were based on her presentations at these forums. In 1748, she published Instituzioni Analitiche Della Gioventu Italiana (Analytical Institutions for the Use of Italian Youth), which encompassed two large volumes and presented her treatment of algebra and both integral and differential calculus. This work was well received by mathematicians all over Europe. A report on it made by a committee of the renowned Académie des Sciences in Paris states: "It took much skill and sagacity to reduce, as the author has done, to almost uniform methods these discoveries scattered among the works of modern mathematicians and often presented by methods very different from each other. Order, clarity, and precision reign in all parts of this work. We regard it as the most complete and best made treatise." One form of her fame came from a cubic curve known in Italian as versiera , which over the years has become confused with the word for witch, namely, versicra and ultimately gave the name in English as the "Witch of Agnesi.

" . [T]his entire work so impressed Pope Benedict XIV that in 1750 he appointed Agnesi to the position of professor of mathematics at the University of Bologna. Soon thereafter, she gravitated more and more to religious studies and actually never visited Bologna again. After her father died in 1752, she completely dedicated herself to religious studies and charitable work. Agnesi died on January 9, 1799, in one of the charity poorhouses that she directed.