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Unexplored Corners of the Earth. In many periods of history, women have been discouraged from applying their minds to mathematics—but a few persevered. The world- altering contributions of these 1. HYPATIAHypatia (c. Her father Theon was a famous mathematician in Alexandria who wrote commentaries on Euclid’s Elements and works by Ptolemy.
Theon taught his daughter math and astronomy, then sent her to Athens to study the teachings of Plato and Aristotle. Father and daughter collaborated on several commentaries, but Hypatia also wrote commentaries of her own and lectured on math, astronomy, and philosophy.
Sadly, she died at the hands of a mob of Christian zealots. EMILIE DU CHATELETMaurice Quentin de La Tour via Wikipedia // Public Domain. Emilie Du Chatelet (1.
Paris in a home that entertained several scientists and mathematicians. Although her mother thought her interest in math was unladylike, her father was supportive.
Chatalet initially employed her math skills to gamble, which financed the purchase of math books and lab equipment. In 1. 72. 5 she married an army officer, the Marquis Florent- Claude du Chatalet, and the couple eventually had three children. Her husband traveled frequently, an arrangement that provided ample time for her to study mathematics and write scientific articles (it also apparently gave her time to have an affair with Voltaire). From 1. 74. 5 until her death, Chatalet worked on a translation of Isaac Newton’s Principia. She added her own commentaries, including valuable clarification of the principles in the original work. SOPHIE GERMAINSophie Germain (1.
French Revolution. Since the fighting raged around her home, Germain could not explore the streets of Paris—instead she explored her father’s library, teaching herself Latin and Greek and reading respected mathematical works. Germain’s family also tried to discourage her academic leanings. Not wanting her to study at night, they denied her a fire in her room, but she lit candles and read anyway, bundled in blankets. Since women’s educational opportunities were limited, Germain studied secretly at the Ecole Polytechnique, using the name of a previously enrolled male student. That worked until the teachers noticed the dramatic improvement in the student’s math skills. Although Germain never worked as a mathematician, she studied independently and wrote about the subject.
Captain James Cook FRS (7 November 1728 – 14 February 1779) was a British explorer, navigator, cartographer, and captain in the Royal Navy. Cook made detailed maps.
She is best known for her work on Fermat’s Last Theorem, considered at the time to be one of the most challenging mathematical puzzles. A 1. 7th century mathematician named Pierre de Fermat claimed he could prove that the equation x^n + y^n = z^n had no integer solution when n was greater than 2, but his proof was never written down.
Germain proposed a new way of looking at the problem. Germain also became the first woman to win a prize from the Paris Academy of Sciences, for writing about elasticity theory.
Today that prize is known as the Sophie Germain Prize. MARY SOMERVILLEThomas Phillips via Wikipedia // Public Domain. Mary Somerville (1.
Scotland, and was not particularly interested in academics as a child—she only attended school for a year. However, when she encountered an algebra symbol in a puzzle at age 1. Her parents tried to discourage her, worried that her intellectual preoccupations might drive her insane. Her second husband, Dr. William Somerville, an inspector of the Army Medical Board, was proud of her work in mathematics and astronomy.
For her work translating a book titled Celestial Mechanics and adding commentary, she was named an honorary member of the Royal Astronomical Society. Physicist Sir David Brewster called her “certainly the most extraordinary woman in Europe—a mathematician of the very first rank with all the gentleness of a woman.” When John Stuart Mill petitioned the British government for women’s votes, he filed his petition with Somerville’s signature first. She was proof that women were men’s intellectual equals. ADA LOVELACEAlfred Edward Chalonvia Wikipedia // Public Domain. The next time you download some electronica, you may want to remember Augusta Ada King- Noel, Countess of Lovelace (1.
Lovelace was born during the brief marriage of poet George, Lord Byron and Anne Milbanke, Lady Wentworth. Her mother did not want her to be a poet like her father and encouraged her interest in mathematics and music. As a teenager, Ada began to correspond with Charles Babbage, a professor at Cambridge. At the time, Babbage was working on his ideas for a calculating machine called the Analytical Engine, now considered a precursor to the computer.
Babbage was solely focused on the calculating aspects, but Lovelace supplied notes that helped envision other possibilities, including the idea of computer- generated music. Lovelace also translated an article about the Analytic Engine by French mathematician Louis Menebrea. Her notes include an algorithm showing how to calculate a sequence of numbers, which forms the basis for the design of the modern computer. It was the first algorithm created expressly for a machine to perform. Lovelace was a countess after her marriage, but she preferred to describe herself as an analyst and a metaphysician.
Babbage called her “the enchantress of numbers”—but she might also be called the world’s first computer programmer. FLORENCE NIGHTINGALEFlorence Nightingale (1. In her efforts to improve the survival rates of hospital patients, Nightingale became a statistician. When the “lady with the lamp” returned from service during the Crimean War, she expressed sadness about how many soldiers had become sick and died while lying in the hospital. The figures she gathered indicated that a lack of sanitation was the primary reason for the high mortality rate. Efforts were instituted to make hospitals cleaner and thus safer. Not only did Nightingale’s discovery save lives and change hospital protocol forever, but she also designed charts that were easy on the Queen’s eyes.
Statistics had been presented with graphics only rarely before, and Nightingale’s work helped pioneer the field of applied statistics. She is particularly known for inventing a new kind of graph known as a coxcomb, which was a variation on a pie chart. She said that the graph was designed “to affect thro’ the Eyes what we fail to convey to the public through their word- proof ears.”7. EMMY NOETHERLike Hypatia, Emmy Noether (1.
Her father, Max Noether, was a German math professor, but becoming a math teacher would be a longer process for her. After being certified to teach English and French, she also wanted a degree in mathematics, but she had to wait—the University of Erlangen in Bavaria did not let women officially enroll until 1. Noether eventually received her doctorate in mathematics, but because her university had a policy against hiring female professors, she instead helped her father in his work at the Mathematics Institute in Erlangen (without being paid), researching and writing papers on the side. In 1. 91. 8 she proved two theorems, one of which is now known as . Finally, in 1. 92. But her teaching career was short- lived. Because of growing anti- Semitism, she and other Jewish mathematicians had to flee Germany in 1.
She moved to the United States, and taught at Bryn Mawr College until her death. After her death in 1. Albert Einstein described Noether in a letter to The New York Times with these words: . MARY CARTWRIGHTMary Cartwright (1. She was the first woman to receive the Sylvester Medal for mathematical research and the first to serve as president of the London Mathematical Society (1.
In 1. 91. 9 she was one of only five women studying mathematics at Oxford University. When she did not score well on her tests, she briefly considered giving up math. Fortunately, she chose to persevere, and went on to lecture at Cambridge University. She later earned a doctorate in philosophy and had her thesis published in the Quarterly Journal of Mathematics. After being awarded a research fellowship, she went on to publish more than 1. One of her theorems, known as Cartwright's Theorem, is still frequently applied in signal processing. She also contributed to the study of chaos theory.
In 1. 96. 9 Queen Elizabeth II honored Cartwright’s accomplishments by proclaiming her Dame Mary Cartwright. DOROTHY JOHNSON VAUGHANDorothy Vaughan (left) at NACA. Image credit: Beverly Golemba via Wikipedia // Public Domain. The excitement of space travel was made possible by years of painstaking work conducted by “human computers”—specifically, a group of mathematically proficient women who calculated a variety of scientific and mathematical data at the National Advisory Committee for Aeronautics (NACA), which later became NASA. Dorothy Johnson Vaughan (1. African- American female mathematicians at NACA in the December 2. Hidden Figures. After working as a math teacher, Vaughan took a job at NACA in 1.
In 1. 94. 9, she was promoted to lead the division’s segregated work group West Area Computers, which was entirely composed of African- American female mathematicians. She became an expert in coding languages such as FORTRAN (now a popular language for high- performance computing). She described working in space research as being on “the cutting edge of something very exciting.”1.
MARJORIE LEE BROWNEMathematician and educator Marjorie Lee Browne (1. African- American women to acquire a Ph. D. Becoming a respected educator meant overcoming personal tragedy (the death of her mother at a young age), as well as race and gender discrimination. Fortunately, her mathematically gifted father and teacher stepmother encouraged her educational interests. She attended a private school, graduated Howard University cum laude and earned her doctorate at the University of Michigan. Browne taught math at North Carolina College (now North Carolina Central University), where she was named chair of the math department in 1. She helped her school acquire grants, including a 1.
Who Was First? But in recent years, as new evidence came to light, our understanding of history has changed. We know now that Columbus was among the last explorers to reach the Americas, not the first. And long before that, some scholars say, the Americas seem to have been visited by seafaring travelers from China, and possibly by visitors from Africa and even Ice Age Europe. After seven years they returned home and reported that they had discovered a land covered with luxuriant vegetation, believed by some people today to have been Newfoundland. All along, of course, the two continents we now call North and South America had already been . While those Native American groups differed greatly from one another, they all performed rituals and ceremonies, songs and dances, that brought back to mind and heart memories of the ancestors who had come before them and given them their place on Earth. Who were the ancestors of those Native Americans?
Where did they come from, when did they arrive in the Americas, and how did they make their epic journeys? Admiral of the Ocean Sea. Christopher Columbus was having trouble with his crew. His fleet of three small sailing ships had left the Canary Islands nearly three weeks earlier, heading west across the uncharted Ocean Sea, as the Atlantic was known.
He had expected to reach China or Japan by now, but there was still no sign of land. None of the sailors had ever been so long away from the sight of land, and as the days passed, they grew increasingly restless and fearful. The Ocean Sea was known also as the Sea of Darkness. Hideous monsters were said to lurk beneath the waves—venomous sea serpents and giant crabs that could rise up from the deep and crush a ship along with its crew.
And if the Earth was flat, as many of the men believed, then they might fall off the edge of the world and plunge into that fiery abyss where the sun sets in the west. What's more, Columbus was a foreigner—a red- headed Italian commanding a crew of tough seafaring Spaniards—and that meant he couldn't be trusted. When he refused, some of the sailors whispered together of mutiny. They wanted to kill the admiral by throwing him overboard. But, for the moment, the crisis passed. Columbus managed to calm his men and persuade them to be patient a while longer. I am told by a few trusted men (and these are few in number!) that if I persist in going onward, the best course of action will be to throw me into the sea some night.
One, which he kept secretly and showed to no one, was accurate, recording the distance really sailed each day. The other log, which he showed to his crew, hoping to reassure them that they were nowhere near the edge of the world, deliberately underestimated the miles they had covered since leaving Spain. There were more rumblings of protest and complaint from the crew. The men seemed willing to endure no more. On October 1. 0, Columbus announced that he would give a fine silk coat to the man who first sighted land.
The sailors greeted that offer with glum silence. What good was a silk coat in the middle of the Sea of Darkness? Later that day, Columbus spotted a flock of birds flying toward the southwest—a sign that land was close. He ordered his ships to follow the birds. The next night, the moon rose in the east shortly before midnight. About two hours later, at two A. M. At dawn, the three ships dropped anchor in the calm, blue waters just offshore.
They had arrived at an island in what we now call the Bahamas. Excited crew members crowded the decks. People were standing on the beach, waiting to greet them.
The natives had no weapons other than wooden fishing spears, and they were practically naked. Install Granite Slab Shower Walls. Who were these people?
And what place was this? They must have reached the Indies, he thought—islands reputedly near India and known today as the East Indies. So he decided that those people on the beach must be . China and Japan, he believed, lay a bit farther to the north. Though Christopher Columbus was an Italian born in Genoa, he had lived for years in Portugal, where he worked as a bookseller, a mapmaker, and a sailor. He had sailed on Portuguese voyages as far as Iceland in the North Atlantic, and down the coast of Africa in the South Atlantic.
During his days at sea, he read books on history, geography, and travel. Like most educated people at the time, Columbus believed that the Earth was round—not flat, as some ignorant folks still insisted.
The Ocean Sea was seen as a great expanse of water surrounding the land mass of Eurasia and Africa, which stretched from Europe in the west to China and Japan in the far distant east. If a ship left the coast of Europe, sailed west toward the setting sun, and circled the globe, it would reach the shores of Asia—or so Columbus thought. In the past, European explorers and traders had taken the overland route to the Far East, with its precious silks and spices.
They traveled for months by horse and camel along the Silk Road, an ancient caravan trail that crossed deserts and climbed dizzying mountain peaks. Marco Polo had followed the Silk Road on his famous journey to China two centuries earlier. But recently, this land route to Asia, controlled in part by the Turks, had been closed to Europeans. And in any case, Columbus was convinced that he could find an easier and faster route to Asia by sailing west. There were plenty of stories circulating in those years about the possibility of sailing directly from Europe to Asia, an idea first considered by the ancient Greeks. Columbus owned a book called Imago Mundi, or Image of the World, by a French scholar, Pierre d'Ailly, who argued that the Ocean Sea wasn't as wide as it seemed and that a ship driven by favorable winds could cross it in a few days. Next to that passage in the margin of the book, Columbus had written: .
Portugal was Europe's leading maritime power. Portuguese explorers in search of slaves, ivory, and gold had already discovered rich kingdoms and colossal rivers in western Africa and would soon reach the Cape of Good Hope at Africa's southern tip. From there, they would be able to sail across the Indian Ocean to the famed Spice Islands of southeast Asia. King John listened to what Columbus had to say, then submitted the Italian sailor's plan to a committee of mapmakers, astronomers, and geographers. The distinguished experts declared that Asia must be much farther away than Columbus thought.
They said that no expedition could be fitted out with enough food and water to sail across such an enormous expanse of sea. Rejected by the Portuguese king, Columbus decided to approach King Ferdinand and Queen Isabella of Spain, a country he had never before visited. Well- connected friends gave him letters of introduction to the inner circle of the Spanish royal court. Ferdinand and Isabella seemed curious about the route to Asia that Columbus proposed.
Like King John, they too appointed a committee of inquiry to consider the matter, but those experts came to the same negative conclusion: Columbus's claim about the distance to China and the ease of sailing there could not possibly be true. Columbus persisted. He talked at length to members of the Spanish court and convinced some of them, but Ferdinand and Isabella twice rejected his appeal for ships. Finally, angry and impatient after six discouraging years in Spain, he threatened to seek support from the king of France. Columbus actually set out for France, riding a mule down a dusty Spanish road. If another king sponsored Columbus, and his expedition turned out to be a success, then the Spanish monarchs would be embarrassed.
They would be criticized in Spain. Let Columbus risk his life, the advisors said. Let him seek out . And so Ferdinand and Isabella decided to take a chance.
They dispatched a messenger to intercept Columbus on the road and bring him back to court. They were ready to grant him a hereditary title, Admiral of the Ocean Sea, and the right to a tenth of any riches—pearls, gold, silver, silks, spices—that he brought back from his voyage. And they agreed to supply two ships for his expedition.
Columbus himself raised the money to hire a third ship. A half hour before sunrise on August 3, 1.
Nina, the Pinta, and the Santa Mar. They were small, lightweight ships called caravels, swift and maneuverable, each with three masts, their white sails with big red crosses billowing before the wind. They had on board food that would last—salted cod, bacon, and biscuits, along with flour, wine, olive oil, and plenty of water, enough for a year. In his small cabin, Columbus kept several hourglasses to mark the passage of time, a compass, and an astrolabe, an instrument for calculating latitude by observing the movement of the sun. The little fleet stopped for repairs at La Gomera in the Canary Islands, a Spanish possession off the coast of Morocco. On September 6, after praying at the parish church of San Sebastian (which still looks out over the ocean today), Columbus and his three ships set sail again, heading due west, moving now through the unknown waters of the Ocean Sea.
Five weeks later, on October 1. Columbus called the place where they landed San Salvador—the first of many Caribbean islands that he would name. The natives who greeted him called their island Guanahani. They themselves were a people known as the Tainos, the largest group of natives inhabiting the islands of what we today call the West Indies.
He was impressed by their good looks and apparent robust health. These are tall people and their legs, with no exceptions, are quite straight, and none of them has a paunch. And as Columbus and his men noticed right away, some of them wore gold earrings and nose rings. They offered gifts to the European visitors—parrots, wooden javelins, and balls of cotton thread. And he wrote enthusiastically in his journal of the lush tropical beauty of the islands, the sweet singing of birds .