Melanoma, the deadliest form of skin cancer, claims more than 9,000 lives in the United States every year. The rate has been rising over the past 30 years and it’s now one of the most common cancers in people younger than 30 years old, particularly young women.
Although genetics can increase your risk of melanoma, the best way to prevent skin cancer is to reduce sun exposure by wearing protective clothing, applying sunscreen and simply staying out of the sun.
The Melanoma Research Alliance has teamed up with experts from the charitable initiative Stand Up to Cancer to clear up common myths about melanoma.
Myth: If your skin tans but doesn’t burn, you cannot get skin cancer.
Fact: Sun exposure of all levels can contribute to cancer development. Even people who don’t usually burn can get melanoma.
Myth: Tanning booths are safe because they are not “real sun.”
Fact:Tanning beds are not safer than natural sun exposure. Most tanning beds utilize UVA rays, which penetrate to the deeper layers of the skin and may increase the risk of melanoma. They also use UVB rays, the cause of most sunburns. The World Health Organization classifies tanning beds as “carcinogenic to humans.” Women who use tanning beds more than once a month are 55 percent more likely to develop melanoma, the U.S. National Cancer Institute reports.
Myth: One application of sunscreen daily is sufficient to protect against sun damage.
Fact:Sunscreen must be applied frequently throughout the day during sun exposure, particularly if it could be washed off by sweat or water.
Myth: “Adequate” use of sunscreen will prevent melanoma.
Fact: Although sunscreen can help prevent skin cancers, it only provides minimal protection. It’s also important to limit sun exposure and cover up with protective clothing and gear.
Myth: If a spot that has been on your body for years changes but hasn’t gotten much bigger, it can’t become melanoma.
Fact:Many melanomas occur in pre-existing spots or moles. A doctor should evaluate all moles, lesions or spots that have changed. People with multiple moles should undergo routine full-body exams by a dermatologist.
Myth: Melanoma can only develop on body parts where the “sun can shine.”
Fact: Some types of melanoma are not related to sun exposure and can occur in unexpected places, such as the vagina, the rectum, inside the mouth, the soles of the feet and the palms of the hands.
Monday 17 June 2013
Thursday 13 June 2013
Before Marie Curie, these women dedicated their lives to science and made significant advances
When it comes to the topic of women in science, Marie Curie usually dominates the conversation. After all, she discovered two elements, was the first women to win a Nobel Prize, in 1903, and was the first person to win a second Nobel, in 1911. But Curie was not the first female scientist. Many other brilliant, dedicated and determined women have pursued science over the years.
Emilie du Chatelet (1706 – 1749)
Gabrielle-Emilie Le Tonnelier de Breteuil, the daughter of the French court’s chief of protocol, married the marquis du Chatelet in 1725. She lived the life of a courtier and bore three children. But at age 27, she began studying mathematics seriously and then branched into physics. This interest intensified as she began an affair with the philosopher Voltaire, who also had a love of science. Their scientific collaborations—they outfitted a laboratory at du Chatelet’s home, Chateau de Cirey, and, in a bit of a competition, each entered an essay into a contest on the nature of fire (neither won)—outlasted their romance. Du Chatelet’s most lasting contribution to science was her French translation of Isaac Newton’s Principia, which is still in use today. At age 43, she fell in love with a young military officer and became pregnant; she died following complications during the birth of their child.
Caroline Herschel (1750 – 1848)
Herschel was little more than the household drudge for her parents in Hanover, Germany (she would later describe herself as the “Cinderella of the family”), when her older brother, William, brought her to England in 1772 to run his household in Bath. After she mastered the art of singing—to accompany William, who was the organist for the Octagon Chapel—her brother switched careers and went into astronomy. Caroline followed. In addition to assisting her brother in his observations and in the building of telescopes, Caroline became a brilliant astronomer in her own right, discovering new nebulae and star clusters. She was the first woman to discover a comet (she discovered eight in total) and the first to have her work published by the Royal Society. She was also the first British woman to get paid for her scientific work, when William, who had been named the king’s personal astronomer after his discovery of Uranus in 1781, persuaded his patron to reward his assistant with an annual salary. After William’s death in 1822, Caroline retired to Hanover. There she continued her astronomical work, compiling a catalogue of nebulae—the Herschels’ work had increased the number of known star clusters from 100 to 2,500. She died in 1848 at age 97 after receiving many honors in her field, including a gold medal from the Royal Astronomical Society.
Mary Anning (1799 – 1847)
In 1811, Mary Anning’s brother spotted what he thought was a crocodile skeleton in a seaside cliff near the family’s Lyme Regis, England, home. He charged his 11-year-old sister with its recovery, and she eventually dug out a skull and 60 vertebrae, selling them to a private collector for £23. This find was no croc, though, and was eventually named Ichthyosaurus, the “fish-lizard.” Thus began Anning’s long career as a fossil hunter. In addition to ichthyosaurs, she found long-necked plesiosaurs, a pterodactyl and hundreds, possibly thousands, of other fossils that helped scientists to draw a picture of the marine world 200 million to 140 million years ago during the Jurassic. She had little formal education and so taught herself anatomy, geology, paleontology and scientific illustration. Scientists of the time traveled from as far away as New York City to Lyme Regis to consult and hunt for fossils with Anning.
Mary Somerville (1780 – 1872)
Intrigued by the x’s and y’s in the answer to a math question in a ladies’ fashion magazine, 14-year-old Mary Fairfax of Scotland delved into the study of algebra and mathematics, defying her father’s injunction against such pursuits. Her studies were sidetracked by a marriage, in 1804, to a Russian Navy captain, but after his death she returned to Edinburgh and became involved in intellectual circles, associating with people such as the writer Sir Walter Scott and the scientist John Playfair, and resumed her studies in math and science. Her next husband, William Somerville, whom she wed in 1812, supported these efforts, and after they moved to London, Mary became host to her own intellectual circle, which included the astronomer John Herschel and the inventor Charles Babbage. She began experimenting on magnetism and produced a series of writings on astronomy, chemistry, physics and mathematics. She translated astronomer Pierre-Simon Laplace’s The Mechanism of the Heavens into English, and although she was unsatisfied with the result, it was used as a textbook for much of the next century. Somerville was one of the first two women, along with Caroline Herschel, to be named honorary members of the Royal Astronomical Society.
Maria Mitchell (1818 – 1889)
Young Maria Mitchell learned to observe the stars from her father, who used stellar observations to check the accuracy of chronometers for Nantucket, Massachusetts, whalers and taught his children to use a sextant and reflecting telescope. When Mitchell was 12, she helped her father record the time of an eclipse. And at 17, she had already begun her own school for girls, teaching them science and math. But Mitchell rocketed to the forefront of American astronomy in 1847 when she spotted a blurry streak—a comet—through her telescope. She was honored around the world, earning a medal from the king of Denmark, and became the first woman to be elected to the American Academy of Arts and Sciences. In 1857 Mitchell traveled to Europe, where she visited observatories and met with intellectuals, including Mary Somerville. Mitchell would write: “I could not help but admire [her] as a woman. The ascent of the steep and rugged path of science has not unfitted her for the drawing room circle; the hours of devotion to close study have not been incompatible with the duties of wife and mother.” Mitchell became the first female astronomy professor in the United States, when she was hired by Vassar College in 1865. There she continued her observations, particularly those of the Sun, traveling up to 2,000 miles to witness an eclipse.
Emilie du Chatelet (1706 – 1749)
Gabrielle-Emilie Le Tonnelier de Breteuil, the daughter of the French court’s chief of protocol, married the marquis du Chatelet in 1725. She lived the life of a courtier and bore three children. But at age 27, she began studying mathematics seriously and then branched into physics. This interest intensified as she began an affair with the philosopher Voltaire, who also had a love of science. Their scientific collaborations—they outfitted a laboratory at du Chatelet’s home, Chateau de Cirey, and, in a bit of a competition, each entered an essay into a contest on the nature of fire (neither won)—outlasted their romance. Du Chatelet’s most lasting contribution to science was her French translation of Isaac Newton’s Principia, which is still in use today. At age 43, she fell in love with a young military officer and became pregnant; she died following complications during the birth of their child.
Caroline Herschel (1750 – 1848)
Herschel was little more than the household drudge for her parents in Hanover, Germany (she would later describe herself as the “Cinderella of the family”), when her older brother, William, brought her to England in 1772 to run his household in Bath. After she mastered the art of singing—to accompany William, who was the organist for the Octagon Chapel—her brother switched careers and went into astronomy. Caroline followed. In addition to assisting her brother in his observations and in the building of telescopes, Caroline became a brilliant astronomer in her own right, discovering new nebulae and star clusters. She was the first woman to discover a comet (she discovered eight in total) and the first to have her work published by the Royal Society. She was also the first British woman to get paid for her scientific work, when William, who had been named the king’s personal astronomer after his discovery of Uranus in 1781, persuaded his patron to reward his assistant with an annual salary. After William’s death in 1822, Caroline retired to Hanover. There she continued her astronomical work, compiling a catalogue of nebulae—the Herschels’ work had increased the number of known star clusters from 100 to 2,500. She died in 1848 at age 97 after receiving many honors in her field, including a gold medal from the Royal Astronomical Society.
Mary Anning (1799 – 1847)
In 1811, Mary Anning’s brother spotted what he thought was a crocodile skeleton in a seaside cliff near the family’s Lyme Regis, England, home. He charged his 11-year-old sister with its recovery, and she eventually dug out a skull and 60 vertebrae, selling them to a private collector for £23. This find was no croc, though, and was eventually named Ichthyosaurus, the “fish-lizard.” Thus began Anning’s long career as a fossil hunter. In addition to ichthyosaurs, she found long-necked plesiosaurs, a pterodactyl and hundreds, possibly thousands, of other fossils that helped scientists to draw a picture of the marine world 200 million to 140 million years ago during the Jurassic. She had little formal education and so taught herself anatomy, geology, paleontology and scientific illustration. Scientists of the time traveled from as far away as New York City to Lyme Regis to consult and hunt for fossils with Anning.
Mary Somerville (1780 – 1872)
Intrigued by the x’s and y’s in the answer to a math question in a ladies’ fashion magazine, 14-year-old Mary Fairfax of Scotland delved into the study of algebra and mathematics, defying her father’s injunction against such pursuits. Her studies were sidetracked by a marriage, in 1804, to a Russian Navy captain, but after his death she returned to Edinburgh and became involved in intellectual circles, associating with people such as the writer Sir Walter Scott and the scientist John Playfair, and resumed her studies in math and science. Her next husband, William Somerville, whom she wed in 1812, supported these efforts, and after they moved to London, Mary became host to her own intellectual circle, which included the astronomer John Herschel and the inventor Charles Babbage. She began experimenting on magnetism and produced a series of writings on astronomy, chemistry, physics and mathematics. She translated astronomer Pierre-Simon Laplace’s The Mechanism of the Heavens into English, and although she was unsatisfied with the result, it was used as a textbook for much of the next century. Somerville was one of the first two women, along with Caroline Herschel, to be named honorary members of the Royal Astronomical Society.
Maria Mitchell (1818 – 1889)
Young Maria Mitchell learned to observe the stars from her father, who used stellar observations to check the accuracy of chronometers for Nantucket, Massachusetts, whalers and taught his children to use a sextant and reflecting telescope. When Mitchell was 12, she helped her father record the time of an eclipse. And at 17, she had already begun her own school for girls, teaching them science and math. But Mitchell rocketed to the forefront of American astronomy in 1847 when she spotted a blurry streak—a comet—through her telescope. She was honored around the world, earning a medal from the king of Denmark, and became the first woman to be elected to the American Academy of Arts and Sciences. In 1857 Mitchell traveled to Europe, where she visited observatories and met with intellectuals, including Mary Somerville. Mitchell would write: “I could not help but admire [her] as a woman. The ascent of the steep and rugged path of science has not unfitted her for the drawing room circle; the hours of devotion to close study have not been incompatible with the duties of wife and mother.” Mitchell became the first female astronomy professor in the United States, when she was hired by Vassar College in 1865. There she continued her observations, particularly those of the Sun, traveling up to 2,000 miles to witness an eclipse.
Tuesday 11 June 2013
When i'll die, only 2 querries appear before me:
When i'll die, only 2 querries appear before me:
1) how much love have i shared, &
2) how much knowledge have i gained ?
1) how much love have i shared, &
2) how much knowledge have i gained ?
Though for me, love is nothing but endocrine hormonal/psyschological disturbances only, we should discuss upon later(2).
Because according to Sir Francis Backon-Knowledge is power
But data isn't information, information isn't knowledge, knowledge isn't understanding and understanding isn't wisdom.
Knowledge & wisdom are related to Education.
Education is the best way to train ourselves that we will secure our own well-being by concerning ourselves with others. It is possible to create a better world, a more compassionate, more peaceful world, which is not only in everyone’s interest, but is everyone’s responsibility to achieve.
Education is the manifestation of the perfection already in man-swami vivekananda.
Live as if u were to die tomorrow.Learn as if u were to live forever-Gandhi Na hi jnanen sadrusham pabitram iha
bidyate- The Gita.Scientia Potentia est (Latin) You r d sole author of ur own
destiny. Even if God is not the co-author.
"Mata sama nasti shareer poshanam,
Chinta sama nasti shareer shosanam.
Bharya sama nasti shareer toshanam
Bidya sama nasti shareer bhushanam."
knowledge only fattens us with gathering invaluable information while Wisdom is a deep understanding and realization of people, things, events or situations, resulting in the ability to apply perceptions, judgments and actions.
In mathematical language, knowledge is neither tangent nor secant to wisdom.
Only Asymptotes to Wisdom.An asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity.
I regret for the day, on which i could not peruse any Biblio(book). I will strive to read.........
Wednesday 5 June 2013
Top 10 Greatest Mathematicians
Often called the language of the universe, mathematics is fundamental to our understanding of the world and, as such, is vitally important in a modern society such as ours. Everywhere you look it is likely mathematics has made an impact, from the faucet in your kitchen to the satellite that beams your television programs to your home. As such, great mathematicians are undoubtedly going to rise above the rest and have their name embedded within history. This list documents some such people. I have rated them based on contributions and how they effected mathematics at the time, as well as their lasting effect. I also suggest one looks deeper into the lives of these men, as they are truly fascinating people and their discoveries are astonishing – too much to include here. As always, such lists are highly subjective, and as such please include your own additions in the comments!
Greek Mathematician Pythagoras is considered by some to be one of the first great mathematicians. Living around 570 to 495 BC, in modern day Greece, he is known to have founded the Pythagorean cult, who were noted by Aristotle to be one of the first groups to actively study and advance mathematics. He is also commonly credited with the Pythagorean Theorem within trigonometry. However, some sources doubt that is was him who constructed the proof (Some attribute it to his students, or Baudhayana, who lived some 300 years earlier in India). Nonetheless, the effect of such, as with large portions of fundamental mathematics, is commonly felt today, with the theorem playing a large part in modern measurements and technological equipment, as well as being the base of a large portion of other areas and theorems in mathematics. But, unlike most ancient theories, it played a bearing on the development of geometry, as well as opening the door to the study of mathematics as a worthwhile endeavor. Thus, he could be called the founding father of modern mathematics.
The only currently living mathematician on this list, Andrew Wiles is most well known for his proof of Fermat’s Last Theorem: That no positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n greater then 2. (If n=2 it is the Pythagoras Formula). Although the contributions to math are not, perhaps, as grand as other on this list, he did ‘invent’ large portions of new mathematics for his proof of the theorem. Besides, his dedication is often admired by most, as he quite literally shut himself away for 7 years to formulate a solution. When it was found that the solution contained an error, he returned to solitude for a further year before the solution was accepted. To put in perspective how ground breaking and new the math was, it had been said that you could count the number of mathematicians in the world on one hand who, at the time, could understand and validate his proof. Nonetheless, the effects of such are likely to only increase as time passes (and more and more people can understand it).
I have placed these two together as they are both often given the honor of being the ‘inventor’ of modern infinitesimal calculus, and as such have both made monolithic contributions to the field. To start, Leibniz is often given the credit for introducing modern standard notation, notably the integral sign. He made large contributions to the field of Topology. Whereas all round genius Isaac Newton has, because of the grand scientific epic Principia, generally become the primary man hailed by most to be the actual inventor of calculus. Nonetheless, what can be said is that both men made considerable vast contributions in their own manner.
Blgollo, also known as Leonardo Fibonacci, is perhaps one of the middle ages greatest mathematicians. Living from 1170 to 1250, he is best known for introducing the infamous Fibonacci Series to the western world. Although known to Indian mathematicians since approximately 200 BC, it was, nonetheless, a truly insightful sequence, appearing in biological systems frequently. In addition, from this Fibonacci also contributed greatly to the introduction of the Arabic numbering system. Something he is often forgotten for.
Haven spent a large portion of his childhood within North Africa he learned the Arabic numbering system, and upon realizing it was far simpler and more efficient then the bulky Roman numerals, decided to travel the Arab world learning from the leading mathematicians of the day. Upon returning to Italy in 1202, he published his Liber Abaci, whereupon the Arabic numbers were introduced and applied to many world situations to further advocate their use. As a result of his work the system was gradually adopted and today he is considered a major player in the development of modern mathematics.
Computer Scientist and Cryptanalyst Alan Turing is regarded my many, if not most, to be one of the greatest minds of the 20th Century. Having worked in the Government Code and Cypher School in Britain during the second world war, he made significant discoveries and created ground breaking methods of code breaking that would eventually aid in cracking the German Enigma Encryptions. Undoubtedly affecting the outcome of the war, or at least the time-scale.
After the end of the war he invested his time in computing. Having come up with idea of a computing style machine before the war, he is considered one of the first true computer scientists. Furthermore, he wrote a range of brilliant papers on the subject of computing that are still relevant today, notably on Artificial Intelligence, on which he developed the Turing test which is still used to evaluate a computers ‘intelligence’. Remarkably, he began in 1948 working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in existence. He would play the ‘part’ of the machine in testing such programs.
French Philosopher, Physicist and Mathematician Rene Descartes is best known for his ‘Cogito Ergo Sum’ philosophy. Despite this, the Frenchman, who lived 1596 to 1650, made ground breaking contributions to mathematics. Alongside Newton and Leibniz, Descartes helped provide the foundations of modern calculus (which Newton and Leibniz later built upon), which in itself had great bearing on the modern day field. Alongside this, and perhaps more familiar to the reader, is his development of Cartesian Geometry, known to most as the standard graph (Square grid lines, x and y axis, etc.) and its use of algebra to describe the various locations on such. Before this most geometers used plain paper (or another material or surface) to preform their art. Previously, such distances had to be measured literally, or scaled. With the introduction of Cartesian Geometry this changed dramatically, points could now be expressed as points on a graph, and as such, graphs could be drawn to any scale, also these points did not necessarily have to be numbers. The final contribution to the field was his introduction of superscripts within algebra to express powers. And thus, like many others in this list, contributed to the development of modern mathematical notation.
Living around 300BC, he is considered the Father of Geometry and his magnum opus: Elements, is one the greatest mathematical works in history, with its being in use in education up until the 20th century. Unfortunately, very little is known about his life, and what exists was written long after his presumed death. Nonetheless, Euclid is credited with the instruction of the rigorous, logical proof for theorems and conjectures. Such a framework is still used to this day, and thus, arguably, he has had the greatest influence of all mathematicians on this list. Alongside his Elements were five other surviving works, thought to have been written by him, all generally on the topic of Geometry or Number theory. There are also another five works that have, sadly, been lost throughout history.
Bernhard Riemann, born to a poor family in 1826, would rise to become one of the worlds prominent mathematicians in the 19th Century. The list of contributions to geometry are large, and he has a wide range of theorems bearing his name. To name just a few: Riemannian Geometry, Riemannian Surfaces and the Riemann Integral. However, he is perhaps most famous (or infamous) for his legendarily difficult Riemann Hypothesis; an extremely complex problem on the matter of the distributions of prime numbers. Largely ignored for the first 50 years following its appearance, due to few other mathematicians actually understanding his work at the time, it has quickly risen to become one of the greatest open questions in modern science, baffling and confounding even the greatest mathematicians. Although progress has been made, its has been incredibly slow. However, a prize of $1 million has been offered from the Clay Maths Institute for a proof, and one would almost undoubtedly receive a Fields medal if under 40 (The Nobel prize of mathematics). The fallout from such a proof is hypothesized to be large: Major encryption systems are thought to be breakable with such a proof, and all that rely on them would collapse. As well as this, a proof of the hypothesis is expected to use ‘new mathematics’. It would seem that, even in death, Riemann’s work may still pave the way for new contributions to the field, just as he did in life.
As well as this, he also solved the Seven Bridges of Koenigsberg problem in graph theory, found the Euler Characteristic for connecting the number of vertices, edges and faces of an object, and (dis)proved many well known theories, too many to list. Furthermore, he continued to develop calculus, topology, number theory, analysis and graph theory as well as much, much more – and ultimately he paved the way for modern mathematics and all its revelations. It is probably no coincidence that industry and technological developments rapidly increased around this time.
10
Pythagoras of Samos
Greek Mathematician Pythagoras is considered by some to be one of the first great mathematicians. Living around 570 to 495 BC, in modern day Greece, he is known to have founded the Pythagorean cult, who were noted by Aristotle to be one of the first groups to actively study and advance mathematics. He is also commonly credited with the Pythagorean Theorem within trigonometry. However, some sources doubt that is was him who constructed the proof (Some attribute it to his students, or Baudhayana, who lived some 300 years earlier in India). Nonetheless, the effect of such, as with large portions of fundamental mathematics, is commonly felt today, with the theorem playing a large part in modern measurements and technological equipment, as well as being the base of a large portion of other areas and theorems in mathematics. But, unlike most ancient theories, it played a bearing on the development of geometry, as well as opening the door to the study of mathematics as a worthwhile endeavor. Thus, he could be called the founding father of modern mathematics.
9
Andrew Wiles
The only currently living mathematician on this list, Andrew Wiles is most well known for his proof of Fermat’s Last Theorem: That no positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n greater then 2. (If n=2 it is the Pythagoras Formula). Although the contributions to math are not, perhaps, as grand as other on this list, he did ‘invent’ large portions of new mathematics for his proof of the theorem. Besides, his dedication is often admired by most, as he quite literally shut himself away for 7 years to formulate a solution. When it was found that the solution contained an error, he returned to solitude for a further year before the solution was accepted. To put in perspective how ground breaking and new the math was, it had been said that you could count the number of mathematicians in the world on one hand who, at the time, could understand and validate his proof. Nonetheless, the effects of such are likely to only increase as time passes (and more and more people can understand it).
8
Isaac Newton and Wilhelm Leibniz
I have placed these two together as they are both often given the honor of being the ‘inventor’ of modern infinitesimal calculus, and as such have both made monolithic contributions to the field. To start, Leibniz is often given the credit for introducing modern standard notation, notably the integral sign. He made large contributions to the field of Topology. Whereas all round genius Isaac Newton has, because of the grand scientific epic Principia, generally become the primary man hailed by most to be the actual inventor of calculus. Nonetheless, what can be said is that both men made considerable vast contributions in their own manner.
7
Leonardo Pisano Blgollo
Blgollo, also known as Leonardo Fibonacci, is perhaps one of the middle ages greatest mathematicians. Living from 1170 to 1250, he is best known for introducing the infamous Fibonacci Series to the western world. Although known to Indian mathematicians since approximately 200 BC, it was, nonetheless, a truly insightful sequence, appearing in biological systems frequently. In addition, from this Fibonacci also contributed greatly to the introduction of the Arabic numbering system. Something he is often forgotten for.
Haven spent a large portion of his childhood within North Africa he learned the Arabic numbering system, and upon realizing it was far simpler and more efficient then the bulky Roman numerals, decided to travel the Arab world learning from the leading mathematicians of the day. Upon returning to Italy in 1202, he published his Liber Abaci, whereupon the Arabic numbers were introduced and applied to many world situations to further advocate their use. As a result of his work the system was gradually adopted and today he is considered a major player in the development of modern mathematics.
6
Alan Turing
Computer Scientist and Cryptanalyst Alan Turing is regarded my many, if not most, to be one of the greatest minds of the 20th Century. Having worked in the Government Code and Cypher School in Britain during the second world war, he made significant discoveries and created ground breaking methods of code breaking that would eventually aid in cracking the German Enigma Encryptions. Undoubtedly affecting the outcome of the war, or at least the time-scale.
After the end of the war he invested his time in computing. Having come up with idea of a computing style machine before the war, he is considered one of the first true computer scientists. Furthermore, he wrote a range of brilliant papers on the subject of computing that are still relevant today, notably on Artificial Intelligence, on which he developed the Turing test which is still used to evaluate a computers ‘intelligence’. Remarkably, he began in 1948 working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in existence. He would play the ‘part’ of the machine in testing such programs.
5
René Descartes
French Philosopher, Physicist and Mathematician Rene Descartes is best known for his ‘Cogito Ergo Sum’ philosophy. Despite this, the Frenchman, who lived 1596 to 1650, made ground breaking contributions to mathematics. Alongside Newton and Leibniz, Descartes helped provide the foundations of modern calculus (which Newton and Leibniz later built upon), which in itself had great bearing on the modern day field. Alongside this, and perhaps more familiar to the reader, is his development of Cartesian Geometry, known to most as the standard graph (Square grid lines, x and y axis, etc.) and its use of algebra to describe the various locations on such. Before this most geometers used plain paper (or another material or surface) to preform their art. Previously, such distances had to be measured literally, or scaled. With the introduction of Cartesian Geometry this changed dramatically, points could now be expressed as points on a graph, and as such, graphs could be drawn to any scale, also these points did not necessarily have to be numbers. The final contribution to the field was his introduction of superscripts within algebra to express powers. And thus, like many others in this list, contributed to the development of modern mathematical notation.
4
Euclid
Living around 300BC, he is considered the Father of Geometry and his magnum opus: Elements, is one the greatest mathematical works in history, with its being in use in education up until the 20th century. Unfortunately, very little is known about his life, and what exists was written long after his presumed death. Nonetheless, Euclid is credited with the instruction of the rigorous, logical proof for theorems and conjectures. Such a framework is still used to this day, and thus, arguably, he has had the greatest influence of all mathematicians on this list. Alongside his Elements were five other surviving works, thought to have been written by him, all generally on the topic of Geometry or Number theory. There are also another five works that have, sadly, been lost throughout history.
3
G. F. Bernhard Riemann
Bernhard Riemann, born to a poor family in 1826, would rise to become one of the worlds prominent mathematicians in the 19th Century. The list of contributions to geometry are large, and he has a wide range of theorems bearing his name. To name just a few: Riemannian Geometry, Riemannian Surfaces and the Riemann Integral. However, he is perhaps most famous (or infamous) for his legendarily difficult Riemann Hypothesis; an extremely complex problem on the matter of the distributions of prime numbers. Largely ignored for the first 50 years following its appearance, due to few other mathematicians actually understanding his work at the time, it has quickly risen to become one of the greatest open questions in modern science, baffling and confounding even the greatest mathematicians. Although progress has been made, its has been incredibly slow. However, a prize of $1 million has been offered from the Clay Maths Institute for a proof, and one would almost undoubtedly receive a Fields medal if under 40 (The Nobel prize of mathematics). The fallout from such a proof is hypothesized to be large: Major encryption systems are thought to be breakable with such a proof, and all that rely on them would collapse. As well as this, a proof of the hypothesis is expected to use ‘new mathematics’. It would seem that, even in death, Riemann’s work may still pave the way for new contributions to the field, just as he did in life.
2
Child prodigy Gauss, the ‘Prince of Mathematics’, made his first major discovery whilst still a teenager, and wrote the incredible Disquisitiones Arithmeticae, his magnum opus, by the time he was 21. Many know Gauss for his outstanding mental ability – quoted to have added the numbers 1 to 100 within seconds whilst attending primary school (with the aid of a clever trick). The local Duke, recognizing his talent, sent him to Collegium Carolinum before he left for Gottingen (at the time it was the most prestigious mathematical university in the world, with many of the best attending). After graduating in 1798 (at the age of 22), he began to make several important contributions in major areas of mathematics, most notably number theory (especially on Prime numbers). He went on to prove the fundamental theorem of algebra, and introduced the Gaussian gravitational constant in physics, as well as much more – all this before he was 24! Needless to say, he continued his work up until his death at the age of 77, and had made major advances in the field which have echoed down through time.
Carl Friedrich Gauss
1
If Gauss is the Prince, Euler is the King. Living from 1707 to 1783, he is regarded as the greatest mathematician to have ever walked this planet. It is said that all mathematical formulas are named after the next person after Euler to discover them. In his day he was ground breaking and on par with Einstein in genius. His primary (if that’s possible) contribution to the field is with the introduction of mathematical notation including the concept of a function (and how it is written as f(x)), shorthand trigonometric functions, the ‘e’ for the base of the natural logarithm (The Euler Constant), the Greek letter Sigma for summation and the letter ‘/i’ for imaginary units, as well as the symbol pi for the ratio of a circles circumference to its diameter. All of which play a huge bearing on modern mathematics, from the every day to the incredibly complex.
Leonhard Euler
As well as this, he also solved the Seven Bridges of Koenigsberg problem in graph theory, found the Euler Characteristic for connecting the number of vertices, edges and faces of an object, and (dis)proved many well known theories, too many to list. Furthermore, he continued to develop calculus, topology, number theory, analysis and graph theory as well as much, much more – and ultimately he paved the way for modern mathematics and all its revelations. It is probably no coincidence that industry and technological developments rapidly increased around this time.
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