Abu Al-Khwarizmi by Rebecca Shoyket
Abu al- Khwarizmi was a famous Islamic mathematician. He was born in Baghdad, ca 780 AD, which is a city now in Iraq. He died around 850 AD, but there is very little information on the life of al- Khwarizmi. He was given the name “father of algebra” because he was the first of many to teach algebra in an elementary way. Along with many other scholars, Abu al- Khwarizmi studied at the House of Wisdom. The House of Wisdom is very similar to the colleges that we have now. It was a key institution in the Translation Movement and considered to have been a major intellectual center of the Islamic Golden Age. The House was an unrivalled center for the study of humanities and for Islamic science, Islamic mathematics, Islamic astronomy, Islamic medicine, Islamic chemistry, zoology and Islamic geography. His first step to earning the name of “the father of algebra”, was writing a book. The title of the book is translated to “The book on calculations by completion and balancing”.
In Al-Khwarizmi’s book, he starts with a discussion of algebra of the first and second degree, today known as linear and quadratic terms. It wasn’t until many years later when Cardano solved equations of the cubic, or third degree terms. The second part of his book, he focuses on the aspect of business and the applications involved. Al-Khwarizmi was probably the greatest mathematician of his time. He wrote and gave examples of linear and quadratic equations, into six standard forms: 1. Squares equal to roots 10x^{2 }= 20x; 2. Squares equal to numbers 10x^{2} = 25; 3. Roots equal to numbers 10x = 20; 4. Squares and roots equal to numbers x^{2} + 10x = 39; 5. Squares and numbers equal to roots x^{2} + 39 = 10x; 6. Roots and numbers equal to squares 10x + 39 = x^{2 }.
Not only is Abu al- Khwarizmi known as the “father of algebra”, but also he was also successful in other things. He also founded some basic concepts to areas like astronomy, and geography. Al- Khwarizmi was also successful in developing trigonometric tables containing the sine function, which he did in great detail. His discoveries also helped many mathematicians. From his development of trigonometric tables, they helped to form the tangent function.
I believe that Abu al–Khwarizmi was very successful in his career, discoveries in math, and in life. He was successful in many of his discoveries, because we use those in our lives still to this day. I recently learned how to find the tangent and how to use the Pythagorean theorem in my math class. If I ever had to think of who developed the theory to finding the tangent, I would have never thought it was from a man who lived a long time ago. This is why Abu al–Khwarizmi was greatly affected by the time period that he lived in. technology back then wasn’t as advanced as it is today, so it would have taken a lot more effort, and hard work to figure out something like that, compared to modern day discoveries and inventions. It also affected him greatly because he lived in a time period where the atmosphere around him provided him with very little institutional support.
Although very little is known about the life of Abu al- Khwarizmi, we do know that he discovered and came up with many theories that we still use in our everyday lives. He will always be known as the “father of algebra” for his success as a mathematician, and in many other subjects.
Charles Babbage by Joseph DiGiovanni
Charles Babbage was a 19^{th} century mathematician, philosopher, and inventor. He is credited with designing the first working mechanical computer, even though it was never fully constructed during his lifetime.
Charles Babbage was born in London, England in 1791. His father was a banker, who was responsible for his early education. Charles Babbage went to private schools and had his own tutors. He was eventually accepted into Cambridge University, where he eventually graduated top in his class of mathematics. As an undergraduate, he formed the Analytical Society with fellow mathematicians John Herschel and George Peacock in 1812. In 1814 he married Georgiana Whitmore, with whom he had 8 children, though only 3 survived to adulthood. In his early career he worked as a mathematician, mainly in the area of the calculation of functions. He spent his professional and academic career at Cambridge, where he became Lucasian Professor of Mathematics (the same post that Isaac Newton held).
The thing that Charles Babbage is remembered for the most is his work on mechanical computing. He felt that it was possible to create machines that were able to perform mathematical operations faster and with greater accuracy then humans can. His first design was something called a “difference machine”, which was designed to do mathematical computations. Babbage received some funding from his university to build a working model, but after years of effort it was never completed. He also designed a printer for his machine, which like the difference machine, was never built in his lifetime. It was not known exactly why the machines weren't completed (as they would be after his lifetime), but finances, impatience, and his own difficult personality probably all contributed. Always with a restless mind, Babbage moved on to the next challenge of designing and building an “Analytical Engine”, which would have been able to program using paper punch cards. This machine, like his difference machine was never fully constructed, though a program was written for it by fellow mathematician Ada Lovelace.
Babbage also had accomplishments in other fields such as, cryptography (decrypting several codes in his time), mechanical engineering, philosophy, and economics (investigated work theories which later became used in assembly-line production methods). He is credited with helping forming the British Association for the Advancement of Science through his paper titled "Reflections on the Decline of Science in England". He is also invented the 'cow catcher' (the steel cage on the front of trains designed to remove any obstructions on the tracks) and the ophthalmoscope (a device to study the retina).
In modern times, two of his designs were completed and functioned fully as he intended them to. This is proof that his ideas were correct, but he lacked either the means or the patience to see them through in his own time. He is considered to be the father of mechanical computer theory, and someone who is certainly ahead of his time. After his death in 1871, one of his sons, Henry Prevost Babbage, continued on his work and constructed working versions of his 'Difference Machines”, some of which survive to this day. He is buried Kensal Green Cemetery in London, England. His brain however, was saved for study, and is now in London's Hunterian Museum in the Royal College of Surgeons.
Mr. Babbage worked as a designer for computers in a time when there was no electronics or working electrical machines. His designs used the only materials that were available to him, such as gears, steam, and paper, to build his inventions. Even though the finished product weighed several tons, the fact that it did work proved that he was a genius. If he lived today, he would probably be doing great things with modern electronic computers.
The Bernoullis by India Shore
The Bernoulli family produced several exceptional mathematicians during the 17^{th} and 18^{th} centuries. Many important mathematical and physical principles were developed by members of this family during that time. Several of the family members also had very strong personalities, which led to competition and conflict between them.
The first important mathematician was Jacob Bernoulli. Jacob was the son of Nikolaus, a wealthy Swiss merchant. He originally studied to be a minster, but fell in love with mathematics and studied with many of the important mathematicians and scientists of his age, including Hudde, Robert Boyle and Robert Hooke, and Gottfried Leibniz. He became the chair of mathematics at the University of Basel, and held that post until his death in 1705. His conflicts with his brother Johann and the University authorities (whom we didn't feel supported him as much as they should), made his stay there interesting. The Bernoulli distribution, the Bernoulli theorem of statistics and probability, The Bernoulli numbers, and Bernoulli polynomials were all named after Jacob Bernoulli. Jacob Bernoulli also made great contributions and calculus and differential equations. He is most well known for his book the *Ars conjectandi*, which was published after his death by his nephew. Jacob had the logarithmic spiral and the inscription “Eadem Mutata Resurgo*”* (I shall arise the same though changed) put on his tombstone.
Johann Bernoulli was Jacob's younger brother and, like his brother, went against his father's wishes when he started to study mathematics. His father wanted him to go into the family business, but with his brother's help he took up mathematics instead. Johann became a mathematics professor at the University of Groningen, and ended up succeeding his brother at the University of Basel when he died in 1705. Even though it was his brother that helped him get started, they ended up as rivals during the time when they were both alive together. Johann, who had a reputation of being prideful, often bragged that he was the better mathematician, with his brother responding that Johann had copied his results. His competition also extended to that of his own son Daniel, with whom he backdated a paper in order for it to appear that it came out earlier than his son's did. Johann did create some important works of his own including important discoveries in calculus and differential equations.
He entered an agreement with Guillaume L'Hopital in which Johann agreed to gift credit to L'Hopital for any discoveries that he had while working for him. For that reason L'Hopital's rule was not named after Johann Bernoulli, even though he was the one that developed it. His other accomplishments include the Catenary solution, Bernoulli's identity, and Bernoulli's rule. Johann died in 1748 at the age of 80 years old, and had the inscription “The Archimedes of our Age” on his tombstone.
Johann's son Daniel was also an important mathematician of the age. Once again, he didn't start out studying mathematics, and, at his father's urging, took up medicine first. An important turning point in his life came after he finished his doctorate in medicine and applied for the chair of anatomy and botany at the University of Basel, which was decided by drawing lots. Daniel lost, and moved to Venice where he started to study mathematics. He also studied at the Saint Petersburg Academy in Russia with his brother Nicolaus, who unfortunately drowned while they were both there together. He ended up returning to Basel, where he counting studying and teaching. In 1734, he entered a competition Paris Academy which he ended up co-winning with his father. Unfortunately, his father was so prideful at his son being considered his equal, that their relationship disintegrated after this point. His accomplishments include the Petersburg paradox, moral expectation, and principles of hydrodynamics called Bernoulli's Principle. Daniel died in 1782 at the age of 82 years old.
The interesting thing about all three of these great mathematicians was that none of their fathers wanted them to be mathematicians; even Daniel’s who was a mathematician himself. All three became mathematicians because they loved the subject and had the talent to succeed. I think that the times that they lived in also helped them with their passion – great discoveries were being made in mathematics and science at this time, with great names such as Newton, Leibniz, and Hooke becoming famous with them. Jacob’s father wanted him to become a merchant, but this age that he lived in made him a mathematician.
Georg Cantor by Mohammad Ullah
Georg Ferdinand Ludwig Philipp Cantor was born on March 3rd, 1845 and died on January 6th, 1918. He was best known for his invention of set theory. He was born in a western merchant colony in Saint Petersburg, Russia, and brought up in the city until he was eleven.
Cantor was the eldest of six children and was an outstanding violinist. He had apparently inherited his parents' considerable musical and artistic talents. When Cantor’s father became ill, his family moved to Germany in 1856, first to Wiesbaden then to Frankfurt, seeking milder winters than those of Saint Petersburg. In 1860, Cantor graduated with excellence from the Realschule in Darmstadt. His exceptional skills in mathematics, in particular trigonometry were noted. In 1862, Cantor entered the Federal Polytechnic Institute in Zürich, today the ETH Zurich. After receiving a sizeable inheritance upon his father’s unfortunate death in 1863, Cantor shifted his studies to the University of Berlin, attending lectures by Leopold Kronecker, Karl Weierstrass and Ernst Kummer. He spent the summer of 1866 at the University of Göttingen, then at a very important center for mathematical research. In 1867, Berlin granted him the PhD for a thesis on number theory.
In 1874, Cantor married Vally Guttmann and had six children. Cantor was able to support a family despite modest academic pay, thanks to his inheritance from his father. During his honeymoon in the Harz Mountains, Cantor spent much time in mathematical discussions with Richard Dedekind, whom he befriended two years earlier while on Swiss holiday. Cantor was promoted to Extraordinary Professor in 1872 and made full Professor in 1879. To attain the latter rank at the age of 34 was a remarkable accomplishment, but Cantor wanted a job at a more prominent university. At that time, Berlin was the leading German university. However, his work was too controversial for that to happen. Kronecker, who headed mathematics at Berlin until his death in 1891, was gradually becoming uncomfortable with the possibility of having Cantor as a colleague. This is due to the fact that Kronecker viewed Cantor as a "corrupter of youth" for teaching his ideas to the younger generation of mathematicians. Worse yet, Kronecker, a well-established figure within the mathematical community and Cantor's former professor, fundamentally disagreed with the thrust of Cantor's work.
As stated before, Cantor was the inventor of set theory. Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. Set theory is used in nearly every mathematical subject, such as Venn and Euler diagrams.
Cantor was gradually becoming more and more depressed as criticism of his work increased. It got so bad that he went to a lecture on philosophy, rather than mathematics. He also studied Elizabethan literature to get his mind off mathematics for a while. This break helped him. In 1899, however, his youngest son, Rudolph, died while Cantor was delivering a lecture on his views on Baconian Theory and William Shakespeare. This tragedy drained much of Cantor’s passion for mathematics. In 1904, Cantor was outraged and agitated by a paper presented by Julius König at the Third International Congress of Mathematicians. The paper attempted to prove that the basic tenets of transfinite set theory were false. Since it had been read in front of his daughters and colleagues, Cantor perceived himself as having been publicly humiliated.
Although Ernst Zermelo demonstrated less than a day later that König's proof had failed, Cantor remained shaken. Cantor suffered from chronic depression for the rest of his life. Cantor retired in 1913, and suffered from poverty, even malnourishment, during World War I. The public celebration of his 70th birthday was canceled because of the war. He died on January 6, 1918 in the sanatorium where he had spent the final year of his life.
Paul Erdos by Stephanie Thomas
Paul Erdos was born March 26, 1913 to a Hungarian family. Paul Erdos parents Lajos and Anna had two daughters, both of which had died of scarlet fever a few days before Paul was born. This had a major effect on how his parents treated him. Paul Erdos parents were extremley protective of him and they introduced mathematics to him, both Lajos and Anna were teachers of mathematics.
While Lajos was captured by the Russian army, Pauls mother kept him home with a tutor to teach him for the earlier years of his life being the over protective mother she was. Then chaos arose by the end of World War I. Anna still worked as a teacher because she didn’t want to see the childrens education suffer. By 1920 Paul Erdos father returned home from captivity. While in captivity he learned english but did not know how to pronounce the words but was still determined to teach Paul. This will give Paul a weird english accent being a defining character in his life.
In the year 1930, even though there were restictions over Jewish people entering the universities Paul Erdos was allowed to enter because he was the winner of the national examination. In 1934 Paul received his doctorate from the University Pázmány Péter in Budapest. He eventually was forced out of Hungary for being Jewish and travelled in the United Kingdom. In 1938 Erdős was on his way to the United States where he took up a fellowship at Princeton. He hoped for his fellowship to be renewed for another 6 months but Paul Erdos did not meet Princeton's standards or specified qualities so he was given only a six month extension instead of the year he expected. Princeton believed that Paul Erdos uncouth and unconventional. Erdos’ friend Ulam asked him to visit Madison to help them out.
Paul Erdos devoted the rest of his live to solving seemingly unsolvable math problems. By the age of 20 Paul had discovered an intriguing proof for Chebyshev's theorem which was famous within the number theory that for each number greater than one, there is always at least one prime number between it and its double. Paul himself founded the amazing field of discrete mathematics, solving math problems in number theory the area of number theory or , and the foundation of computer science. Paul has wrote 1500 papers of working. An Erdos number was the “collaborative distance” between Paul Erdos and a mathematician. It became an honor to collaborate with Paul Erdos by other mathematicians.
Paul Erdos devoted his entire life to mathematics. Paul never had much he considered property a nuisance and refused settling down in fear that it would mess up his ability to focus on difficult problems and collaborating with distant collegues. He lived with other mathematians, sharing his ideas from one place to the next.
Paul Erdos lived in a time of discrimination and hate. He was sent out of the country he was born in. Paul opted to immigrate to the United States because of the political tensions from WWII, and this didn’t alow him to further himself in mathematic achievement in any way possible. Also in the later years he was denied to return back to his homeland because he was Jewish. Paul Erdos was an bizarre man, even though he was a genius he had social flaws and never really attached to anything but his numbers.Paul then worked on mathematics more thoroughly and spent the remainder of his life doing so.
Pierre de Fermat by Julia Zubrovich
*"I have a truly marvelous demonstration of this proposition which this margin is too small to contain." -Pierre de Fermat*
Pierre de Fermat was born on August 17, 1601 in Beaumont-de-Lomange, France. Fermat’s father and uncle were wealthy merchants and his mother’s family was involved with legal professions. He had one brother and two sisters. It is not certain, but he probably attended the Franciscan monastery in his hometown. In the 1620s, Fermat attended the University of Toulouse. He then moved to Bordeaux, and after that he moved to Orleans to study law. He gained a Bachelor’s Degree in law in 1631. Fermat went on to practice law, as well as get married in 1631 and have five children. He and his children were very involved in the Catholic religion. Fermat also became a government official. He rose in government office very quickly. He had to change his name from Pierre Fermat to Pierre de Fermat because of the office he held. Apart from his impressive career, he was also known as an excellent linguist. He spoke Latin, Basque, Greek, Italian, and Spanish.
Fermat is considered one of the greatest mathematicians of the seventeenth century. Fermat never wanted any of his math published, for it was more of a hobby to him. Fermat only published his work once, and it was published anonymously. Fermat sent many of his theories to famous French mathematicians. He did not want to let his love of math take over the little time he had besides work. He, along with his good friend Blaise Pascal, is considered to be one of the founders of the probability theory. He, along with Rene Descartes, is considered as a founder of analytic geometry. Fermat discovered a simpler method of quadrating parabolas, which were originated by Archimedes. He also provided a law on light travel, as well as finding a way to calculate the greatest and smallest ordinates of curved lines.
His most important and most memorable work was done in the development of a modern number theory. His theory (known as Fermat’s Last Theorem) states that *x*^{n}^{ } + *y*^{n} = *z*^{n} has no non-zero integer solutions for *x*, *y*, and *z* when n is greater than two. Fermat provided little to no proof of the procedures for reaching his conclusions, including his theorems. Even the theorem above was not proven until 1993 because he didn’t leave any proof on the original document. Andrew J. Wiles proved it. Fermat was dubbed the “Prince of Amateurs” because of his great achievements in mathematics.
In the 1650s, there was a plague that broke out that killed many older men. Fermat caught this sickness and someone assumed he died of the plague. His death was wrongly reported in 1653. It was later corrected that he was in fact, alive and that they no longer feared for his health. Fermat gained little recognition for his discoveries in his time. The only reason he is recognized today is because the letters he sent to other famous mathematicians were saved.
Pierre de Fermat died in Toulouse on January 12^{th}, 1665. His son, Samuel de Fermat, edited his father’s works.
Sophie Germain by Julia Zubrovich
Sophie Germain was born in Paris, France on April 1st, 1776. Her father, Ambroise-Fransois, was a wealthy silk merchant who became the Bank of France's director later. Her mother was Marie Madeleine Gruguelin. Sophie also had two sisters, Marie-Madeleine and Angelique-Ambroise.
Sophie took an interest in mathematics when she was 13 years old. She was staying at home because there was unrest in Paris during the French Revolution. Sophie started teaching herself math by reading her father’s books after she felt inspired by a story of Archimedes’ death. According to the story, he was killed while reading geometry. Her family considered math to be an inappropriate subject for a girl and didn't support her studies at first. Sophie’s parents wanted her to stop studying so they took away her light, her fire, and her clothes. She would wrap herself in covers and still study. She taught herself math, Latin, and Greek by reading the books from her father's library.
The Ecole Polytechnique was founded in Paris in 1795. Sophie was not able to attend because women weren't accepted into that school. She gained the notes from the lectures and studied from them. Sophie took an identity of M. LeBlanc and submitted a paper under his name to J. L. Lagrange who taught in the school. The teacher was very impressed with her work and even though she was a girl from the middle class family, he became her mentor, and even included some of her work in the second edition of his book "Theorie".
In 1804, Sophie started writing to German mathematician Carl Friedrich Gauss. She sent him her work on number theory and once again she used the identity of M. LeBlanc. Gauss praised her work and found out several years later that M. LeBlanc was really a gifted woman. He also mentioned that Sophie Germain was one of the reasons he restarted his own work on number theory.
In 1808, the Institute de France announced a competition where the challenge was to explain a theory of Elasticity. Sophie German spent next several years working on it and she was the only person to enter the contest in 1811. She didn't win the award because there were errors in her calculations. Two years later, she was once again the only entrant to that competition, and she now got the honorable mention. Third time she submitted the work, she finally won the medal in 1815.
She continued her research until her death. She never married and didn’t have any children. Germain’s father supported her for the most of her life. Before she died of breast cancer in 1831, she wrote papers on number theory, proving that for prime exponents that are smaller than 100, there was no solution relatively prime to the exponent. Her studies made progress towards proving Fermat's Last Theorem. Another important achievement of hers is a theorem that was named after her. She also wrote a philosophy essay that was published after her death.
Today, a street, la rue Germain, and a school in Paris, L’Ecole Sophie Germain, are named after her. She is an important figure in math history, because even though she lived at the times when women weren’t allowed to enroll in the university and only aristocratic women were able to study math and sciences privately, she was a woman who taught herself and continued her research and worked on something she truly loved - Math!
G. H. Hardy by Edmond Loi
G.H. (Godfrey Harold) Hardy was an eccentric and shy man, but nevertheless he was a brilliant mathematician. Born on February 7^{th}, 1877, Hardy considered his work to be “pure mathematics.” (In other words, this math is not done to be applied elsewhere.) But, in 1908, Hardy offered a law stating that the dimensions of dominant and recessive traits would be reproduced in a large population, which __was__ important for blood group distribution. Let’s take a closer peek into this English mathematician’s life, shall we?
G.H. Hardy was born in Cranleigh, Surrey, England and both of his parents were teachers. They were also really good at math. Speaking of being really good at math, Hardy was a gifted child. For example, at age two he could write numbers up to millions. However, Godfrey Harold simply wanted to beat the other kids in math, he wasn’t passionate about it. Godfrey went to Cranleigh School until he was twelve years of age.
In 1889, Hardy was awarded a scholarship to Winchester College. This was a brilliant school, and yet the man disliked it except for the learning. G.H. Hardy entered Trinity College in Cambridge in 1896. He received fourth place on the Mathematics Tripos test after only studying for two years. He took part II of the Tripos in 1900 and was awarded a prize. Three years later Hardy earned an M.A, at that time being the highest academic degree given at English universities. Then, starting in the year 1906, he became a lecturer. In 1919 he left Cambridge to Oxford, where he was a geometry professor. In 1931 he returned to Cambridge to be a professor until 1942.
For 35 years, starting in 1911, he collaborated with John Edensor Littlewood, working in topics such as the mathematical analysis and number theory. Some of the stuff they did included the proving results in the prime number theory. This was one of the most successful mathematical collaborations in history! G.H. Hardy also collaborated with Srinivasa Ramanujan, after Ramanujan sent Hardy mathematical papers from India in 1913. (They started work in 1914) In Cambridge the duo wrote five math papers together! Godfrey calls this collaboration,” his greatest contribution to math.” Collaborating came naturally to Godfrey Harold, and he also wrote papers with mathematicians like Edmund Landau. Another one of Godfrey’s passions was cricket, and he befriended C.P. Snow for this common interest.
G.H. Hardy lived through two world wars, so the time in which he lived most defiantly affected him. He volunteered for World War 1, but was not healthy enough. He also did not believe in the fighting, but greatly respected Germany. (That opinion made it hard for G.H. to make friends) Both wars were painful for Godfrey Harold (he suffered a heart attack in 1939, age 62) and after 1945 he started to lose his intelligence and ability to play the sports. Also, this mathematician was involved in political groups like the “Union of Democratic Control” during WW1.
This mathematician’s work was greatly appreciated. Some of his honors include receiving the Sylvester Medal of Society in 1940 and the Copley Medal of Royal Society in 1947. “A mathematician’s apology”, written in 1940, was Hardy’s book describing a mathematician’s mind and math pleasures. Its power moved many towards math. The book and Hardy showed true rigor, not common in British mathematics. Also, many of his papers have been published by the Oxford University Press, in seven volumes! Of course these are not all the details about his life, but some truly significant ones. Godfrey Harold Hardy passed away on December 1^{st}, 1947. Hardy never married and his sister looked over him for the last few years he was alive. As you can see, we can remember G.H. Hardy with respect and fascination.
Joseph-Louis Lagrange by Mohammad Ullah
Joseph-Louis Lagrange was born on January 5, 1736 in Turin, Sardinia-Piedmont. Lagrange was a mix; his mother’s side was Italian and his father’s side was French. He was the oldest of his ten siblings and one of the 2 that survived to become an adult. He was mostly self-taught and was not interested in mathematics until his late teens. He went to college at Turin and joined the Berlin Academy at age 23.
Lagrange published his first mathematical work in 1754 (an analogy between the binomial theorem and the successive derivatives of the product of functions). Lagrange made his first important discovery at age nineteen, by solving the isoperimetric problem. He sent a letter to Euler that was about a more efficient way of solving the problem. In 1766, Lagrange was chosen by Euler to be the director of the Berlin Academy.
In 1758, Lagrange and his students created the Royal Academy of Science of Turin and wrote *Miscellanea Taurinesia*, five volumes of transactions. While working at the Berlin Academy for 20 years, he became good friends with Lambert. During those 20 years, Lagrange regularly won the prize from the Académie des Sciences of Paris. Only in 1772, he shared the prize with Euler. In addition to working on mathematics, Lagrange also worked on science in the Berlin Academy (he mostly worked on science).
In 1770, Lagrange proved that every positive integer is the sum of four squares. During the same year, he also created a fundamental investigation of why equations of degrees up to 4 could be solved by radicals. In 1771, Lagrange proved Wilson’s theorem to be true (*n* is prime if and only (*n*-1)! + 1 is divisible by *n*).
In 1787, Lagrange left Berlin because the death of his wife made him less happy (in 1792, Lagrange got married again, to Renée-Françoise-Adélaide Le Monnier and still had no children). He became a member of the Académie des Sciences of Paris and remained one for the rest of his life. Later on, Lagrange wrote *Mécanique analytique* to define his contributions to mechanics (because he did not write anything yet that discussed his contributions). This work made mechanics a branch of mathematical analysis. In 1790, Lagrange and other members of the committee of Académie des Sciences worked on the metric system and supported a decimal base. After this, some people referred to Lagrange as the founder of the metric system.
In 1794, Ecole Polytechnique was founded and Lagrange became its first professor of analysis. In 1797, he published the first theory of functions with a real variable in *Théorie des fonctions analytique*. Later on, Lagrange gained the respect of Napoleon and was named to the Legion of Honour and Count of the Empire in 1908. In 1910, Lagrange started to make revisions of *Mécanique analytique* but was not able to finish due to his death. He died on April 10, 1813.
Lagrange did not make many enemies while working with other mathematicians. He was lucky to survive the French Revolution and be able to work more in the field of mathematics (and science). Although Lagrange did not spend most of his life working in the field of mathematics, the contributions he made were important.
Ada Lovelace by Lester Lee
Augusta Ada Byron, famously known as Ada Lovelace, was a mathematician during the nineteenth century. She was born on December 10, 1815 and died on November 27, 1852. Her father was Lord Bryon, a famous British poet. Her mother was Anne Isabella Byron, who was highly talented in mathematics. Lord Bryon left the family a month after Augusta was born and died when she was eight. Lord Byron was the only one who called Augusta, Ada.
Ada was not allowed to walk the same path as her father because of her mother’s hatred towards her father. Therefore, Lady Byron forced Ada to have tutors in math. She was also forced to learn music, because her mother felt that music was something that can teach a girl her social skills. Personally, Ada’s favorite subject was geography, but when her mother found out, she replaced Ada’s geography classes with more math. She wanted her daughter to work hard and long on her lessons. Punishments were: being locked in, staying still, and writing apologies. People in the family were afraid that Lady Byron pushed Ada too hard. From a young age, Ada was often very ill. She had terrible headaches at 8 that blocked some of her vision. At age 13, she was paralyzed from measles. From that, she had to rest for a year and walk in crutches.
One of Ada's tutors, William King, complemented on how Ada excelled his own mathematical studies. Another tutor, the mathematician Augustus De Morgan, also predicted that Ada might be a real mathematician later on in life. At the age of seventeen, Ada met Mary Somerville. She sent math books to her, and nourished Ada into loving mathematics. She was a friend of Charles Babbage, so she introduced him to her at a party. Ada became fascinated by Babbage's invention of the difference engine. They became great friends after that.
The two developed a working relationship between themselves. A memoir was written about Babbage's Analytical Engine, and she was the one to translate it. Along with translating it, from Babbage's suggestion, Ada even added her own comments and notes to it. It became three times as long as the original memoir filled with her notes. They even exchanged letters about Babbage's invention. Ada even personally created a way for it to calculate Bernoulli numbers becoming the first computer programming language. Charles Babbage gave her the nickname, “Enchantress of Numbers.” From that, Ada started becoming famous. Her notes were published through the initials of AAL. Back then, it was not encouraged for women to work on such complicated studies. She was even lucky for being able to have her papers published despite the fact that she was a woman.
In her personal life, Ada married William King. When he became the Earl of Lovelace, Ada became the Countess of Lovelace. People often relate to her as Ada Lovelace. They had three children together. The family was mainly dominated by her mother, Lady Byron. If only her husband was as good as being a leader as she was smart with numbers, family problems wouldn't have occurred from her mother's ruling.
With all the pressure, Ada Lovelace flirted with some of the males around her. Her husband got furious and destroyed many of her letters to her friends. Ada started drinking wine excessively. She went from drinking wine with meals to drinking wine instead of meals. Then she even took up gambling. She sold her jewels to get money for horse races. By the time of her death, Lovelace was in debt of £2000 from gambling.
Throughout her years, Ada Lovelace became weaker and weaker because of her cancer. At the young age of thirty-six, she died from uterine cancer and bloodletting by her doctors. Ada Lovelace was buried next to the father she never knew.
Srinivasa Ramanujan by Mohammad Ullah
Srinivasa Ramanujan was born on December 22, 1887 in Erode, British India, in the house of his mother’s parents. Ramanujan lived in a traditional house in India called Kumbakonam, and the house is now a museum. When Srinivasa was only two years old, he suffered a case of smallpox, notorious at the time for causing many deaths, but he miraculously recovered from it. His mother gave birth a few times, but he was the only one who made it passed infancy. Ramanujan moved back and forth from his house in Kumbakonam to his maternal grandparents’ house in/near Madras. His father was at work most of the day, so Srinivasa’s mother had a close relationship with him. She taught him traditions and cultural activities.
When he enrolled in the Kangayan Primary School, he excelled, and generated the best score in his district. This achievement brought him to Town Higher Secondary School, where he began learning true mathematics. He understood it fully, and began to even create theorems of his own. In the years following, he received many awards and recognitions for his outstanding skill, and completed exams with plenty of time to spare. He was awed by his classmates for his amazing knowledge and understanding of complex mathematics. He was offered a scholarship from his school, but lost it because of his failures in any other subjects.
He ran away from home, and enrolled in a school near Madras. Here, he was also outstanding in mathematics, but he again suffered in other subjects, leaving him in desperate poverty. When he was 21, he married a 9- year old girl, Janaki Ammal. After he married, he developed a condition in his body that required a surgery. His family couldn’t afford the operation, but a kind doctor agreed to perform the operation for free. After the surgery, Ramanujan searched for a job, and ended up tutoring college students in math. In March, 1914, he took a ship from Madras to England, where he worked with Hardy and Littlewood. Ramanujan went to England because he sent his results to G. H. Hardy, who was amazed by the work. Hardy arranged a trip for Srinivasa to go to Cambridge, England, so Hardy could see proof of Ramanujan’s work. After living in England for awhile, Srinivasa then became homesick, sick of the war’s effect on England, and literally sick. He died soon after he returned on April 26, 1920, from tuberculosis and a vitamin deficiency.
Ramanujan started his interest in mathematics very early in his life, and progressed through many types of it. He mastered general math skills in his primary school, mastered formal mathematics in secondary school, and mastered the trigonometry book he was lent. He wrote down hundreds of theorems he created in his notebook, many experimenting with pi and radicals. Ramanujan also worked on continued fractions and integrals. When he moved to England, Srinivasa received a PhD for highly composite numbers research. His last major study before he died was elliptic functions.
One thing that may have affected Ramanujan’s life during his time would be World War I. Towards the end of his life, the Great War took place, and since England controlled India, there was much involvement in his life. It was said that one reason he became ill was the scarcity of vegetarian food during the war. Also, he lived in a time where there was much sickness. He died young (age 32) because of tuberculosis, liver infection and a severe vitamin deficiency. He also spent a large amount of time in Madras, which was determined to be the source of his liver problems, because amoebiasis was a common parasitic infection of the liver in that area. He also suffered from poverty after he ran away from home, due to the economy at the time.
John von Neumann by Ilana Kelmanskiy
John von Neumann was born on December 28, 1903 in Budapest, Hungary. Throughout the course of his short life, he made multiple discoveries that revolutionized mathematics. His presence can be felt in almost every branch of mathematics. He made sizable contributions to the fields of geometry, game theory, economics, and quantum theory, and his involvement was instrumental in the ending of World War II. To this day, he is still regarded as one of the best mathematicians of his time.
He was a banker’s son, and his father realized John’s talent at an early age. Although he recognized his son was a genius with incredible skills of memorization, he did not believe he could make a living as a mathematician. Instead of encouraging his son to continue his studies of mathematics, he asked his son to memorize pages of the phone book to amuse guests at parties. He attempted to get his son to study something more practical than math, and as a result John began to study chemistry. At 23, he received his PhD in mathematics, and he never had to resort to chemistry to make money ever again.
Neumann became a professor at Princeton in 1933 as a teacher at the Institute for Advanced Studies. He was one of the first six math teachers there, alongside some other brilliant people (most notably Albert Einstein). He quickly became known as an incredible pure mathematician, collaborating with people like Howard Aiken and Alan Turing.
Von Neumann is considered to be the founder of game theory. He improved the minimax theorem, among other things. The minimax theorem states that in a game where all information is revealed, there is always a method with which each player can minimize their maximum losses in a game. He applied the theorem to games with more than two players and games where not all the information was revealed.
He continued his work solely in the field of pure mathematics until 1940. With the onset of World War II, von Neumann's areas of interest changed towards applied mathematics. He became one of the few mathematicians to be skilled with explosions, and his talent led to him being selected to assist with the Manhattan Project (the project that led to the creation of the atomic bomb). He is responsible for the so-called “explosive lens” design of the atomic bomb, and was on the committee deciding where to launch the bomb.
To help with his work at Los Alamos, he needed to work with computers. He used an early digital computer to run simulations, and as a result needed to create a basic random number generator of sorts. He proposed the middle-square method. The method would multiply a six-digit seed number to the power of two, take the middle six digits, and make that the new seed number. His work with the middle-square method eventually led to the creation of the Monte Carlo method.
He married Mariette Kovesi in 1930, and with her he had his only daughter, Marina von Neumann Whitman. (She later followed in her father’s footsteps and became a mathematician.) Later, after his wife’s death in 1938, he married Klara Dan. He always wore a grey flannel suit, no matter what the situation. He once wore one while riding a camel! He also was a notoriously bad driver, often reading a book at the wheel and consequently crashing into the trees.
In 1955, he was diagnosed with cancer. Upon being informed of this, he was forced to realize that he would soon cease to exist, and as a result cease to think. His close friends who visited him during his time said that watching him struggle was heartbreaking. He suffered for a year and a half under military custody (he feared he might reveal state secrets while medicated) and died on February 8, 1957. The number of advancements he made in the field of mathematics is immeasurable, and to this day he remains one of the greatest mathematicians of the 1900s. |