These women were capable of so much in many of their cases in a short lifetime. It is amazing women in their time had to overcome and like Prof Kim said even today women in many cases are not seen as equals. To rebelling against parents wishes to doing work under another’s name to working at a university that will not even allow a woman to become full time staff, these women fought against the odds and won. Thanks to their stories of strength and tenacity it inspires all of humanity, especially women like me.

Thank you Prof. Gottlieb and Prof. Kim for exposing me to the richness of this subject.

Grace Chisholm Young was born in Haslemere, England. Although her brother was sent to grammar school, a prestigious boarding school, where he could earn a top scholarship to Oxford, Grace and her sister were educated by a governess at home. In these times, this was the custom. Grace became involved in social work helping the poor in London. She had aspirations of studying medicine, but her family would not allow it. However, Grace wanted very much to continue her studies, so she entered Girton College, part of Cambridge University to study mathematics. Girton was the first school at the university level that was dedicated to educating women. In 1893, Grace passed her final examinations and scored the equivalent of a first-class degree. However, women were not awarded formal degrees at that time.
In order to continue her studies, Grace had to go to Gottingen in Germany to study. Women were not allowed to attend graduate school in England.
While at Girton, Grace had a tutor by the name of William Young, whom she married the year after she received her Ph.D. at Gottingen. Grace and William spent the next 44 years together. They produced more than 200 mathematical papers and books, many of which were in William’s name. Grace had a very major role in producing these papers. William noted in an article in 1914 that he had discussed the major idea of the work with his wife, and Grace had elaborated on the argument and put it into publishable form. Grace produced many papers on her own despite the fact that her husband was away from the family for large parts of the year and she was left in Switzerland to take care of the children. She wrote a paper in 1915 on the foundations of calculus that won the Gamble Prize at Cambridge. She and her husband also published books on geometry and set theory.
Grace and William had six children together in a span of nine years. Most of their children went on to become mathematicians. Besides being a great mathematician, Grace completed all the requirements for a medical degree except the internship. She also learned six languages and taught each of her children a musical instrument. With the approach of World War II, Grace left Switzerland in 1940 to take two of her grandchildren to England. Grace was to return immediately, but because of the fall of France, she could not. This left William alone, and he died two years later in 1942. Two years after that, Grace died of a heart attack.
Of their six children, three continued on to study mathematics, one daughter became a physician, and one son pursued a career in finance and business. Sylvia Wiegand, her brandchild, is a mathematician at the University of Nebraska and is a past president of the Association for Women in Mathematics.

Emmy Noether was born in Erlangen, Germany 1882. She was the eldest of four children, Her father was Max Noether, a noted mathematician of his time.. Her brother, Fritz also made a career of mathematics.
As a child, Emmy Noether did not concentrate on mathematics. She spent her time in school studying languages, with a concentration on French and English. Her mother taught her the traditional skills of a young woman of that time. She learned to cook, clean, and play the clavier. At the time of her graduation from high school, she passed a test that allowed her to teach both French and English at schools for young women.
At the age of 18, Emmy Noether decided to take classes in mathematics at the University of Erlangen. Her brother, Fritz, was a student there, and her father was a professor of mathematics. Because she was a woman, the university refused to let Emmy Noether take classes They granted her permission to audit classes. She sat in on classes for two years, and then took the exam that would permit her to be a doctoral student in mathematics. She passed the test, and finally was a student in good standing at the University. After five more years of study, she was granted the second degree to a woman in the field of mathematics. The first graduated a year earlier.
Now that Emmy Noether had her doctorate in mathematics, she was ready to find a job teaching. The University of Erlangen would not hire her, as they had a policy against women professors. She decided to help her father at the Mathematics Institute in Erlangen. She began doing research there, and helped her father by teaching his classes when he was sick. Soon, she began to publish papers on her work.She helped in working on further defining one of Einstein’s theories at the University of Gottingen.
During her time at the University of Gottingen, she accumulated a small following of students known as Noether’s boys. These students traveled from as far as Russia to study with her. Noether was a warm person who cared deeply about her students. She considered her students to be like family and was always willing to listen to their problems. Her teaching style was very difficult to follow, but those who caught on to her fast style became loyal followers. Noether’s teaching method led her students to come up with ideas of their own, and many went on to become great mathematicians themselves. Many credited Noether for her part in teaching them to teach themselves.She kept up her charismatic teaching style, often lapsing into German if she was having trouble getting her ideas across to the students. Noether’s death in 1935 surprised nearly everyone, as she had told only her closest friends of her illness. She was also a teacher that was able to inspire her students to make their own contributions to the field of mathematics. She died in 1935
We also talked about some of the contributions made by Mary Somerville and Ada Byron Lovelace.

I always wondered about the front of the Math book and what thats pattern was. We learned that it is part on Somerville’s work as she was interested in Chladmi (German Physist) and his collection of physical science in 1854. The collection of patterns made by the vibrations of plates. The example of what those patters looked like were on the cover of the book above. Somerville worked on 4 books to educate people about this discovery. Using a violin bow along the edge of a plate were how these patterns were formed. Chladmi observed these patterns of vibration and called them symmetry and isometry.

Ada Lovelace worked on contriutions such as Difference Algorithm which are reaccuring relations taking difference of consecutive term until constant difference.
Thus came Fibonacci sequence as explained was by mathematitian Fibonacci (Leonardo Pisano) posed the following problem in his treatise Liber Abaciit is easy to see that 1 pair will be produced the first month, and 1 pair also in the second month (since the new pair produced in the first month is not yet mature), and in the third month 2 pairs will be produced, one by the original pair and one by the pair which was produced in the first month. In the fourth month 3 pairs will be produced, and in the fifth month 5 pairs. After this things expand rapidly, and we get the following sequence of numbers:

1, 1, 2, 3, 5, 8, 13, 21,
an example Prof Kim showed us in class was using Rabbits like the image below

The equation looks like this:
F5=F4=F3 (the number are supposed to be little and lowered to the right but I can so it in word.
Ada was also interested in trigonomatry and Prof Kim told us about a way her students would remember the
formulas of a right-triangle and their trigonometric functions being:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent

Some
Old Sin(0)=O/H
Hag

Caught Cos(0)=A/H
An
Hippy

Tripping Tan(0)=O/A
On
Acid

<The puzzle was invented by the French mathematician Édouard Lucas in 1883. There is a legend about a Vietnamese or Indian temple which contains a large room with three time-worn posts in it surrounded by 64 golden disks. The priests of Brahma, acting out the command of an ancient prophecy, have been moving these disks, in accordance with the rules of the puzzle, since that time. The puzzle is therefore also known as the Tower of Brahma puzzle. According to the legend, when the last move of the puzzle is completed, the world will end. It is not clear whether Lucas invented this legend or was inspired by it. The reason why puzzles like these is because Ada Byron Lovelace was intrigued with such puzzles.
She was born December 10, 1815 in a house overlooking London’s Green Park. Annabella Milbanke and Lord Byron were her parents and were together for about a year before they had her. They had a rocky relationship, mostly because her father was a difficult man. He had a temper and though he loved her mother when they had arguments his temper would flair up. He was a poet and though he could be very loving to her he enjoyed tormenting Annabella. Annabella, her mother, was very different she was cool calm and collected and enjoyed math. She loved him very much but the love was not reciprocated. Ada father left her mother shortly after she was born. So Annabella raised her child alone. Lord Byron later died in Greece when Ada was only 8 years old, in 1824. Though Ada was much like her mother, in terms of her cheerful demeanor she looked a lot like her father.
Ada would eventually grow into a fascinating woman. She was mathematician and an accomplished violinist and linguist. Unlike many of the others we learned about Ada was encouraged by her mother to carry out her math abilities. She would marry at 19 to William Lord King, who later became the Earl of Lovelace. He was 10 years older than her but they had a good relationship. Her husband took pride in her many accomplishments. They had 2 children a boy and a girl.
Ada was amazed by the math and science world. Her teacher/coworker, Charles Babbage was designing and constructing one of the first Difference Engine, later known as Analytical Engine. Ada was marveled by it. She began assisting him with such projects. Math was her baby as she referred to it as her eldest child, she was so eager to learn and was a dedicated student. She had a very flirtatious relationship with Babbage but her dedication to him was shown through her work. When Menebrea, an Italian mathematician wrote about the Analytical Engine she understood it and translated the explanation to English for others to learn from too. One Ada came into her own she was proven to be Babbage’s intellectual equal. She became a major contributor to him work. She had a mind for the future and predicted computer and the ability to create music with them.
Though the end of her life was unsettled with financial strife and failing health, she remains one of the notably accomplished women in math history. Overcoming odds and persevering. As she never knew her father she had many similarities to him, even in death, for they died at the same young age of 36. She chose to be close to him in death though she was able to be in life and was buried beside him.

Mary Fairfax Somerville

This extraordinary woman was born in Scotland in 1780.  She was going to live for a long time and in her life she would become quite accomplished.  She would write about new discoveries in science and mathematics.  Like Sophie Germain, she too was self educated and struggled against her parents who did not want her to learn too cuch in respect to academics.  Eventhough Sophie and Mary were from different countries bothcountries had limiting idea about educating women.  The study of mathematics was seen to be very strange for a woman to be engaged in.  Women of her class were not brought up to attend urban charity schools like poor children.   Since she was from a wealthy class she was to brought up and educated in a convent.  These children were taught the elements of reading and writing at home and often tutor were reserved for male children. 

Mary Somerville’s life as a child was rich but very lonely.  She was the daughter of an admiral and grew up in a village by the sea called Burtisland.  Her mother taough her to read the bible and explore nature.  She encouraged her to say her prayers twice a day.  When she was 9 years old she was sent to boarding school to learn to write.  She recalls not liking this experience.  She was teased and harrassed by others.  Her education there including memorizing by heart the dictionary.  There was also a lot of churchgoing because some of the girls at the school were Presbyterian and others were Anglican so they attend services for both.  After her father died her aunt began to criticize her mother for allowing Mary to read more than she sewed so then she went to school for needlework.

While she was doing this she then came upon a fasion magazine that would change her life forever.  The magazine had arithmetical questions which contain numbers and letters.  This intrigued her and she asked her younger brother to help her learn more about it.  She then began to study math again so that she could learn what she had found.

Mary then spent much of her time studying this new passion of hers.  Though she did not let go of other activities like playing the piano, painting, sewing.  She had many talents but her parents grew fearful that all this studying would cause her to go insane.  She was a very busy young woman and enjoyed all the other things in her life like going to balls, gossiping with her friend, attending the theater and making clothes. 

In 1804 she married Samuel Grieg the captain of the Russian navy.  He thought very little of women with education or of those aspiring to learn more about the sciences.  It was during these years that her studies ended for a while.  However, after 3 years her husband died.  She was only 27 and had to young sons to raise on her own.  However, Mary was free to do her own thing.  She then got a set of books from a friend who was a professor from the University of Edinburge.  This will be the only thing that was to be considered education.  It was during this that she had come across the word Algebra for the first time. She was very excited.

She began a regimen.  She would take part of an active social like but would study day early for a few hours.  In 1812 she met her second husband, which was her cousin Wiliam Somerville.  He was a surgeon in the British navy, and unlike her former husband, her was extremely supportive of her learning.  He took great pride in her.  He supported her and encouraged her and was very proud of her and took great pleasure in helping her pursue her goals.  Helping her search for library book, her daughter considered her father helping her mother calling it a “labour of love.” Given all this support she was still criticized by people like her then future sister-in-law writing her to tell her that she hoped she would become a useful wife for her brother. 

Mary Somerville at the age of 47 began her first project.  She had two little girls and one of her children had died in 1823 causing her much grief.  However, Mary carried on and produced a popular explanation of Laplace’s Celestial Mechanics.  This account help to explain these findings and knowledge to a wider audience.  She entitled her book Mechanisms of the Heavens, which was extremely successful.  Mary Somerville had a talent for understand complex things so profoundly that she could then rewrite the works for all to benefit from.  She also did this in her book Connection of the Physical Sciences and then in Physical Geography.  She got much praise in her lifetime and when she died she also did something remarkable during that time, she died at the age of 92, which was rare in those times and she died peacefully in her sleep.    She had lived in Italy for many years and died in Naples with her daughters, whom were the only ones that survived her.   She is a great woman then and still today. 

Another way of saying this is that a prime number is a positive integer that is not the product of two smaller positive integers.

Note that the definition of a prime number doesn’t allow 1 to be a prime number: 1 only has one factor, namely 1. Prime numbers have exactly two factors, not “at most two” or anything like that. When a number has more than two factors it is called a composite number.

Here are the first few prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.

In class we’ve been leaning about prime numbers, perfect number and Sophie Germain’s Germain primes!  She has contribed much in this sence but first let me explain a little about what we have learned from class:

A perfect number is a number which is the sum of its proper divisors.

Thus, 6 = 1 + 2 + 3 is a perfect number, since 1, 2 and 3 are the numbers which divide 6 evenly. The next perfect number is 28, as 28 = 1 + 2 + 4 + 7 + 14.

Perfect numbers are related to Mersenne primes (prime numbers that are one less than a power of 2): if M is a Mersenne prime, then M×(M+1)/2 is a perfect number. (This was proved by Euclid in the 4th century BC.) Furthermore, all even perfect numbers are of this form (as proved by Euler in the 18th century). So we have a concrete one-to-one association between even perfect numbers and Mersenne primes.

Only finitely many Mersenne primes (hence even perfect numbers) are presently known. It is unknown whether there are infinitely many of them. See the entry on Mersenne prime for additional information concerning the search for these numbers.

It is unknown whether there are any odd perfect numbers. Various results have been obtained, but none that have helped to locate one or otherwise resolve the question of their existence. It is known that if an odd perfect number does exist, it must be greater than 10³⁰⁰. Also, it must have at least 8 distinct prime factors (and at least 11 if it is not divisible by 3), and it must have at least one prime factor greater than 10⁷, two prime factors greater than 10⁴, and three prime factors greater than 100.

Considering the sum of proper divisors gives various other kinds of numbers. Numbers where the sum is less than the number itself are called deficient, and where it is greater, abundant; these, together with perfect numbers, come from Greek numerology. A pair of numbers which are the sum of each other’s proper divisors.

An example of a perfect number  is 6 see

2+3+1=6

2×3=6

1×6=6 

Germain prime is an number (most of are odd) Its a germain prime if it comes from a Germain Prime if it come from this equation Sp=2^p+1

Marin Mersenne was born into a working class family in the small town of Oizé in the province of Maine on 8 September 1588 and was baptised on the same day. From an early age he showed signs of devotion and eagerness to study. So, despite their financial situation, Marin’s parents sent him to the Collège du Mans where he took grammar classes. Later, at the age of sixteen, Mersenne asked to go to the newly established Jesuit School in La Flèche which had been set up as a model school for the benefit of all children regardless of their parents’ financial situation. It turns out that Descartes, who was eight years younger than Mersenne, was enrolled at the same school although they are not thought to have become friends until much later.

Mersenne’s father wanted his son to have a career in the Church. Mersenne, however, was devoted to study, which he loved, and, showing that he was ready for responsibilities of the world, had decided to further his education in Paris. He left for Paris staying en route at a convent of the Minims. This experience so inspired Mersenne that he agreed to join their Order if one day he decided to lead a monastic life. After reaching Paris he studied at the Collège Royale du France, continuing there his education in philosophy and also attending classes in theology at the Sorbonne where he also obtained the degree of Magister Atrium in Philosophy. He finished his studies in 1611 and, having had a privileged education, realised that he was now ready for the calm and studious life of a monastery.

The Order of the Minims, having been set up by St Francis of Paula in 1436, was thriving at this time. They believed they were the least (minimi) of all the religions on earth, and devoted themselves to prayer, study, and scholarship. They wore a habit made of coarse black wool with broad sleeves and girded by a thin black cord (as seen in the portraits of Mersenne). Charles VIII introduced the Order into France and, due to their great simplicity, the monks were named ‘les bons hommes’. After the French Revolution the Order dwindled considerably in number and today there exists only a few convents in Italy. Mersenne entered the Order on 16 July 1611, and was ordained a priest in Paris in July 1612 after a two and a half month probationary period in the monasteries at Nigeon and Meaux. His first posting was in 1614 to the monastery in Nevers where he taught philosophy and theology to the younger members of the community. In fact one of his students, Hilarion de Coste, later became his confidant and biographer. It was during this period of his life that he is thought to have discovered the cycloid – a geometric curve.

After two years teaching Mersenne was elected superior of the Place Royale monastery in Paris where he remained, except for brief journeys, until his death in 1648. It is believed that the Church supported him for most of his life, although in later years a fellow monk, Jacques Hallé, helped out with money and granted him access to his library. From the beginning of his time in Paris, mathematical problems played an important role in his life. Very early on he had links with important scholars in Paris whom he met often, exchanging ideas and discussing projects. The Minims realised that the biggest service he could give was through his books and they never asked any more of him.

In 1623 he published his first two papers consisting of studies against atheism and scepticism in France; L’usage de la raison and L’analyse de la vie spirituelle. Continuing his theological writing he had then wanted to disprove magic, however a fellow monk pointed out that it wasn’t appropriate, leading to his publication of Quaestiones celeberrime in genesim that includes the disapproval of magicians in the Scriptures. This book contains 1900 columns of text from the Bible in its first six chapters. It was because of this publication that, in September 1624 when he returned to Paris, he met Gassendi who had been asked to comment on Mersenne’s results, and later became his closest friend.

At this time France was going through a period of anti-witchcraft, expelling any sorcerers. L’impiété des deistes, in French, was aimed at the French public so that they might read and understand what was happening. It was during this time that Mersenne started to think about the theological criticism directed against Descartes and Galileo. In fact Mersenne’s attitude to Galileo changed over a number of years:

Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of influential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace him by a new philosophy. … In the early 1620s, Mersenne listed Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne had become one of Galileo’s most ardent supporters.

Mersenne was beginning to realise that alongside religion it was science that really interested him. Mathematics was the area he studied in greatest depth, believing that without it no science was possible. He always had a philosophical approach to mathematics and believed that the cause of the sciences is the cause of God. So, in La vérité des sciences he proved, via many great discoveries, the value of the human mind. It was around this time that Mersenne started to become a coordinator for all European scholars. From 1623 he began to make a careful selection of savants who met at his convent in Paris or corresponded with him from all across Europe and even from as far afield as Constantinople and Transylvania (present-day Hungary). His regular visitors, or correspondents, included Peiresc, Gassendi, Descartes, Roberval, Beeckman, J B van Helmont, FERMAT, Hobbes, Etienne Pascal, and his son Blaise Pascal. He set up meetings of scholars from around Europe during which they would read and review scientific papers, both national and international, exchange contacts with other scholars and plan and discuss experiments and other work. This came to be known as the Académie Parisiensis and sometimes among friends as the Académie Mersenne. It was notably one of most resourceful centres of research at that time, meeting weekly at members’ houses and later in Mersenne’s cell due to his weakened health. The list of Mersenne’s correspondents kept increasing and Mersenne himself did not hesitate to travel to meetings with scholars all around Europe.

Mersenne had a strong interest in music and spent a lot of time researching acoustics and the speed of sound. In 1627 he published one of his most famous works, L’harmonie universelle. In this work he was the first to publish the laws relating to the vibrating string: its frequency is proportional to the square root of the tension, and inversely proportional to the length, to the diameter and to the square root of the specific weight of the string, provided all other conditions remain the same when one of these quantities is altered. Mersenne had already started encouraging the talents of others and helped them to share their ideas and results with other scholars. When Roberval arrived in Paris, after joining Mersenne’s circle of scholars, his talent was soon recognised by Mersenne who encouraged him to work on the cycloid.

The period between 1627 and 1634 was a transitional period in Mersenne’s life. During this time he travelled to Holland for several months between 1629 and 1630. His main reason was to seek a cure for an illness with the help of spa water but he used the opportunity to visit scholars in the surrounding areas. The greater maturity in his writing in the seven years since his last publication became apparent when Questions inouyes and Questions harmoniques were printed in 1634. In October 1644 Mersenne travelled to Provence and Italy where he learnt of the barometer experiment from Torricelli. On his return to Paris, he reported this news to encourage French scholars to carry out the experiments too.

Throughout his lifetime Mersenne helped many potential scientists by steering them in the right direction and advising some on the next step to take. He became a role model for Huygens whom Mersenne took under his wing and through his encouraging letters inspired Huygens” Theory of Music. Huygens had intended to move to Paris in 1646 to be near Mersenne in order to enable them to contact each other more easily, however Huygens didn’t move until several years after Mersenne had died so they never met.

Galileo also has to be grateful to Mersenne for making his work known outside Italy. Mersenne insisted on publishing Galileo’s work and without this Galileo’s ideas might never have become as widely known. Continuing his travels into his old age, in 1646 Mersenne set off on a trip to Bordeaux. There he met Pierre Trichet whom he helped make his mark. The success of the scientific life over in Bordeaux and Guyenne, which later formed the Académie Royale des Sciences, was largely due to the advice and experience Mersenne was able to offer. He returned to Paris in 1647.

Mersenne fell ill after his visit to see Descartes in July 1648 and, unfortunately, his health never improved. He was advised to mix wine with his water to help him get better, however Minims do not drink wine. He had an abscess on the lung but the surgeon was unable to find it. Mersenne himself pointed out that the incision, which he asked for, had been attempted too low. Gassendi was there for Mersenne throughout his illness and remained with him until his death on 1 September 1648 in Paris, just 8 days from his 60^th birthday. He never gave up his life-long desire to advance science. He even asked, in his will, that his body be used for biological research.

After Mersenne’s death, letters in his cell were found from 78 different correspondents including Fermat, Huygens, Pell, Galileo and Torricelli. Also several physics instruments were found in his cell and a lot of Mersenne’s library was retrieved from which L’optique et la catoptrique was published in 1651. Inside this publication one of Roberval’s texts was inserted. Later all the letters he sent and received from other scholars were accumulated and published in several volumes. These letters read like an international review of mechanics in the early 17th century. Mersenne was aware of all the science that was going on, what all the scientists were doing, and only wanted for them all to work together in advancing science.

Mersenne studied the cycloid for several years quoting his research in Quaestiones in Genesim (1623), Synopsis mathematica (1626) and Questions inouyes (1634). He gave the definition of a cycloid as the locus of a point at distance h from the centre of a circle of radius a, that rolls along a straight line. He stated the obvious properties including the length of the base line equals the circumference of the rolling circle. We note that Mersenne referred to the cycloid as the ‘roulette’ but the term cycloid was adopted later. He attempted to find the area under the curve by integration but having failed, so he put the question to Roberval. In 1638 he announced that Roberval had indeed found the area under the cycloid.

Mersenne’s name is best remembered today for Mersenne primes.

Less than a year after the 43rd Mersenne prime was reported (MathWorld headline news: December 25, 2005), the Great Internet Mersenne Prime Search (GIMPS) project has discovered the 44th known Mersenne prime. The candidate prime was flagged prime by Dr. Curtis Cooper and Dr. Steven Boone who, rather amazingly and against staggering odds, are also the discoverers of the 43rd known Mersenne prime, thus proving (in the words of the GIMPS website) that lightning can strike twice! Additional details can be found in the Mersenne.org press release.

Mersenne numbers are numbers of the form M_n = 2ⁿ – 1, giving the first few as 1, 3, 7, 15, 31, 63, 127, …. Interestingly, the definition of these numbers therefore means that the nth Mersenne number is simply a string of n 1s when represented in binary. For example, M₇ = 2⁷ – 1 = 127 = 1111111₂ is a Mersenne number. Mersenne primes are Mersenne numbers that are also prime, i.e., have no factors other than 1 and themselves. So, since the number 127 is prime and is a Mersenne number, it is a Mersenne prime.

The last Mersenne Prime found Aug. 23, 2008 by Edson Smith.

This information was found on worldmath.org a great source for information!

Who was Christian Goldbach?

Born, March 18, 1690,in the Duchy of Prussia’s capital Königsberg, part of Brandenburg-Prussia, Goldbach was the son of a pastor. He studied at the University of Königsberg and went on to work at the newly opened St Petersburg Academy of Sciencesin 1725. Later on, he was a tutor to the later Tsar PeterII in 1728. In 1742 he entered the Russian Ministry of Foreign Affairs.

Goldbach traveled widely throughout Europe and met with many famous mathematicians, such as Gottfried Leibniz, Leonhard Euler, and Nicholas I Bernoulli. He is most noted for his correspondence with these mathematicians, especially in his 1742 letter to Euler stating his Goldbach’s Conjecture. He also studied and proved some theorems on perfect powers, such as the Goldbach-Euler theorem, and made several notable contributions to analysis.

Goldbach died November 20, 1764

 Goldbach’s original conjecture (sometimes called the “ternary” Goldbach conjecture), written in a June 7, 1742 letter to Euler, states “at least it seems that every number that is greater than 2 is the sum of three primes”

 Thanks to mathworld.wolfram.com this is a little more about Goldbach Conjeccture!

FERMAT is further explained in the blog entry about his life and other contributions!

Fn=2^2n +1 these are some of the only prime numbers that have come from this equation.  n/Fn

                                                                                                                                                                                            0/3

                                                                                                                                                                                             1/5

                                                                                                                                                                                             2/17

is some of the example given to us in class.