Evariste Galois

Evariste Galois was born in Bourg-la-Reine. His father was the mayor of the town and his mother being women with an education she taught Galois until he was 12 yrs. old. Although he did well in school he quickly became bored with it and started to self- teach.  At the age of 16 he found a mathematician teacher Louis Richard. By 17 he published his first paper on continuous fractions. When he was 16 and 18 years old he applied to Polytechnique, He failed both times. The second time he failed because of his anger and lack of patience, he was then banned from re-applying again. He wrote 3 papers while attending a university that ended up being lost.

In 1830 he joined the National Guard. He was then jailed for threatening the king but was not convicted.

At the age of 20 his anger got him into a duel and he ended up getting shot in the gut and died the next day.

Twenty years after his death his manuscripts were edited and published by Joseph Liouville.  Galois manuscripts only filled 60 pages.  Liouville said this about his work:

"I experienced an intense pleasure at the moment when, having filled in some slight gaps, I saw the complete correctness of the method by which Galois proves, in particular, this beautiful theorem: In order that an irreducible equation of prime degree be solvable by radicals it is necessary and sufficient that all its roots be rational functions of any two of them."

He was one of the mathematicians that constructed the idea of groups in algebra. He was known for developing what is known as a normal subgroup which he stated as the decomposition of a group into its left and right cosets a proper decomposition if the left and right cosets coincide. He also made the discovery of infinite field. He is also known for constructing general linear group over a prime field, GL(ν, p) and computing  its order and the projective special linear group PSL(2,p). He also noted the fact that PSL (2,p) is simple and acts on p points if and only if p is 5, 7, or 11.

Galois is mostly known for his theory which was named after him, the Galois theory. This theory is described as:

“the algebraic solution to a polynomial equation is related to the structure of a group of permutations associated with the roots of the polynomial, the Galois group of the polynomial. He found that an equation could be solved in radicals if one can find a series of subgroups of its Galois group, each one normal in its successor with abelian quotient, or its Galois group is solvable. This proved to be a fertile approach, which later mathematicians adapted to many other fields of mathematics besides the theory of equations to which Galois originally applied it.”

http://en.wikipedia.org/wiki/%C3%89variste_Galois

http://scidiv.bellevuecollege.edu/Math/Galois.html

Jean Baptiste Joseph Fourier

Jean Baptiste Joseph Fourier was born in 1768. After dabbling in religion and teaching he was swept up in the French Revolution although he was a revolutionary he ended up being thrown in jail for his support for the victims of the Reign of Terror, by other revolutionaries. After a while and change in politics he was released.

At the age of 27 in 1795, Fourier took a job as a faculty member at the Ecole Polytechnique. Although after a bit of time the politics once again found him and he was put back into jail for his past offense. After some input from some well-known colleagues, he was release and posted overseas working for Napoleon during his takeover of parts of Egypt, in 1798. It is thought that his “heat obsession” started while he was posted in Egypt.

Napoleon made Fourier the secretary of the Institute of Egypt, and then soon after he was appointed Baron. To avoid being entangled in Napoleons downfall he cut ties and resigned his post.

After this he started back on his research, mainly on heat flow. He published a paper on the analytical theory of heat, to the Academy of Science. In this paper he reported how to show heat as solid bodies and he also created mathematics that allowed scientist to be able to solve problems that were once thought impossible. He introduced the idea that “an arbitrary function, even one defined by different analytic expressions in adjacent segments of its range (such as a staircase waveform), could nevertheless be represented by a single analytic expression”.

Formula:

x/2 = sin x - (sin 2x)/2 + (sin 3x)/3 + � � �

Fourier considered heat flow in a ring, or bar that has been bent into a circle. By doing this, the temperature distribution is forced to be spatially periodic. There is almost no loss of generality because the circumference of the ring is supposed larger than the greatest distance that could be of physical interest on a straight bar conducting heat.

 Like most great inventors his works were subject to many skeptics, some of which were his past colleagues. He fought for 15 years to get his works published. Finally in 1822 it was published and by this time it had evolved in to an entire book.

www.uh.edu/engines/epi186.htm

www.uh.edu/engines/epi1878.htm

http://www.swarthmore.edu/NatSci/echeeve1/Ref/Fourier/FourierBio.html

Marin Mersenne

http://www.imss.fi.it/vuoto/emerse.html

Marin Mersenne was born on September 8th 1588 in the town on Oize, He was baptized on the day that he was born. His family was not well off, but despite this they sent him to the College du Mans to study grammar. When he was sixteen he attended the new established Jesuit school in La Fleche. This was a school that provided for students no matter their financial situation. After a while he decided to to venture to Paris to further his education. Once he was there he attended the College Royale du France. At this college he studied philosophy and attended many classes in theology at the Sorbonne. He also obtained the degree of Magister Atrium in philosophy. In 1611 he decided to be done with his studies and start a life in the monastery.

On July 16 1611 Mersenne enter the Order of Minims. This particular order was set up in 1436 by the St Francis of Paula. They are devoted to prayer, study and scholarships. They were very simple and wore robes of wool tied with a cord. In July 1612 Mersenne was ordained as a priest in Paris.  He was first posted to the monastery in Nevers. There he taught philosophy and theology.

He published his first two paper in 1623, L’usage de la raison and L’analyse de la vie spirituelle. These two papers were against atheism and skepticism.  He then wanted to write a paper on disproving magic. But after having another monk point out that this might not be the best idea he reconsidered. At this time there was a large anti magic and the expelling of sorceres in France. He then published L’impiete des deists. This paper was aimed at the French public, to help them understand what was going on.

“Mathematics was the area he studied in greatest depth, believing that without it no science was possible.” He put together a group of scientists and scholars from all over Europe. they would get together to compare notes and discuss the different experiments that they had been doing and were going to do. This group of was known as Academie Parisienis. They would meet weekly at each other’s houses.

Mersenne also had an interest in music. He spent a lot of time researching the speed of sound and acoustics. He published a paper on vibrating strings, L’harmonie universelle.

He spent most of his life teaching and helping other scholars further their scientific research. He died on September 1 1648. Even in death he wanted to further science, so he left his body for science.

Nicolaus Copernicus

http://www.notablebiographies.com/Co-Da/Copernicus-Nicolaus.html

Nicolaus Copernicus was born Feb 14^th 1473 in the town of Torun. His father was a well to-do merchant and his mother was a daughter of a wealthy merchant. He was the youngest child in his family. His father died when he was 10. After this his father’s brother, Lucas Watzelrode became his guardian. Lucas was bishop in the Catholic church. Nicolaus took after his uncle and became involved in the church. Between 1941 and 1942 he completed his matriculation, he also studied mathematical science. In 1497 he continued his studies at three Italian universities, Bologna, Padua and Ferrara. While in Italy he completed his Bi-doctorate in medicine and law.

Copernicus was many things, he was an astronomer, a mathematician, a translator, an artist, a physician, and a scholar. He also “ made maps, attended legislative bodies, held a variety of fiscal posts, acted as a diplomat and as a civil and military inspector, even wrote a treatise on the minting of money by the new Prussian states”.(Morrison.1)

In 1505 he returned to Poland where he was appointed at the Canon in the cathedral of Frauenburg. While there he continued to research astronomy and medical information. In 1513 he started his work on his heliocentric theory. In his early thirties he had documented a developed heliocentric theory of the solar system. His theory spread quickly through out the scientific world. Many astonomers and mathematician flocked to Nicolaus to get more information on this theory.

In 1543 his entire volume of On the Revolutions of Celestial Spheres was published, this is also the year that he passed away.

Here is a passage from Copernicus on his views:

We draw life from the glorious, incandescent sun. It rises daily in the east, until by nightfall it hides behind some horizon, whether land, sea or cloud, diving unseen to reappear at dawn in a different part of the starry background. The glittering stars move as a whole; each year the sun returns to a backdrop of bright points very near the one it left. The moon shows us a disk as wide as the sun's; its changing details are bright but cold, never a hot blaze. In about one month any viewer stationed on Earth can see the moon pass across the entire Zodiac. The outline of the bright, inconstant moon attends strictly to the position of the sun. When the sun lies behind any moon viewer, the moon is full face. When the moon lies right before us and the sun close to the same direction, we have a new moon. That new moon is unseen, for the moon, a cold and lightless rock, glows only under the sun's rays, and is lost to us whenever it is masked within the sun's power of brightening a skyful of blue air.

 I find Copernicus very intriguing because of his deep involvement with the Catholic Church. Even though he was so involved he still had amazing scientific views, which went against what the church believed. I find it interesting that the church would allow him to hold such high positions inside the clergy while still researching his theories. I also wonder what happened after the church discovered his theories?

Copernicus in his prime. (Marginalia). Philip Morrison. American Scientist. 91.2 (March-April 2003)

http://www.famousscientist.org/nicolaus-copernicus/

Creation of Mayan Math

The Mayan civilization made many important achievements in the math world. The created an accurate calendar, a way to represent number, a sign to represent zero and many more.

The first recorded date we have for the Mayans is around 2000BCE in southern Mexico. After a while they started to build burial mounds and step pyramids. “The peak of the Mayan culture was in 900 CE.”(Brown 2).

In 1505 Hernan Cortes left Spain to explore the New World. He left with 11 ships, 506 soldiers and 10 horses. He arrived at the Yucatan Peninsula on Feb 18, 1519. The Mayans that he encountered there offered little hostility towards the explorers. Diego de Landa was 17 years old when he joined Cortes expedition. He is the man who brought the Mayans mathematics to present society. He started out helping the Mayans, spending lots of time throughout their community and protecting them from the Spanish. After a while he started to view them as devil worshipers. He then had all of their idols and writings destroyed. Although later he wrote a book about the Mayans culture.

There were a few documents that survived the destruction ordered by Landan, two of which are the Madrid Codex and the Dresden Codex. Although these artifacts do not say how the Mayans calculated, it does have the results of these calculations, which are incredibly accurate. In the Dresden Codex it has what appears to be a representation of negative numbers. This is supposedly represented by a unit surrounded by a red loop tied with a knot at the top.

The Mayans had a mathematical system that consisted of a cipher system combined with a place value system. This number system was a base 20 system. The thought behind this was that they counted their fingers and toes to a total of twenty. Although this system was not fully a base twenty system, instead of them using a 400’s place there was a 360’s place. The thought behind this is that they wanted to be a close to the days in a year.

There were two basic units that the Mayans used one was a dot, used to represent numbers 1-4, and a bar that was used to represent 5. They combined these two symbols to represent numbers up to twenty. They wrote their number vertically with the lowest denomination on the bottom. The Mayans were the first to come up with the concept of zero. This was commonly represented by a shell.

The most common thought is that the calculations were used to create the calendar. They had two separate calendars; the first one was the “Haab” which was a civil calendar similar to the current day one. The second one was the “Tzolkin” which was the ritual calendar. These two calendars operated separately creating a huge cycle.

http://www.math.wichita.edu/history/topics/num-sys.html#mayan

http:/www.math.utah.edu/~opstall/3010/mayan.pdf

Babylonian number system

The Babylonian Number system

               The Babylonian number system was developed in Mesopotamia from the Sumerians to the fall of Babylon in 539 BC. The Sumerians started with a simple number system where they wrote on soft clay tablets with a wedge shaped tool. This type of calculation was known as cuneiform. The main reason for these calculations was crops. Mesopotamia was mainly a farming community with barley being the main the crop. So they needed a way to keep track of the trading. The sign for barley started off as more of a rough tree shape, a vertical line with slanted lines on either side. After a while it transformed as the tools did to a more wedge shaped object that was pressed in to the clay multiple times.

    

                                                                    

http://www.mesopotamia.co.uk/writing/story/sto_set.html

Eventually the system was developed in to base 60 counting system. A few different things that came out of this are the 360 degrees that we use and how we count time, the hours, minutes, and seconds. It also was used for weights and measure and astronomy. This system is known as the Sexagesimal system. On one tablet has a list of all of the squares up to the square of 60. All the numbers past 60 are written as 60+. An example would be 67, it would be written as 60 +7.

The basic decimal system came out of Babylon also. They used different positions to place the integers. This idea was lost until around sixth century BC.  Fractions are another idea that came out of the base 60 system. “They expressed a half as ‘30’ (30 sixieths) and ‘15’ (15 sixieths).” Greece adopted this system as the main way to record fractions. Later on however they used more of a decimal system.

This system was based in astronomy. The Babylonians wanted to have an accurate calendar so that they could track the different turning of the seasons. With the understanding of the seasons they could plant at the best time. They based their numerical system off there being 360 days in a year. They then divided this is to degrees which represented the movement of the sun throughout the sky. “They then transferred this into measuring circles by diving degrees into minutes.”

Geometry was not something that the Babylonians study much of. They had more of a trial and error system to put up buildings.

It’s most likely that the Greeks learned numerical systems from the Babylonians when Alexander the great conquered the area. It is said that he sent the records of astronomy to Aristotle to study.

Sources

The British Museum

http://www.mesopotamia.co.uk/writing/story/sto_set.html

                   Experiment Resources

                   Http://www.experiament-resources.com/babylonian-mathematices.html

Hello!

Hey everyone!
My name is Dominique Piccini. Im doing this blog as a class assignment for my Humanites 299 class. Im new to blogging, and really not that great with computers so this should be a learning experiance for me! Im looking forward to this class and learning alot about the history of math!