Womans Contributions To Mathematicss Essay, Research Paper
Abstraction
Womans in the universe of mathematics is a topic that people seldom hear about. The lone
clip people do is if it? s a female math instructor. But what many do non cognize is that
adult females have made highly of import parts to the universe of mathematics.
Womans have been documented to be involved in mathematics, since every bit early as the fifth
century A.D. Women such as Hypatia, Maria Gaetana Agnesi, Sophie Germain, Emmy
Noether, Ruth Moufang and Sun-Yung Alice Chang. These adult females have lived through
hard times such as adult females? s subjugation, the Gallic Revolution, World War I and II,
which included Hitler? s disposal over adult females? s schooling, and societal biass.
This did non halt their longing for math though. These adult females combined have earned
many different awards, specifically 1s normally given to work forces. They have conquered the
prejudices people have had towards them and made what they do best count. Many of their
theorems and equations are still used today, and some are even being perfected by others.
It is of import that the reader realizes that educating kids about adult females in
mathematics is of import. Many kids think of mathematicians as work forces, and that is
wholly untrue. That thought could perchance lend to the fact that adult females are less
probably to come in the mathematics field compared to work forces. This is because they are non
educated decently on the topic, and are non given the chance to stand out. There are
many more adult females in mathematics so mentioned above, but the 1s named are really
of import to the field and kids need to cognize that. By taking these 6 adult females? s
parts and concentrating on how they apply to the in-between school course of study would be
really utile to any instructor. The kids could each pick a female mathematician, and
do a posting and make a presentation about their findings. It could besides be done as a
group undertaking. Equally long as the subject gets discussed and that the misss come out feeling like
they could besides acquire involved in mathematics.
Womans? s Contributions to Mathematicss
In the universe of mathematics, you seldom hear anything about adult females
mathematicians. Although non much is said about adult females and math, there are many
adult females mathematicians who have made important parts to the field. From as
early as 370 AD, adult females have been lending to the survey of equations, theorems, and
even work outing jobs that have deemed themselves in the mathematical universe as
impossible. Because of the clip period that these adult females lived, many were non
recognized for their accomplishment ; some were even banished or killed. Name callings such as
Hypatia, Maria Gaetana Agnesi, Sophie Germain, Emmy Noether, Ruth Moufang, and
Julia Bowman Robinson may non be common to the mundane individual. But to
mathematicians around the universe, particularly adult females, they are a mark of accomplishment and
finding in a field dominated by work forces. In order to do adult females recognized in the
field of mathematics, pedagogues need to pass clip learning their pupils that math is non
merely for males. Because of the parts of the adult females named above, math
geographic expedition has been furthered and many inquiries have been answered, although some
are still to this twenty-four hours unresolved.
Hypatia
370? -415 Ad
Hypatia is the first, genuinely documented adult female mathematician. Her plants have
given manner to celebrated male mathematicians such as Newton, Descartes, and Leibniz.
Raised in ancient Egypt during the clip that Christianity started to take over many other
faiths, it was difficult for Hypatia to analyze anything in an age where males dominated
many Fieldss of survey. Hypatia was looked at, though, as a adult female of strong character, and
as a strong speechmaker, astrologer, astronomist, and mathematician. Raised largely by her
male parent, Theon, a known mathematician of the times, Hypathia gained a batch of cognition
at a immature age. She studied under her male parent? s supervising, which gave her the wanting to
cognize the unknown in mathematics.
Hyapthia made many parts to the survey of mathematics, her most celebrated
being her work on conelike subdivisions. A conelike subdivision is when a individual divides cones into
different parts utilizing planes. Because she edited a book written by Apollpnius so good, her
work survived all the manner up until today. Her constructs later developed into what is today
called, hyperbolas, parabolas, and eclipsiss.
Hypatia died a really tragic decease in 415 AD. Because she was a adult female in the
field of mathematics and scientific discipline, many rumours were dispersed about her. One of the
Christian leaders named Cyril heard of these rumours and because he did non like the civil
governor of Alexandria, where Hypatia lived, he made Hypatia a mark. She was really
respected and he knew that killing her would decidedly ache the metropolis. On her manner place
one dark, she was attacked by a rabble and literally skinned with oyster shells. Some say
she died for the love of mathematics ( Adair, 1995 ) .
Maria Gaetana Agnesi
1718-1799
Maria Gaetana Agnesi was non truly considered a mathematician in her clip. But
now that some people look back, she made a really important part to the universe of
mathematics. She practiced mathematics during the Renaissance in Italy. During this
clip, it was considered an award to be an educated adult female. So Maria was both looked up
to and considered a prodigy by the clip she was really immature. This could be attributed to
the fact that her male parent was an solid mathematician and professor in Milan, Italy.
He frequently had talks and seminars at his house for people to come and hear about math.
She liked to listen to these talks which may hold sparked her involvement in mathematics.
There are two achievements that Maria is accredited with. Her first is her
book that she got published called Analytical Institutions, which was about built-in
concretion. Some say that it was originally written for her younger brothers, to aide them in
math. Now that the book has been translated, many mathematicians are utilizing her work
and it is used as a text edition.
Her 2nd achievement is a curve called the Witch of Agnesi. Maria came
up with the equation for this well known curve: y= a*sqrt ( a*x-x*x ) /x. The manner to
bring forth the curve is xy2=a2 ( a-x ) ( Golden & A ; Hanzsek-Brill, no day of the month ) The ground why it
is called the Witch of Agnesi is because the adult male who translated the name of the curve
may hold mistranslated the Latin word versiera. It can either intend? to turn? or? the married woman
of the devil. ? This curve is really utile in the field of mathematics ; even Fermat studied
this curve. Fermat besides made the celebrated job called Fermat? s Last Theorem, which
celebrated female mathematician Sophie Germain studied ( Unlu, 1995 ) .
Sophie Germain
April 1, 1776-June 27,1831
Sophie Germain, was born right before the Gallic Revolution. She was born into
the in-between category, and this meant that she had to conceal her individuality in order to pattern math.
The in-between category was non supportive of adult females analyzing math, therefor much of her work
is done under her anonym M. Leblanc. Because of the Revolution, Sophie had to
pass many yearss in her house, for fright of being killed in a rebellion. She was intrigued by
the narrative of Archimedes and how he got killed because he would non react to a soldier
while looking at a math job. Some people think this is why Sophie choose to analyze
mathematics.
Sophie Germain studied under celebrated mathematician of the clip, Carl Friedrich
Gauss. Gauss was truly into figure theory and Fermat? s Last Theorem. Fermat? s Last
Theorem is closely related to the Pythagorean theorem. Alternatively of utilizing x2+y2=z2,
Pierre de Fermat used x, Y, and omega raised to powers of 3, 4, 5, etc. Many think that this
job was insolvable, but Fermat said that he had cogent evidence it could work. The enigma is
though, that Fermat ne’er wrote down his solution. It was up to future mathematicians to
happen the solution that Fermat claimed.
Sophie was up to the challenge, and in a missive to Gauss, written in 1808 she came
up with a computation that said something about several solutions. Fermat? s theory says
there are no positive whole numbers such that for n*2. But Sophie proved in her theorem that if
ten, Y, and omega are to the fifth power than N has to be divisible by five. Sophie said that this
would work merely with what are now called Germain primes. Germain primes are primes
such that when you take a premier, multiply it by two, and so add one, your reply will
be premier. Some Germain primes are 2, 3, 5, 11, 23 and 29 ( Singh, no day of the month ) . In 1825,
she proved, that for the first portion of Format? Last theorem, these primes would work.
There are many other mathematicians that have followed up on Sophie? s work on
Fermat? s Last Theorem. Number theoretician, Euler and Legrange, proved that if p=3 is
prime, 2p+1 is besides premier if and merely if 2p+1 divides 2p-1. In 2000, celebrated figure
theoretician, Henri Lifchitz, found an easier manner to find a Germain premier. He says that
if p*=5 is premier, q=2p+1 is besides premier if and merely if q divides 3p-1. It turns out though in
1994, Andrew Wiles, a research worker at Princeton, claimed to hold cogent evidence of the theorem.
His manuscripts have been reviewed and it is among the bulk that he has proved it
( Swift, 1997 )
Emmy Noether
March 23, 1882-April 14, 1935
Still in the late 1800s, it was non proper or allowed for a adult female to travel to college.
Emmy Noether became one of these adult females, when she was denied registration at the
University of Erlangen. They did let her, though, to sit in on two old ages of math
categories and take the test
that would allow her be a doctorial pupil in math. She passed the
trial and after traveling for five more old ages, she was given a sheepskin. After graduation,
Emmy decided to take up instruction, but the university would non engage her because she was
a adult female. So she decided to work along side her male parent, who at the clip was a professor
at the university. Emmy Noether & # 8217 ; s first piece of work was finished in 1915. It is work in
theoretical natural philosophies, sometimes called the Noether & # 8217 ; s Theorem, which proves a relationship
between symmetricalnesss in natural philosophies and preservation rules. This basic consequence in the
general theory of relativity was praised by Einstein, where he commended Noether on her
accomplishment.
During the 1920s Noether did foundational work on abstract algebra, working in
group theory, pealing theory, group representations, and figure theory. During the clip that
she was a instructor, Germany was involved in WWI and WWII. Because of the war, and
since Noether was a Jew, she was forced out of Germany and went to populate in the United
States ( ? Emmy Noether? , no day of the month ) .
While in the United States, Noether taught at an all misss college. Her pupils
loved her and many followed her instructions. Some say that they manner she taught was
phenomenal. She was clear and used many different methods of learning so that her
pupils could understand math easier. She was praised by Einstein invariably on her
theory of relativity. Albert Einstein paid her a great testimonial in 1935: & # 8220 ; In the opinion of
the most competent life mathematicians, ( Emmy ) Noether was the most important
originative mathematical mastermind therefore far produced since the higher instruction of adult females
began. & # 8221 ; Throughout her calling she worked with many mathematicians such as Emanuel
Lasker, Bartel new wave der Waerden, Helmut Hasse and Richard Brauer. Twice Noether was
invited to turn to the International Mathematical Congress ( 1928, 1932 ) . In 1932 she
received the Alfred Ackermann-Teubner Memorial Prize for the Advancement of
Mathematical Knowledge. It is said that her greatest work was that of abstract algebra
( Taylor, 1995 ) .
Ruth Moufang
January 10, 1905-November 26, 1977
Like the Nazis refused Emmy Noether the right to learn, Ruth Moufang was besides
denied the right. Because of this, Ruth Moufang decided to come in the field of industrial
mathematics, and work on the snap theory. She was the first German adult female to hold
a doctor’s degree in this field. Ruth Moufang published one celebrated paper on group theory.
This paper was foremost written based on the Hagiographas of Hilbert. Ruth? s most celebrated
instructions were on figure theory, knot theory, and the foundations of geometry. She besides
is celebrated for what we call today, Moufang planes and Moufang cringles. Moufang loops
are a category of cringles which arise of course in many other Fieldss such as finite group theory
and algebraic geometry ( O? Conner & A ; Robertson, 1996 ) .
Sun-Yung Alice Chang
March 24, 1948-present
Sun-Yung was born in Ci-an, China. During research, no information was found
on the clip period when she was born. What was found though is an copiousness of
information on her college life and what her parts to mathematics were.
Sun_Yung Chang received her doctor’s degree in mathematics from University of
California. She so went to learn college math at UCLA. Presently, she still teaches at
UCLA, but since she started many things have happened to her.
Her greatest achievement is when she received the Ruth Lyttle Satter award for
her parts to mathematics over the last five old ages. She was awarded the award for
her parts to partial differential equations and on Riemannian manifolds. The
survey of manifolds holding a complete Reimannian Metric is called Reimannian geometry
( Weinsstein, 1996-2000 ) . This is a subject that Sun-Yung studied a batch. Sun-Yang says, in
her address at the American Mathematical Society, ? Following the early work of J Moser
and influenced by the work of T Aubin and R Schoen on the Yamabe job, P. Yang
and I have solved the partial differential equation of Gaussian/scalar curvatures on the
sphere by analyzing the extremal maps for certain fluctuation functionals. We have besides
applied this attack in conformal geometry to the isospectral concentration job on
3-manifolds when the prosodies are restricted in any given conformal category. More late
we have been analyzing the extremal prosodies for these functionals. We are working to
derive farther geometric effects. This latter piece of work is a natural extension of
the earlier work by Osgood-Phillips-Sarnak on the log-determinant functional on compact
surfaces. ? ( O? Conner & A ; Robertson,1998, p. 2 ) Sung-Yung is already considered to be a
great mathematician, even though she says there is still work to be done.
Womans in Mathematics connected to the Middle School Curriculum
In Sun-Yung? s address, given at the credence of her award in 1995 she states,
? Since the Satter Prize is an award for adult females mathematicians, one can non assist but to
reflect on the position of adult females in our profession now. Compared to the state of affairs when I
was a pupil, it is clear that there are now many more active adult females research
mathematicians. I can personally attest to the importance of holding function theoretical accounts and the
company of other adult females co-workers. However, I think we need even more adult females
mathematicians to turn out good theorems and to lend to the profession. ? ( O? Conner
& A ; Robertson, 1998, p. 2 )
This is precisely why this subject needs to be discussed in the in-between classs. Girls
demand to cognize that mathematics is non merely for work forces. Young misss may be less disposed to travel
into the field of mathematics based on the prejudices that have been traveling for old ages.
Teachers need to state about the importance of mathematical accomplishments for both male childs and misss,
and besides necessitate to be after activities centered around adult females in mathematics. By speaking to
immature misss in in-between school about female mathematicians, pedagogues could perchance
light a fire, under perchance, another great female mathematician.
Although many do non believe of adult females as mathematicians, there are many adult females
who have proved themselves in the mathematical universe. Through their theorems and
job resolution, these adult females have furthered the universe of mathematics, for others to
someday conquer.
Mentions
Adair, G. ( 1995 ) . Hypatia. Agnes Scott College [ Online ] . Available:
hypertext transfer protocol: //www.agnesscott.edu/lriddle/women/agnesi.htm [ 1 March 2000 ] .
Emmy Noether ( no day of the month ) . [ Online ] .
Available: hypertext transfer protocol: //www.coastal.edu/academics/science/jump/biography/enoether.ht
milliliter [ 5 March,2000 ] .
Golden & A ; Hanzsek-Brill. ( no day of the month ) . Probe of the Witch Curve. [ Online ] .
Available: hypertext transfer protocol: //jwilson.coe.uga.edu/Texts.Folder/Agnesi/witch.html [ 1 March,
2000 ] .
O? Conner, J.J. , & A ; Robertson, E.F. ( 1996 ) . Ruth Moufang. [ Online ] . Available:
hypertext transfer protocol: //www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Moufang.html [ 24
February 2000 ] .
O? Conner, J.J. , & A ; Robertson, E.F. ( 1998 ) . Sun-Yung Alice Chang. [ Online ] . Available:
hypertext transfer protocol: //www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Chang.html [ 6
March 2000 ] .
Singh, Simon. ( no day of the month ) . Math? s Hidden Women. [ Online ] . Available:
hypertext transfer protocol: //www.pbs.org/wgbh/nova/proof/germain.html [ 1 March 2000 ] .
Swift, Amanda. ( revised in 1997 ) . Sophie Germain. Agnes Scott College [ Online ] .
Available: hypertext transfer protocol: //www.agnesscott.edu/lriddle/women/germain.htm [ 1 March
2000 ] .
Taylor, Mandie. ( 1995 ) . Emmy Noether. Agnes Scott College [ Online ] . Available:
hypertext transfer protocol: //www.agnesscott.edu/lriddle/women/noether.htm [ 2 February 2000 ] .
Unlu, Elif. ( 1995 ) . Maria Gaetana Agnesi. Agnes Scott College [ Online ] . Available:
hypertext transfer protocol: //www.agnesscott.edu/lriddle/women/agnesi.htm [ 1 March 2000 ] .
Weisstein, Eric. ( 1996-2000 ) . Riemannian Geometry. Wolfram Research Inc. [ Online ] .
Available: hypertext transfer protocol: //www.mathworld.wolfram.com/RiemannianGeometry/html [ 7
March 2000 ] .
Bibliography
Mentions
Adair, G. ( 1995 ) . Hypatia. Agnes Scott College [ Online ] . Available:
hypertext transfer protocol: //www.agnesscott.edu/lriddle/women/agnesi.htm [ 1 March 2000 ] .
Emmy Noether ( no day of the month ) . [ Online ] .
Available: hypertext transfer protocol: //www.coastal.edu/academics/science/jump/biography/enoether.ht
milliliter [ 5 March,2000 ] .
Golden & A ; Hanzsek-Brill. ( no day of the month ) . Probe of the Witch Curve. [ Online ] .
Available: hypertext transfer protocol: //jwilson.coe.uga.edu/Texts.Folder/Agnesi/witch.html [ 1 March,
2000 ] .
O? Conner, J.J. , & A ; Robertson, E.F. ( 1996 ) . Ruth Moufang. [ Online ] . Available:
hypertext transfer protocol: //www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Moufang.html [ 24
February 2000 ] .
O? Conner, J.J. , & A ; Robertson, E.F. ( 1998 ) . Sun-Yung Alice Chang. [ Online ] . Available:
hypertext transfer protocol: //www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Chang.html [ 6
March 2000 ] .
Singh, Simon. ( no day of the month ) . Math? s Hidden Women. [ Online ] . Available:
hypertext transfer protocol: //www.pbs.org/wgbh/nova/proof/germain.html [ 1 March 2000 ] .
Swift, Amanda. ( revised in 1997 ) . Sophie Germain. Agnes Scott College [ Online ] .
Available: hypertext transfer protocol: //www.agnesscott.edu/lriddle/women/germain.htm [ 1 March
2000 ] .
Taylor, Mandie. ( 1995 ) . Emmy Noether. Agnes Scott College [ Online ] . Available:
hypertext transfer protocol: //www.agnesscott.edu/lriddle/women/noether.htm [ 2 February 2000 ] .
Unlu, Elif. ( 1995 ) . Maria Gaetana Agnesi. Agnes Scott College [ Online ] . Available:
hypertext transfer protocol: //www.agnesscott.edu/lriddle/women/agnesi.htm [ 1 March 2000 ] .
Weisstein, Eric. ( 1996-2000 ) . Riemannian Geometry. Wolfram Research Inc. [ Online ] .
Available: hypertext transfer protocol: //www.mathworld.wolfram.com/RiemannianGeometry/html [ 7
March 2000 ] .
