The Finished Masterpiece

Hello again,

I am writing to you for the last time. It has been a while since I have last wrote and have lots to tell. I have recently just finished the final chapter of the Brahmasphutasiddhanta. It has been my best work yet and can’t wait to see how it will impact Ujjain and other Mathematicians and astronomers within the area. As I have previously shared with you in one of my earlier posts I have come to an estimate of how long a solar year. I believe the length of a solar year is around 365 days, 5 minutes, and 19 seconds. I hope it is someone of an accurate estimate so I can make my mark in Astronomical history. before I go on further about the discoveries I have made over the course of my life I think that it is appropriate to address what influenced me in my work. Given that I am an orthodox Hindu, the Hindu yuga system has had a tremendous impact on my work because I was first interested in making estimations for planet rotations and solar years by first starting out using the Hindu yuga system of measuring the ages of mankind. I am so thankful for the Ujjain observatory for it has given me some many resources I have needed to complete my work and without it I wouldn’t have discovered many of my findings. I decided to devote the last couple of chapters to the instruments and units of measure that I used throughout my work in hope that further mathematicians and astronomers will be able to use them to try to further my work because I know there is still plenty of uncovered mysteries out there and will unfortunately not be able to discover them all. I have reached an age where I need to start enjoying life as it is and not always be so invested in my work. As I get old I fear that my life will soon come to an end so it is hard for me to balance both my work and social life due to wanting to discover as much as I can in the fields of mathematics and astronomy. Throughout writing my book I have shared a couple of theories with my fellow mathematicians specifically the number zero and they have given me a new nickname of “The Father of Zero”. I kind of like this new nickname of mine because it makes me feel that I will make a mark in history because it is such a big finding. I hope that I will be able to write to you again soon and tell you the news on how my findings have influenced society. I don’t know if I will discover much more in my life but I feel content with what I have already done because I have achieved a lot more than I anticipated.

A draft of one of my concepts that has been sitting on my desk for quite a while

Farewell, Brahmagupta

1831: Reflection in my final days

Dear Journal,

            I’m afraid this will be my last entry, for I write to you with number days. A few months ago I was diagnosed with a deadly disease, which I believe in modern days is now known as breast cancer. I know that death is an inevitable outcome of life, and these 55 years of life are a gift, compared to all the young lives taken in the Revolution, but I still cannot help but feel melancholy. I feel disappointed, not in my supposed “failure” to marry and move out of the house, but disappointed that death is a finite end to the work that I have done in mathematics and physics. There is so much to be discovered, and it pains me that death is my only restriction in conquering the vast amounts of information that remain untouched. I do think I have made my mark in history through the work that I’ve done, and I am proud of that. I have even won the recognition of Napoleon himself; in 1816, I won the grand prize in his mathematical challenge, on the third try. I was recognized in this victory as myself, Sophie Germain, and not Monsieur Le Blanc. Winning this prize gave me a well-timed boost in esteem, for I had lost confidence in my mathematical prowess when Gauss, my writing correspondent, stopped replying to my letters. I found that after our correspondence died out, pure mathematics no longer satisfied my interests and I began to delve into the world of physics. My interest in vibrating surfaces began in 1808, when I saw the acoustician Chlandni demonstrate the vibrating nodes of plates with grains of sand at the French Academy of Sciences. Napoleon was impressed by his demonstration, and offered a prize of three thousand francs for anyone who could provide a theoretical description of the nodes patterns. My final entry contained the basic hypothesis that the elasticity of the nodes was proportional to the sum of the inverses of the principal radii of the curvature of the surface, and I proved this by utilizing concepts from Euler and algebraic reasoning. To compile my findings, I wrote “Memoir on the Vibrations of Elastic Plates” (Tanzi). 

                              These are sketches of my theory of elasticity, dating to 1821.

            Although this was the first mathematical explanation for the resonance of nodes vibrating, my prestige still lay on my work with the Fermat theorem. In my later years, I received a medal from the Institut de France for my discoveries on this theorem, thus becoming the first woman to attend lectures at the Academy of Sciences in Paris. It was through this that I reconnected with my esteemed mentor Gauss. I think in part to mend our friendship; he has been lobbying to the University of Göttingen to award me an honorary degree. However, I have little faith that I will live to receive this degree, for this disease is painful and it weakens me. This is where I must stop my account dear journal; I have lost the strength to hold my quill any longer.

Au revoir,

Sophie Germain


Tanzi, Cristina. "Sophie Germain's Early Contribution to the Elasticity Theory." MRS Bulletin 1 Nov. 1999, Issue 11 ed.: 70-71. Web. http://journals.cambridge.org/action/displayFulltext?type=1&fid=9029787&jid=MRS&volumeId=24&issueId=11&aid=9029786

Eureka! I think I figured it out!

Archimedes, 265 BC

War is on the horizon. There is no way to avoid it. The Roman forces approach closer and closer every day that passes by. Despite this, I am still able to have immense successes in Syracuse. It started a while ago when King Hiero II, who happens to be a close family member to me, approached me with a question he wanted answered. As a token of his appreciation for being selected as king, he asked a goldsmith to make him a pure golden crown. Soon after he received the crown, rumors spread to him that the crown was not made of pure gold, but rather had a large amount of silver instead. You might think that this is the part of the story where Hiero has the goldsmith executed. Instead, he managed to approach the situation with a calm mind and asked me if there was any way to figure out his dilemma. While my education and studies in math had prepared me well for any problem that arose in mathematics, I was ill prepared when he asked me to help. I began to ponder the many ways to figure out his dilemma. While the most obvious would have been to just melt it down, Hiero needed it unharmed for when he offered it to the gods as a sign of thanks. No other ways were emerging in my head. The stress began to creep into my soul, so I decided that his crown could wait until after I took a bath. The water felt marvelous as I lowered myself into the water, and the water rose to meet my face. Wait! That was it! That was how I would be able to figure out his crown problem. The volume of any object submersed in water would be the exact same as the volume of water that was displaced. I stood up and shouted “Eureka,”

I even yelled this my entire way back to my house where I began to formulate ideas on how to test it. It was an obvious fact to someone like me that gold is denser than silver. Therefore, a piece of gold and a piece of silver, even if they had the same weight, would have different volumes. So if I was able to figure out the amount of water that was displaced from the crown, and compare it to the amount of water that was displaced from a chunk of gold weighing the same amount, then I could figure out if the goldsmith had cheated our king. After performing our tests, I determined that the crown was not made of pure gold. My fame and popularity are at an all time high now because of this. Despite the highs that come out of this, I am getting tired of being a second hand man to Hiero. He uses me when it is convenient, then just assumes that I am okay with it. For example, he was having issues with the irrigation of his fields. In order to fix this, he dumped the responsibility on me. I came up with an ingenious invention, if I do say so myself. It is a water screw, it takes water from a lower source, and brings it to a higher source. This drawing will explain it better.

When I came up with this idea, not only did he not show much appreciation, but he also tried to take the credit for it. These are the type of things that a king should not do. I hope he realizes for my sake and his that he is wrong. Until next time.

Archimedes

Picture 1:

"Presenting Warren "Archimedes" Buffett's Amazing 24 Hour Monster Bank of America Due Diligence Session." Http://www.zerohedge.com/. Zero Hedge. Web. 20 May 2014.

Picture 2:

Wikipedia. "Archimedes' Screw." Wikipedia. Wikimedia Foundation, 16 May 2014. Web. 20 May 2014.

What Happens When You Go Below Zero? I Know!

Hello,

I write to you today because I wish to share a recent discovery I have made. The discovery that I am talking about is that quadratic equations can have two solutions. Previous mathematicians have always just come up with one answer to a quadratic equation but they did not take negative numbers into account. Most people do not understand the concept of negative numbers yet I knew there had to be something more when a small number was subtracted by a larger number. I was in the local market sitting against a wall in downtown Ujjain when I thought about the concepts of negative numbers and was so excited by the theory that I ran all the way back to my observatory to write everything down. I believe that this concept of negative numbers will be a huge contribution to society because it will allow people to calculate debt, a new concept used in todays world.

I have started to like living in Ujjain a lot more now. The Gurjara dynasty covers a large amount of India and was started right here in Ujjain. I believe that its presence in town has given me a new insight on life and will be able to view my work in many different perspectives.

Brahmagupta's formula for cyclic quadrilaterals which he used
to calculate approximate and exact answers for areas of large spaces

I am glad to report that I have made tremendous progress on my book the Brahmasphutasiddhanta but still have a lot of work to do given that I am only on chapter twelve of twenty-five. With all of this Information that I need to include in this book I cannot even wrap my head around the fact that this will take me a very long time to complete. Hopefully I will be able to finish it before I am washed away from this earth.

I have decided to write my book in my own Sanskrit language so it will be most beneficial to Western mathematicians for I hope to keep the Indian mathematicians on top.

I have also begun to get distracted from my work due to the recent argument I am having with my fellow mathematicians and astronomers in the Jain religion. They believe that the earth rotates on a central axis… Can you believe it. I told them that if that were true then large buildings would come crumbling down. Though I do reject the ancient Hindu belief that the earth is flat or bowl-shaped which is one thing that we were able to agree on because if that was true then orbiting planets around us would have much different courses.

The chapter that I am currently working on is dealing with the rising and setting of stars, planets, and the moon. With the new formulas that I have recently discovered, I will be able to talk about about these specific subjects which I am very pleased about.

I must leave now for I have an important meeting with the King on my work for me has become very interested in astronomy.

Farewell and I hope to write again soon to let you know of my progress

Brahmagupta

Archimedes Education 275 BC

Archimedes 275 BC

As I walk back to my living quarters after yet another day at school, I think that I will delve further into my education, and what inspired me to study math. As a young child, I never had one specific passion for any subject, but rather I chose to indulge myself in all subjects. I had a liking for both math and science, but I also enjoyed myself doing anything from poetry to military strategy. While growing up as part of a young current greek family, I was expected to receive a strong education. You can imagine my happiness when I was accepted into a very prestigious school founded by none other than Euclid himself. (Here is a painting that I came to love of him.)

One of the greatest minds of all time, and I was about to attend his school! I traveled to Egypt to receive this amazing education.  Upon arrival, I met some kids who were among the brightest kids in all of the world. I began to study under the wing of both Conon of Samos, and Eratosthenes of Cyrene. With their supervision, my passion for science and math was fostered. My obsession started with Euclid’s Elements, while this is an amazing piece of work, I felt as though I could improve some of his most impressive theorems and postulates. Here is a page from his book.

 

 

So I set to work, studying, obsessing almost with his work. During my time here at Euclid’s school, I studied many of this theorems and conjectures, while at the same time, indulging myself in activities such as astronomy, and physics. I enjoy looking back and appreciating how much this school has given and taught me. As a child, I could never have imagined myself becoming a mathematician in any medium. Now I look at my life, and I see a very likely path for me following math or science. Wherever that takes me. I believe that I will return home to Syracuse after I finish my education. I have heard rumors that a war is on the horizon. That a force much stronger than our own is coming to attack us. While we are not unprepared for a situation like this, our defenses are not as strong as they could be. I have a few ideas that might turn the way in our favor if a war did break out. I can not quite formulate these ideas into drawings or concepts, but using some of the principles that I have learned from Euclid, and my education, I feel as though I may play a significant role in any upcoming war. Until I write again.

Archimedes

Picture 1:

Soylent Communications. "Euclid."http://www.nndb.com/. Soylent Communications, n.d. Web. 16 May 2014. <http://www.nndb.com/people/724/000087

Picture 2:

Blogspot.com. "Mathematical Treasures: Christopher Clavius's Edition of Euclid's Elements."http://mathtreasures.blogspot.com/. Blogspot, n.d. Web. 16 May 2014. <http://mathtreasures.blogspot.com/2012/06/christopher-claviuss-edition-of-euclids.html>.

1807: Monsieur Le Blanc Uncovered

Dear Journal,

            My identity as a woman as a woman as been revealed once again, and for the second time, it has not had nearly as negative repercussions as I had anticipated! The first time I was discovered to be Sophie and not Monsieur Le Blanc was by Joseph-Louis Lagrange, a professor at L’École Polytechnique. Since women are not allowed to study at the Polytechnique, I took on the name of a former student, Antoine-August Le Blanc, and managed to obtain the lecture notes and problems intended for him. After turning in problem sheets under his name for months, Lagrange requested a meeting with Le Blanc. Apparently, he was not only impressed with my solutions but the remarkable transformation of Le Blanc, who was known to be particularly abysmal at math during his time spent at the University. I was quite scared, for I feared my meeting with Lagrange would jeopardize his perception of my mathematical prowess, and that once he saw that I was a woman he would dismiss me with disgust. Nonetheless, I decided to follow through with his request, and was pleased to find that he was both astonished and impressed to meet my true self. I am very grateful to Lagrange, for he took my work seriously, unlike my previous mentors, and gave me the feedback and guidance that I was looking for. His support gave me confidence in my studies, and I soon began to delve into unexplored areas of math, especially in number theory. This is when I began to take a keen interest in Fermat’s Theorem. His theorem is:

xⁿ  + yⁿ = zⁿ

 

                                Pierre Fermat                                          Joseph-Louis Lagrange

            Fermat’s theorem was found without proof in about AD 250, in the margin of an ancient Greek text.  After several years, I finally made a breakthrough on his theorem and felt compelled to discuss my ideas with a fellow number theorist. I contact the renowned Carl Friedrich Gauss under my pseudonym Monsieur Le Blanc. My approach to the theorem was different from past attempts in that my goal was not to prove that only one equation had no solutions, but to say something about several equations. I relayed to Gauss that I discovered if ‘p’ is a prime number, then 2p + 1 is also prime. Therefore, for values of n with these primes, there are probably no solutions to the equation. I say probably because if there were a solution, then either x, y, or z would be a multiple of n. I was rather nervous about this first letter, for Gauss is regarded as one of the finest mathematicians in the world. To my delight, he responding enthusiastically, saying, "I am delighted that arithmetic has found in you so able a friend"(Singh).

            However, I write to now because the inevitable has occurred; Gauss has discovered I am not truly Monsieur Le Blanc. I have just finished reading his response to my letter, and his acceptance was genuinely heartwarming. I have taped an excerpt of his to the page so I never forget these words.

I hope this is a sign that in future, intellectual women will begin to be recognized with the same respect as men in their endeavors.

À bientot,

Sophie Germain

Singh, Simon. "Math's Hidden Woman." PBS. PBS, 26 Oct. 0097. Web. 16 May 2014. <http://www.pbs.org/wgbh/nova/physics/sophie-germain.html>.

The Beginning of a Great Masterpiece

Today will be one to remember, for I have started work on a new text. I have decided to called it Brahmasphutasiddhanta which translates to “Corrected treatise of brahma”. I hope to make it my best book yet. For I have had tremendous breakthroughs recently within my work. I plan to write this text within twenty-five different chapters starting with my most basic work around mean longitudes of the planets, problems of diurnal rotation, along with information involving solar and lunar eclipses. It is to be a more accurate version of the astronomical text I have learned a lot from called the Brahma Siddhanta. I am also very excited to finish this piece of writing because many of my fellow mathematicians and I have conflicting views about certain equations and theories so I hope my book will prove them wrong. I have also decided to put my most important finding that i have made thus far and maybe in my entire life into the book. I am talking about the number zero. I have discovered that the term zero is representative to nothing. I believe that this will be a very key factor in my attempt to improve the counting system. I also believe that the use of “zero” will greatly improve my predictions for planets orbital paths.

I was born in a small village called billamalla in Rajasthan in the year of 598 CE. I then decided to move to Ujjain in central India for a famous school of mathematics and have lived there ever since where I have become the Head researcher at the Ujjain observatory.

I think that I am doing a pretty good job with my astronomical theories because for some reason everyone thinks that the earth is flat where it clearly is round because of the orbital paths the planets around earth take. In terms of my advancements in astronomy I am currently trying to figure out exactly how long a lunar year is exactly. I hope I can come to a conclusion soon.

There is still a lot more i have to learn in terms of my research and hope to keep up the great work. I want to get as accurate as possible with my calculations so I can leave my mark in history

It has been a pleasure working as court astronomer for King Vyaghramukha but I feel as though i need something else going on in my life. That is why I decided to create my book. As I begin to improve my knowledge in the different fields of math I must keep in mind my great predecessors in Ujjain where I attended school. Both Varahamihira and Aryabhata are the reason why I know what I know today and without them I would be nothing.

I must leave now to continue my work because there is a lot to be done. Farewell and I hope when I write next that I will have new findings that I can share with you. 

Farewell, Brahmagupya

This is me working on my orbital calculations this past week.

1795: L'École Polytechnique

Dear Journal,

            I write to you now in a state of great frustration. It seems that there will be no end to the obstacles that arise in my mathematical endeavors. Mother and Father have been bombarding me with an insufferable chorus of “I told you so” since yesterday’s rejection from L’École Polytechnique, the new school of math and physics that has been established here in Paris. They see this as yet another opportunity to impress upon me that society women, such as myself, have no business getting an education, much less in the world of mathematics. Despite the Polytechnique’s strictly male admittance policy, I still indulged in the hope that my sleepless nights of studying Calculus under the bed-sheets would somehow pay off. I refuse to acknowledge, however, that this is a sign my studies have been in vain. When the Bastille fell, France had begun its revolution and I, sheltered from the turmoil in my father’s library, had discovered math. At thirteen years of age, I had paid no mind to the radical social and political transition France was making. It was the story of Archimedes death, an ancient Greek mathematician, that captured my interest. Archimedes was so engrossed in the study of a geometric figure that he failed to respond to the questioning of a Roman soldier was speared to death. Upon reading this initially, I was puzzled – how could a simple geometric figure be so interesting that he failed to realize the chaos surrounding him, much less that his life was at risk? However, as I began to explore his discoveries further, I began to understand. I caught the same fever as Archimedes, that addictive feelings of needing to understand a theorem or equation, striving to attain the personal satisfaction of figuring out a complicated concept.

This is L'École Polytechnique, just 4 kilometers from my house.

This is the illustration of Archimede's death, which was one in one of my father's books.

 After that, there weren’t many days I didn’t spend reading in Father’s library, studying everything from Newton to Euler. Mother and Father attempted to curb my learning at first, confiscating my candles, clothes, and any form of heating. While I certainly to do not have their approval now, their efforts to prevent me from educating myself have lessoned. I think the complete mess that is our new form of government has them distracted, with everyone getting beheaded by the Guillotine and all. The wealthy are particularly targeted in this practice, and this should probably worry me more than it does.

            I am currently trying to devise a way in which I can learn the material being taught in L’École Polytechnique without actually having to attending classes. This is particularly important to me because I think I’m on to something with Fermat’s theorem, but I want the feedback of some professors on my findings. I think my best bet in achieving this goal is to assume the identity of male when I send in my work. I’ve been playing around with potential pseudonyms. I’ve also talked to people that are attending the school now, and they’ve agreed to send me their notes from their classes in number theory. It’s not ideal, but this is the only way I can think of to pursue what I love sans public criticism.

À bientot,

Sophie Germain 

Archimedes' Advances

Archimedes, 214 B.C.-

As I feel my life drawing closer and closer to an end, as the Roman forces continue to push towards Syracuse, I would like to take this time to point out some of the discoveries that I treasure most. While I do not feel as though my work, will be fully appreciated during my time, I think that it will lay a solid foundation for math to build off of in the near future. Currently my inventions are what i am most known for. My contraptions that were put to use during the war defending Syracuse were very useful, but my largest contribution to mathematical history was my discoveries in the field of geometry. My theorems and postulates will always be useful.

While the number system that was in place before my time was adequate, it was in no way sufficient for the calculations that I used. For this reason I had to make a completely new system (with a few newly invented numbers as well). There was no way to express very large numbers. With this knowledge, I calculated the number of grains of rice that would fill what we know to be the universe. With the creation of this new system, I was able to invent integral calculus, which may have been my best invention ever. The level at which I studied Integral Calculus may be too advanced for you, but I will say that it was very important. None of this would be possible without my close backing from powerful people inside of Syracuse. Before I go into details about these relationships, I feel as though I should give some background about myself. I was born in 278 BC in Syracuse, Sicily. I have lived there all of my life except for a short period where I studied in Alexandria. While there, I was immersed into the brilliant mind of Euclid. Here fostered my passion for math. When I returned to Syracuse, my relationship with King Hiero was strengthened during the first Punic war. I was also able to play a major role during the war by using my two inventions, the Death Ray, and the “archimedes claw”.  The Death Ray was a series of mirrors when in shone in a concentrated enough beam, are able to light a wooden boat on fire.

Here is a painting of its effectiveness.

The hook was a pulley system that had a hook hanging into the water. If enemy boats got close enough, it was able to pull them out of the water and sink them. (See drawing below)

Both of these inventions played a very important role in the war and even turned the tide in our favor.

In addition to my inventions, my principles on water displacement were very important. I helped king Hiero figure out that a crown he had received had not been made out of only gold, but rather with silver as well. I figured out that the amount of water that was displaced should be the same as a piece of solid gold that occupied the same weight would displace the same amount of water. When I tested this I figured out that the amount of water that was displaced was different, therefore proving that the crown was not made of pure gold. I still remember when I figured out that theory, I was in the bathtub, and I screamed “Eureka!” This is one of my proudest moments.

Although the Romans are pushing farther towards Syracuse, I hope that I will be able to offer more contributions before my time is up.

-Archimedes

Picture 1 :

"Archimedes Death Ray: Idea Feasibility Testing." http://web.mit.edu/. Massachusetts Institute of Technology, n.d. Web. 13 May 2014. <http://web.mit.edu/2.009/www/experiments/deathray/10_ArchimedesResult.html>.

Picture 2:

"Archimedes' Claw: Illustrations."http://www.math.nyu.edu/. N.p., n.d. Web. 13 May 2014. <http://www.math.nyu.edu/~crorres/Archimedes/Claw/illustrations.html>.