Janos Bolyai was born in December 1802 in Kolozsvar, Hungary. Janos’ father, Farkas Bolyai, was also a mathematician. This most likely where Janos attained his touch in mathematics. He taught Janos much about mathematics and other skills. Janos proved to be a sponge soaking up every bit of knowledge given to him. Farkas Bolyai was a student of mathematical genius Carl Friedrich Gauss, a German mathematician who had made many mathematical discoveries. He tried to persuade Gauss to take Janos and give him the education that Farkas himself had gotten, but Gauss turned him down. This didn’t slow down Janos in his education. He had an amazing learning ability and was able to comprehend complex mathematics at a young age as well as quickly learning new languages. Farkas claimed that Janos had learned everything that Farkas could teach him by the time he was fifteen. Janos could speak many languages, and was very knowledgeable in calculus, trigonometry, algebra, and geometry. He was also a student at the Academy of Military Engineering in Vienna at the young age of 16. He studied for 4 years completing his degree in a little over half the time it took most students. Janos became interested in the problem of the axiom of parallelism or Euclid’s 5th postulate which states, “if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.” This was a theory that many mathematicians had tried to prove or disprove using the other postulates since it was created. He was determined to solve the problem despite the attempted dissuasion of his father as his father had also studied the subject extensively with little result. Janos continued to study this subject for sometime even though the college he attended did not have much to teach him in the mathematics field as he already knew most all of it. There is evidence that while still in college, Janos had created a new concept of the axiom of parallelism and a new system of non-Euclidian Geometry. Janos found that it was possible to have consistent geometries that did not fall under the rule of the parallel postulate. Janos’ conclusion was this “The geometry of curved spaces on a saddle-shaped plane, where the angles of a triangle did not add up to 180° and apparently parallel lines were NOT actually parallel.
Ancient Greece's philosophers and mathematicians have made contributions to western civilizations. Socrates believed that a person must ask questions and seek to understand the world around them. Aristotle, another famous philosopher, is known for believing that if people study the origin of life, they will understand it more. Reasoning is what makes human beings unique. Hippocrates was a mathematician and a doctor. He created the Hippocratic oath. The oath states that Hippocrates will treat his patient to the best of his abilities that he will refuse to give deadly medicine. This oath is still used by doctors today. Another Greek mathematician was Euclid. His ideas were the starting point of geometry, which is still studied around the world today.
Euclid’s Elements are predominantly the most fundamental concepts of mathematics, but his perspective on geometry was the model for over two millennia. He is believed by many to be the leading mathematics teacher of all time. However, little is known about his life outside of mathematics, or even when he was born or when he died. According to a passage written by Proclus, Euclid probably lived after Ptolemy and the pupils of Plato, but came before Archimedes and Eratosthenes. This places his existence sometime around 300 B.C. Euclid is most famous for having set the guidelines for geometry and arithmetic written in Euclid’s Elements, a series of thirteen books in which Euclid states definitions, postulates, and theorems for mathematical concepts that are still used today. What is most remarkable about the Elements is the simple, rational, and very logical structure in which Euclid presents the accumulated geometrical knowledge from the past several centuries of Greek mathematicians. The manner in which the propositions have been derived is considered to be the prime model of the axiomatic method. (Hartshorne 296).
For centuries, mathematicians tried to contradict Euclid's Postulate V, and determine that there was more than one line parallel to that of another. It was declared impossible until the 19th century when Non-Euclidean Geometry was developed. Non-Euclidean geometry was classified as any geometry that differed from the standards of Euclidean geo...
Zeno of Elea was a Greek philosopher and a mathematician. Zeno is particularly known for his paradoxes that helped build both mathematics and logic, they specifically targeted the concepts of continuity and infinity. Zeno was born in 495 BCE and died in 430 BCE. In his lifetime he contributed some great things to the subject of math. He studied at the Eleatic School, a leading school in Greek philosophy. He is said to have been a good friend of the philosopher Parmenides. After his studies he went on to write a book containing 40 paradoxes! Unfortunately none of Zeno’s writing has ever been found. Zeno contributed to mathematics greatly and he will always be remembered for this.
While there he studied theology, philosophy, mathematics, and astronomy. After his intellectual abilities became well known he was offered a professorship in Graz, Styria. One of his responsibilities was to make astrological predictions, and after his predictions of a cold winter and the Turks invading came true he was promoted. One day, while teaching a class, he observed that his drawing of circles and triangles could explain the solar system. He strongly believed in the Copernican system and with much examining he found that the solar system was three dimensional, not two dimensional.
Leonhard Euler was an outstanding mathematician. He was born on April 15, 1707 in the old city of Basel in Switzerland. His father Paul Euler was a Calvinist priest and an amateur mathematician. His early education and training was based on theology and related subjects. Because his father wants him to become a priest. That’s why he entered the University of Basel to study theology and Hebrew. At the age thirteen, he graduated from the University in philosophy major. Fortunately, famous University professor Johann Bernoulli recognized his early extraordinary ability in mathematics and physics. Who also gave him a private lesson in mathematics every Saturday afternoon. Johann Bernoulli soon realized that Euler would become a great mathematician
Greek mathematics began during the 6th century B.C.E. However, we do not know much about why people did mathematics during that time. There are no records of mathematicians’ thoughts about their work, their goals, or their methods (Hodgkin, 40). Regardless of the motivation for pursuing mathematical astronomy, we see some impressive mathematical books written by Hippocrates, Plato, Eudoxus, Euclid, Archimedes, Apollonius, Hipparchus, Heron and Ptolemy. I will argue that Ptolemy was the most integral part of the history of Greek astronomy.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
Even though Aristotle’s contributions to mathematics are significantly important and lay a strong foundation in the study and view of the science, it is imperative to mention that Aristotle, in actuality, “never devoted a treatise to philosophy of mathematics” [5]. As aforementioned, even his books never truly leaned toward a specific philosophy on mathematics, but rather a form or manner in which to attempt to understand mathematics through certain truths.
There have been many great mathematicians in the world, though many are not well known. People have been studying math for ages, the oldest mathematical object dated all the way back to around 35,000 BC. There are still mathematicians today, studying math and figuring out ways to improve the mathematical world. Some of the most well-known mathematicians include Isaac Newton, Albert Einstein, and Aristotle. These mathematicians (and many more) have influenced the mathematical world and mathematics would not be where it is today without them. There were many great individuals who contributed greatly in mathematics but there was one family with eight great mathematicians who were very influential in mathematics. This was the Bernoulli family. The Bernoulli family contributed a lot to mathematics, medicine, physics, and other areas. Even though they were great mathematicians, there was also hatred and jealousy between many of them. These men did not want their brothers or sons outdoing them in mathematics. Most Bernoulli fathers told their sons not to study mathematics even if they wanted. They were told to study medicine, business, or law, instead, though most of them found a way to study mathematics. The mathematicians in this family include Jacob, Johann, Daniel, Nicolaus I, Nicolaus II, Johann II, Johann III, and Jacob II Bernoulli.
Carl Friedrich Gauss was born April 30, 1777 in Brunswick, Germany to a stern father and a loving mother. At a young age, his mother sensed how intelligent her son was and insisted on sending him to school to develop even though his dad displayed much resistance to the idea. The first test of Gauss’ brilliance was at age ten in his arithmetic class when the teacher asked the students to find the sum of all whole numbers 1 to 100. In his mind, Gauss was able to connect that 1+100=101, 2+99=101, and so on, deducing that all 50 pairs of numbers would equal 101. By this logic all Gauss had to do was multiply 50 by 101 and get his answer of 5,050. Gauss was bound to the mathematics field when at the age of 14, Gauss met the Duke of Brunswick. The duke was so astounded by Gauss’ photographic memory that he financially supported him through his studies at Caroline College and other universities afterwards. A major feat that Gauss had while he was enrolled college helped him decide that he wanted to focus on studying mathematics as opposed to languages. Besides his life of math, Gauss also had six children, three with Johanna Osthoff and three with his first deceased wife’s best fri...
Euclid, who lived from about 330 B.C.E. to 260 B.C.E., is often referred to as the Father of Geometry. Very little is known about his life or exact place of birth, other than the fact that he taught mathematics at the Alexandria library in Alexandria, Egypt during the reign of Ptolemy I. He also wrote many books based on mathematical knowledge, such as Elements, which is regarded as one of the greatest mathematical/geometrical encyclopedias of all time, only being outsold by the Bible.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
Euclid, also known as Euclid of Alexandria, lived from 323-283 BC. He was a famous Greek mathematician, often referred to as the ‘Father of Geometry”. The dates of his existence were so long ago that the date and place of Euclid’s birth and the date and circumstances of his death are unknown, and only is roughly estimated in proximity to figures mentioned in references around the world. Alexandria was a broad teacher that taught lessons across the world. He taught at Alexandria in Egypt. Euclid’s most well-known work is his treatise on geometry: The Elements. His Elements is one of the most influential works in the history of mathematics, serving as the source textbook for teaching mathematics on different grade levels. His geometry work was used especially from the time of publication until the late 19th and early 20th century Euclid reasoned the principles of what is now called Euclidean geometry, which came from a small set of axioms on the Elements. Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor.
Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know whether they are true or not. The first one is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre. This is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. The next type of information is that Euclid was born at Megara. But this is not the same Euclid that authors thought. In fact, there was a Euclid of Megara, who was a philosopher who lived approximately 100 years before Euclid of Alexandria.