Euclis
Leonard Euler:
- (April 15, 1707 - September 18, 1783) was a Swiss mathematician and physicist who made key contributions to the fields of infinitesimal calculus and graph theory.
- Euler introduced much of the mathematical terminology and notation that are still in use today, especially in mathematical analysis. One of these systems was mathematical function.
- At the age of twenty, he received second prize in the annual Paris Academy Prize Problem, a competition who went on to win twelve times.
- Euler has two numbers named after him.
- The first is the Euler's Number in calculus, represented simply as e, which has an approximate value of 2.71828.
- The second is the Euler-Mascheroni Constant γ (gamma), which is often referred to simply as "Euler's constant;" it has an approximate value of 0.57721.
- Of all of his notations, Euler's most important may be the idea of the function, as he was the first mathematician to designate the function by writing it f(x).
(n.d.). Leonhard Euler Facts. Retrieved from http://www.softschools.com/facts/scientists/leonhard_euler_facts/826/#targetText=Interesting Leonhard Euler Facts:&targetText=He is also widely remembered,greatest mathematicians who ever lived.
Gottfried Wilhelm Leibniz
- Leibniz developed the study of calculus, wholly independently of the similar work of Sir Isaac Newton.
- His mathematical notation was well received and has been used extensively ever since its original publication.
- In the 20th century, Leibniz's Law of Continuity and Transcendental Law of Homogeneity met mathematical implementation.
- He went on to become one of the most productive inventors of mechanical calculators, inventing both the pinwheel calculator and the Leibniz wheel.
- Leibniz introduced several mathematical notations, an important one being the elongated S us in Calculus to represent an integral.
- The Leibniz wheel was used in the arithmometer, which was the first real, mass-produced mechanical calculator.
- Leibniz also restructured the binary number system, the system which forms the basis of nearly all computer code.
- Along with two other philosophers, René Descartes and Baruch Spinoza, Leibniz was one of the greatest 17th century advocates of rationalism.
- Leibniz anticipated some of the more modern ideas in thought and philosophy, while still staying true to his scholastic roots.
- After his father's untimely death when Leibniz was only six, he inherited his father's extensive library and derived the basis for much of his philosophical reasoning from this reading material.
- He was a strong supporter of applying reason to principles and definitions rather than to empirical evidence.
Gottfried Leibniz Facts. (n.d.). Retrieved from http://www.softschools.com/facts/scientists/gottfried_leibniz_facts/823/.
Sophie Germain
- Late 18th and early 19th-century mathematician, scientist, and philosopher. She is remembered for her contributions to number theory, differential geometry, and elasticity theory.
- She did a good deal of work on Pierre de Fermat's famous Last Theorem.
- She and her two sisters were the daughters of a Parisian silk merchant.
- She corresponded early in her career with German mathematician Carl Friedrich Gauss
- Her gender barred her from higher education; nevertheless, she corresponded with famous scientists and mathematicians and earned a high degree of proficiency in her chosen fields.
- One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. Before her death, Gauss had recommended that she be awarded an honorary degree, but that never occurred.
Learn about Sophie Germain. (n.d.). Retrieved November 5, 2019, from https://www.famousbirthdays.com/people/sophie-germain.html.
Emmy Noether
- From 1908 until 1915, she worked at the Mathematical Institute of Erlangen without pay while conducting research studies. Renowned mathematicians Felix Klein and David Hilbert invited Emmy to join the mathematics department faculty at the University of Gӧttingen in 1915. Accepting the offer, Emmy lectured students for four years under Hilbert’s name, and was criticized by many of her colleagues at the time for working at the university.
- In 1919, she was granted a “Privatdozentin” title, which certified her to teach, but she still did not get paid. It was only in 1922, when Emmy became an associate professor, that she received a menial salary for her service.
Despite her brilliant contributions, Emmy was not promoted to professor because of gender bias. She spent the next few years as a guest lecturer at various institutions, including University of Moscow from 1928 to 1929, University of Frankfurt in 1930, and International Mathematical Congress in Zurich in 1932. She remained a faculty member of the Gӧttingen mathematics department until 1933. - Göttingen served as one of the foremost centers of mathematics in Germany until the Nazi party rose to power. Emmy Noether, an educated Jewish woman and philosophical activist, continued to teach there until she was dismissed by the new Nazi racial laws in 1933.
- With a grant from the Rockefeller Foundation and help from Albert Einstein, she was able to find refuge at the Bryn Mawr College in Pennsylvania as a guest professor, where she received a full salary and was accepted as an official teaching staff member. She also began to teach at the prestigious Princeton University’s Institute of Advanced Study.
- From 1907 to 1919, Emmy worked in the field of algebraic invariant theory, Galois theory, and physics. She was able to prove two theorems that were significant for elementary particle physics and general relativity. “Noether’s Theorem” is considered as one of the important contributions in the advancement of modern physics that helped Albert Einstein formulate his relativity theory.
- Between 1920 and 1926, Emmy devoted her time to studying the theory of mathematical rings. Her works became a breakthrough in abstract algebra when she postulated a number of principles unifying topology, logic, geometry, algebra, and linear algebra. Her study based on chained conditions on the ideals of commutative rings were praised by many mathematicians from different countries and generations.
- Her 1921 paper “Idealtheorie in Ringbereichen” (Theory of Ideals in Ring Domains) became the foundation for commutative ring theory, with the “Noetherian rings” and “Noetherian ideals” forming part of her mathematical contributions.
- Between 1927 and 1935, her studies revolved around non-commutative algebras, representation theory, hyper-complex numbers, and linear transformations.
- While working at the Erlangen, Emmy Noether published several papers on theoretical algebra in which she worked with Algebraist Ernst Otto Fischer. She also collaborated with Felix Klein and David Hilbert on a study focusing on Einstein’s general relativity theory.
- For her groundbreaking discoveries, Emmy was awarded the Ackermann-Teubner Memorial Prize in Mathematics in 1932.
Emmy Noether Facts, Worksheets, Career, Math Achievements For Kids. (2019, December 10). Retrieved from https://kidskonnect.com/people/emmy-noether/.
Euclid
1. His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics, especially geometry, from the time of its publication until the late 19th or early 20th century.
2. In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms.
3. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.
4. Euclid is the anglicized version of his Greek name, which means “renowned or glorious.”
5. He is believed to have done most of his work and teachings during Ptolemy I’s reign, between 323 BC and 283 BC.
6. What we know about him today stems from a mention of Euclid by Archimedes, mentioning him as a contemporary and fellow mathematician.
7. Even though commentators have stated that Euclid’s ideas in Elements are all based on earlier, more simplified principles, until he produced the work there was nothing like it in terms of easy and organized reference.
8. He developed mathematical proofs that are highly regarded for their completeness, and are still in use more than 2,000 years later.
9. It wasn’t until the 19th century that any other type of geometry was devised, with only Euclid’s work being considered “geometry.”
10. A detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. However, the biography is generally believed to be fictitious.
11. If he came from Alexandria, he would have known the Serapeum of Alexandria, and the Library of Alexandria, and may have worked there during his time.
12. Euclid’s arrival in Alexandria came about ten years after its founding by Alexander the Great, which means that he arrived around 322 BC.
13. Proclus introduced Euclid only briefly in his Commentary on the Elements. According to Proclus, Euclid supposedly belonged to Plato’s “persuasion” and brought together the Elements, drawing on prior work of Eudoxus of Cnidus and several pupils of Plato.
14. Euclid died in 270 BC, presumably in Alexandria.
15. Because of the lack of biographical information, which is unusual for the period in which he lived, some researchers have proposed that Euclid wasn’t, in fact, a historical character and that his works were written by a team of mathematicians who took the name Euclid from the historical character Euclid of Megara.
16. There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are, “from the edition of Theon,” or the “lectures of Theon,” while the text considered to be primary, held by the Vatican, mentions no author.
17. Although best known for its geometric results, the Elements also includes number theory.
18. Euclid’s Elements considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid’s lemma on factorization and the Euclidean algorithm for finding the greatest common divisor of two numbers.
19. The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible.
20. Today, Euclid’s geometry is known as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century.
21. The Papyrus Oxyrhynchus 29 is a fragment of the second book of the Elements of Euclid, unearthed by Grenfell and Hunt in 1897 n Oxyrhynchus.
22. Euclid’s Data deals with the nature and implications of “given” information in geometrical problems.
23. In his Divisions of Figures, which survived only partially in Arabic translation, deals with the division of geometrical figures into two or more equal parts or into parts in given ratios.
24. In his Catoptrics, he looks at the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors.
25. Euclid’s Phaenomena is a treatise on spherical astronomy. It survives in its original Greek writing and is very similar to On the Moving Sphere by Autolycus of Pitane.
26. His Optics is the earliest surviving Greek treatise on perspective. In its definitions, Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye.
12, J. (2018, June 12). 26 Fun And Interesting Facts About Euclid. Retrieved from http://tonsoffacts.com/26-fun-and-interesting-facts-about-euclid/
Pythagoras
- Pythagoras was an Ancient Greek mathematician and philosopher.
He was born on the Greek island of Samos around 570 BC and died in Greece probably around 495 BC.
- In 530 BC he moved to Italy and established a religious group known as the Pythagoreans. The group was very secretive and were vegetarians who worshipped the God Apollo. They didn’t own any possessions.
- He is best known for the Pythagorean theory named after him. Often referred to as Pythagoras’ Rule, Pythagoras’ Theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides
- He believed that science and religion were connected. He also believed that the human soul returned over and over again into people, animals and even vegetables.
- Pythagoras believed that he had already lived four lives, all of which he could remember. Others claimed that he was able to travel through space and time and could talk to plants and animals.
- Pythagoras believed the Earth was round and that mathematics could explain the physical world. He also devised the triangular figure of 4 rows, adding up to 10 and believed the design to be sacred, and called the number one, the monad.
- A special type of cup is credited to Pythagoras. The cup works normally when the user sips from it, although the contents are spilled if the user drinks too quickly.
- Pythagoras may have had a condition known as synesthesia. A person with the condition is said to be able to hear colours and see music, or associate smells with people’s names.
- No books or writings by Pythagoras have survived. He probably taught by speaking to his followers, although in the centuries after his death, several forgeries were discovered.
Carl Friedrich Gauss
- Gauss is occasionally referred to as the "princeps mathematicorum,"or "the prince of mathematicians." Others have referred to him as "the foremost of mathematicians" or "the greatest mathematician since antiquity."
- These accolades are a result of Gauss's remarkable influence in so many fields of mathematics and science; he is categorized as one of history's most significant mathematicians.
- Despite being born to poor, illiterate parents who were not able to even write down the date of his birth, Gauss was a child prodigy and was educated.
- His work in groundbreaking discoveries in mathematical theory attracted the attention of a nobleman who became his patron, and supported his higher education.
- Gauss's most influential writing was drafted when he was only 21, and still defines the understanding of number theory to this day.
- Some of his most important findings, however, had practical implications, as he proposed a number of theorems on shapes that had a direct impact on architecture and construction.
- Gauss was the first mathematician to construct a 17-sided heptadecagon using a compass and a straight edge, and more importantly was the first to prove the laws of quadratic reciprocity.
- Gauss's work was instrumental to the understanding of algebra, as he proved its central theorem which states that "every non-constant single-variable polynomial with complex coefficients has at least one complex root."
- He is also responsible for the prime number theorem, which broadly still applies to mathematics today.
- One of Gauss's most important contributions to astronomy stemmed from using conic equations to track the dwarf planet Ceres, whose own discoverer Giuseppe Piazzi could not locate it months after its discovery due to the limitations of available tools.
- This successful work in astronomy led Gauss to not only secure a position as head of astronomy at the observatory in Gottingen, but also to produce further work in planetary motion.
- His work on using conic sections originating from the position of the sun replaced the difficult mathematical formulas that had been used in astronomy until then.
- Gauss is attributed to a number of other major discoveries in different related fields, including non-Euclidean geometry and Gaussian geometry, important in land surveys and determining curvatures.
Carl Friedrich Gauss Facts. (n.d.). Retrieved from https://www.softschools.com/facts/scientists/carl_friedrich_gauss_facts/827/