Few mathematicians had the good chance to change the course of mathematics more than once; Luitzen Egbertus Jan Brouwer is one of the remarkable people who managed to do so. He came as a young student where before he could finish school he had already published his first original research papers on rotations in 4-dimensional space. Brouwer was a Dutch mathematician who founded mathematical intuitionism, which is a doctrine that views the nature of mathematics as mental constructions governed by self-evident laws, and whose work completely transformed topology which is the study of the most basic properties of geometric surfaces and configurations.
The life of Brouwer is easily summarized. His upbringing was entirely uneventful. Luitzen Egbertus Jan Brouwer was born on February 27, 1881 in Overschie, Amsterdam and passed away on December 2, 1966, Blaricum, Netherland was known as L. E. J. Brouwer but known to his friends as Bertus. He attended high school in Hoorn, a town on the Zuiderzee north of Amsterdam. His performance there was outstanding and he completed his studies by the age of fourteen. As a student of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis. He was an excellent student and quickly progressed through university studies. Brouwer studied mathematics at the University of Amsterdam from 1897 to 1904. Within those seven years he received his bachelors and masters in mathematics and applied mathematics. At that point, his interest was starting to arouse in philosophical matters. In his doctoral thesis, Brouwer attacked the reasonable basics of mathematics.
Brouwer was well known for his philosophy on Intuitionism. In the philosophy of mathematics, intuitionism...
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... 1903 to 1909, Brouwer did his important work in topology, presenting several fundamental results, including the fixed-point theorem. The fixed point theorem in topology states that for any continuous function f with certain properties there is a point x0 such that f(x0) = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a curved compact subset K of Euclidean space to itself. Suppose there exist a continuous function f where B squared goes to B square and they have no fixed points. Now consider the ray is in 2 real numbers on a two dimensional space that runs from some function of x through the value x. Because f has no fixed points, the function of x do not equal the value of x and for every x there exist a number raised to a power, so the ray is well defined.
Euler was one of the mathematical giants of the 18th Century. Leonard Euler (1707-1783) was born in Basel, Switzerland. His father was a Lutheran minister and wanted him to follow his path. Euler’s interest was different however, he was a natural mathematician. Johann Bernoulli helped Euler pursue his path by convincing his father of his mathematical abilities. Bernoulli became Euler’s teacher at the St. Petersburg Academy of Science. Euler’s personal life was more on the tragic side. He married and had 13 children, but only 5 survived their infancy. It is said that Euler made some of his greatest discoveries while holding his baby
Gottfried Wilhelm Leibniz was born to a highly educated family on July 1, 1646 in Leipzig. Leibniz’s father, Friedrich Leibniz, was a professor of Moral Philosophy at the University of Leipzig and Catharina Schmuck, his mother, was the daughter of a professor of law. With the event of his father’s death, Leibniz was guided by his mother and uncle in his studies. He was also given access to the contents of his father’s library. In 1661 Leibniz began his formal university education at the University of Leipzig. While attending the university he soon met Jacob Thomasius. Thomasius instilled in Leibniz a great respect for ancient and medieval philosophy. After accepting his baccalaureate from Leipzig, Leibniz began studying at the University of Altdorf. While in attendance at Altdorf, Leibniz published Dissertation on the Art of Combinations (Dissertatio de arte combinatoria) in 1666 (Brandon C. Look, 2007). It sketched a plan for a “universal cha...
AUTHOR: Oswald Spengler, (1880-1936), was a German philosopher who acquired his conservative views from his father, a postal official in Germany. Spengler attended the Universities of Munich, Berlin and Halle in Germany, where he studied natural science and mathematics. In 1903, he wrote his dissertation on a Greek philosopher named Heraclitus, though he failed due to a lack of references. Spengler resubmitted his revised thesis in 1904, earning him his doctorate degree. Shortly after earning his degree, Spengler suffered a mental break down, secluding himself from the world. In 1906, he recovered and began working as a teacher in secondary schools until he received some money from his mother. In 1911, Spengler gathered his inheritance and moved to Munich as a private scholar.
...y, M.C. Escher’s artworks are among the most widely recognized. His timeless and intriguing pieces drive thousands of admirers to his exhibitions around the world. Incorporating numerous mathematical concepts into his works, he elegantly demonstrated the distinct art and math relationship. Escher died on March 27th, 1972. However, his legacy lives on, along with controversy surrounding the question: was Escher an artist or mathematician?
Robert, A. Wayne and Dale E. Varberg. Faces of Mathematics. New York: Harper & Row Publishers, Inc., 1978.
...ibutions to analytic geometry, algebra, and calculus. In particular, he discovered the binomial theorem, original methods for expansion of never-ending series, and his “direct and inverse method of fluxions.”
Fundamentally, mathematics is an area of knowledge that provides the necessary order that is needed to explain the chaotic nature of the world. There is a controversy as to whether math is invented or discovered. The truth is that mathematics is both invented and discovered; mathematics enable mathematicians to formulate the intangible and even the abstract. For example, time and the number zero are inventions that allow us to believe that there is order to the chaos that surrounds us. In reality, t...
His father taught his Latin but after a while saw his son’s greater passion towards mathematics. However, Andre resumed his Latin lessons to enable him to study the work of famous mathematicians Leonhard Euler and Bernoulli. While in the study of his father’s library his favorite study books were George Louis Leclerc history book and Denis Diderot and Jean Le Rond Encyclopedia, became Ampere’s schoolmasters (Andre). When Ampere finished in his father’s library he had his father take him to the library in Lyon. While there he studied calculus. A couple of weeks later he was able to do difficult treaties on applied mathematics (Levy, Pg. 135). Later in life he said “the new as much about mathematics when he was 18, than he knew in his entire life. His reading...
However, his greatest contribution to mathematics is considered to be logic, for without logic there would be no reasoning and therefore no true valid rules to the science of mathematics.
Furthermore, during 1619 he invented analytic geometry which was a method of solving geometric problems and algebraic geometrically problems. After, Rene worked on his method of Discourse of Mindand Rules for the Directions of th...
Throughout his early school career, his parents would often push him to better his education. He would often receive books and encylopedias from his parents so that he could further expand his knowledge. During his final high school year his parents arranged for him to take advanced mathematics courses at a community college that was local to them.
Born in Minden, Westphalia, Germany, in 1858, from a Jewish family, Boas early thinking was based on the ideals of the 1848 German revolution and followed his parents’ intellectual freedom (Stocking, 1974). However, Boas did not set out with the specific ambition to study human cultures, and after attending the universities of Heidelberg, Bonn and Kiel, in 1881 he earned a PhD. in Physics, with a minor in geography. Marked by the influence of Rudolf Virchow,
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.