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...
... middle of paper ...
... 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.
Overall George Boole’s life was filled with many moments of success, but was Boole an advance towards where mathematics is today? As many times that Boole was recognized his work finally paid off. At one point even Albert Einstein used Boole’s methods of mathematics to continue to advance of his own mathematics and sciences.
Born in the summer of September 17, 1826 in Breselenz, Kingdom of Hanover what’s now modern-day Germany the son of Friederich Riemann a Lutheran minister married to Charlotte Ebell was the second of six children of whom two were male and four female. Charlotte Ebell passed away before seeing any of her six children reach adult hood. As a child Riemann was a shy child who suffered of many nervous breakdowns impeding him from articulating in public speaking but he demonstrated exceptional skills in mathematics at an early age. At the age of four-teen Bernhard moved to Hanover to live with his grandmother and enter the third class at Lynceum two years later his grandmother also passed away he went on to move to the Johanneum Gymnasium in Lunberg and entered High School. During these years Riemann studied the Bible, Hebrew, and Theology but was often amused and side tracked by Mathematics. Showing such interests in mathematics the director of the gymnasium often time allowed Riemann to lend some mathemat...
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...
...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?
Euler was born in Basel, Switzerland where he was destined to be a clergyman. Yet, it was obvious that Euler had a different calling in life. His aptitude for mathematics was evident even in his early life. His propensity for higher learning was so great that he studied with Johann Bernoulli, who was Jakob’s brother, as a young boy. His time with Johann urged his sense of mathematic discovery. Euler attended University of Basel where he earned his Master’s degree while he was still a teenager. While at the school he barely learned any mathematics because the school was basically a poor school. Due to his own mathematic curiosity and Johann’s private lessons, at the under-ripened age of 16, Euler became a college graduate with a Master’s degree. His curiosity in mathematics allowed Euler to study the works of other brilliant ...
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...
... relationship in one problem that doesn’t appear in others. Among all of this, there is such vastness in how one person might approach a problem compared to another, and that’s great. The main understanding that seems essential here is how it all relates. Mathematics is all about relationships between number and methods and models and how they all work in different ways to ideally come to the same solution.
A turning point in his educational career came in 1906. He began researching under his tutor E.W. Barnes. Barnes was so impressed with how quickly he was solving each problem he was given, he was then presented with the Riemann hypothesis to work on.
Ludwig Wittgenstein (1889-1951) developed his interest in philosophy while studying aeronautical engineering at Manchester University. This interest was in the philosophy of pure mathematics and ultimately led him to Gottlob Frege, who advised him to go to Cambridge and study with Bertand Russell, in 1911 (Biletzki & Matar, 2011). This was the inception of Wittgenstein’s early philosophy, which lasted from 1911 – 1921. He joined the Austrian army at the start of World War I and was eventually taken captive in 1917. During his time in captivity at a prison camp, he wrote his first important work, Tractatus Logico-Philosophicus.
Born in the Netherlands, Daniel Bernoulli was one of the most well-known Bernoulli mathematicians. He contributed plenty to mathematics and advanced it, ahead of its time. His father, Johann, made him study medicine at first, as there was little money in mathematics, but eventually, Johann gave in and tutored Daniel in mathematics. Johann treated his son’s desire to lea...
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.
Before we examine Stevin’s work and how it impacted modern mathematics, we must first understand Stevin’s past and what inspired him to publish his masterpiece. Stevin was born in the year 1548 in modern day Belgium. (O’Conner) Stevin was assumed to be raised a Calvinist by the family his mother married into. In his younger years, Stevin became a bookkeeper and cashier in a firm in Antwerp. Then in the year 1577, he acquired a job in a tax office in Brugge. (O’Conner) These early jobs make it clear that Stevin was very fluent with the arithmetic already used in those days. From these jobs, he must have seen the need for a more simple type of arithmetic. When Stevin was 35, he attended the University of Leiden. It was at this university, Stevin became acquainted with the second son of William Prince of Orange who was the ruler of the Northern area of the Netherlands at the time. Stevi...
Wigner, Eugene P. 1960. The Unreasonable Effectiveness of Mathematics. Communications on Pure and Applied Mathematics 13: 1-14.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.