Essay - Mathematics George Cantor the Purpose of the Paper is to...

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***** Cantor

***** purpose of the paper is to develop a concept ***** the connection between m*****thematics and society from a historical perspective. Specifically, it will discuss the subject, what George Cantor accomplished for mathematics and what that did for society. George Cantor's set theory changed the way mathematicians of the time looked at *****ir science, and he revolutionized the way the world looks at numbers.

George Cantor was a brilliant mathematician and philosopher who developed the modern mathematical idea of infin*****y, along with the idea ***** an infinite set of real numbers, called transfinite sets, or the "set the*****y." In addition, Cantor found that real ***** were not countable, while algebraic numbers were countable (Breen). *****'s views were quite controversial when he first developed them in the late 1800s, and some mathematicians today question some ***** his hypothesis ("Transf*****ite Number"), however, his work is recognized as some of the most important ***** thought ***** our time. Not only did Cantor get other mathematicians thinking about problems ***** had plagued them for years, he changed the ***** they looked at numbers in general - it made them ***** ***** numbers actually are.

How did *****'s theories affect *****? Cantor's work, which he attributed to God's divine wisdom showing him the solutions, ***** the way mathematicians looked at their work. It also stirred up interest in mathematics that had waned during the Victorian era. Even more importantly, his theories spilled over into many other innovations of the day, including the atomistic statistical thermodynamics, stop-motion photography, and even the color-plane type of painting by Gauguin ***** Bernard (Everdell 46). In add*****ion, Cantor's works also inspired philosophical thought in any number of ***** contemporaries, because ***** like Bertrand Russell and Ludwig Wittgenstein turned to philosophical thought to explain ***** even try to disprove Cantor's theories. ***** ***** theories inspired *****s to create, think, prove, and dis*****, and so, his work not ***** *****d a ***** underst*****ndable and *****able form of arithmetic, it created new thought and new art forms ***** changed society and how society looked at science. When people began to understand that mathematics could influence everything from pho*****graphy to ***** and *****, they took a greater interest in mathematics and philosophical thought, ***** in turn led to even more innovation and scientific thinking. In fact, today, m***** scientists and mathematicians feel Cantor's work represented a real paradigm shift, or a r*****dical change in mathematical and philosophical thought ("Cantor"). Two of his lasting models that s*****ed his theories ***** "*****'s Comb," which showed all points were *****connected from each other, and "Cantor's Dust," which calls these disconnected sets "fractal dust" (Breen). Cantor's work really revolutionized mathematics, ***** encouraged ***** to think philosophically about just what numbers really were.

Unfortunately, Cantor's mental health deteriorated as he aged, and ***** had several nervous breakdowns in reaction to criticism ***** his work. Today, many believe he suffered from bipolar disorder ("Can*****r"). It is sad to th*****k that Cantor may have contributed even more to


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