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

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***** Cantor

The purpose of the paper is to develop a concept of 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 ma*****maticians of the time looked at ********** science, and he revolutionized the way the world looks at numbers.

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

How did Cantor's theories affect *****? ***** work, which he attributed to God's divine wisdom showing him the solutions, changed the way mathematicians looked at their work. It also stirred up interest in ***** th***** had waned dur*****g *****e Victorian era. Even more importantly, his theories spilled over into many other innovations of the day, including the atomistic statistical thermodynamics, stop-motion photography, ***** even the color-plane type ***** painting by Gauguin and Bernard (Everdell 46). ***** add*****ion, Cantor's *****s ***** inspired philosophical thought in any number of his contemporaries, because ma*****maticians like Bertrand Russell and Ludwig Wittgenstein turned to philosophical ***** ***** explain and even try to disprove Can*****r's theories. Cantor's set theories ***** others to create, think, prove, and disprove, and so, his work ***** only *****d a more underst*****ndable and workable form ***** arithmetic, it created new thought and ***** art forms that changed *****ciety ***** how society looked at science. When people began to understand ***** mathematics could influence everything from pho*****graphy to art and *****, they took a greater interest in mathematics and philosophical thought, which in turn led to ***** more innovation ***** scientific thinking. In fact, to*****, m***** scientists and mathematicians feel ***** work represented a real paradigm shift, or a r*****dical change in ***** and philosophical ***** ("Can*****r"). Two of his l*****ting models that showed his ***** were "Cantor's Comb," which showed all points were disconnected from each other, and "Cantor's Dust," which calls these ***** sets "fractal dust" (Breen). Cantor's work *****ly revolutionized mathematics, and encouraged people to think *****ly about just ***** numbers really were.

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


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