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

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George Cantor

***** purpose of the paper is to develop a concept ***** the connection between mathematics and society from a his*****rical perspective. Specifically, it will discuss the subject, what George Cantor accomplished for mathematics and what that did for society. ***** Cantor's set theory changed the way ma*****maticians of the time looked at their 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 infinity, along with the idea ***** an infinite set of real numbers, called transfinite sets, or ***** "set *****." In addition, Cantor found that real ***** were not countable, while algebraic numbers were countable (Breen). Cantor's views were quite controversial when he first developed them in the late 1800s, and some mathematicians today question some of his hypothesis ("Transf*****ite Number"), however, his work is recognized as some of the most important mathematical thought of our time. Not only ***** Cantor get other mathematicians thinking about problems ***** had plagued them for years, he changed the ***** they ***** at ***** in general - it made them question ***** numbers actually are.

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

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


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