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David Hilbert praised Cantor as the greatest mathematician since before [[Leonard Euler]].  Hilbert declared, "No one shall expel us from the paradise that Cantor has created for us."  Yet Cantor never lectured at a university about his breakthrough, and his work is an example of the [[best of the public]].

David Hilbert praised Cantor as the greatest mathematician since before [[Leonard Euler]].  Hilbert declared, "No one shall expel us from the paradise that Cantor has created for us."  Yet Cantor never lectured at a university about his breakthrough, and his work is an example of the [[best of the public]].

Cantor was the first to "put infinity on a firm logical foundation."<ref name="Cantor bio">http://scidiv.bellevuecollege.edu/Math/infinity.html</ref>  His invention of set theory helped him achieve this extraordinary goal.<ref>http://www.engr.iupui.edu/~orr/webpages/cpt120/mathbios/gcant.htm</ref>  He "described a way to do arithmetic with infinite quantities useful to mathematics."<ref name="Cantor bio"/>

Cantor was the first to "put [[infinity]] on a firm logical foundation."<ref name="Cantor bio">http://scidiv.bellevuecollege.edu/Math/infinity.html</ref>  His invention of set theory helped him achieve this extraordinary goal.<ref>http://www.engr.iupui.edu/~orr/webpages/cpt120/mathbios/gcant.htm</ref>  He "described a way to do arithmetic with infinite quantities useful to mathematics."<ref name="Cantor bio"/>

Cantor invented the concept of cardinality and ordered pairs, and proved that some infinities are larger than others.<ref>http://www.economicexpert.com/a/Cardinal:number.html</ref>

Cantor invented the concept of cardinality and ordered pairs, and proved that some infinities are larger than others.<ref>http://www.economicexpert.com/a/Cardinal:number.html</ref>