Infinity: The End Is Not What It Seems

            The last episode of the Story of Maths entitled “To Infinity and Beyond” showcased the continuous development of Mathematics at the modern era. Du Sautoy took us to another journey into the other realm of infinity mathematics.

            The episode started with the introduction of Hilbert’s twenty-three (23) unsolved problems in mathematics discussed at the International Congress of Mathematics in Paris on August 1900. The concept of infinity was championed by George Cantor in 1878. Cantor relates similarities between two infinite sets of numbers. While constructing a list of numbers, he found that bigger infinity was produced. This led to another problem where Cantor deduced the Continuum Hypothesis where it describes that “there is no set whose cardinality is strictly between that of the integers and the real numbers.” Grasping the concept of infinity is ambiguous, leading me to confusion.

            Another prominent figure who rose during the early 20^th century was Kurt Godel, famous for the line “This statement cannot be proved.”  He ignited thinking that proving mathematics and the concept of uncertain is considered an important concept in mathematics. He also examined the works of the American mathematician Paul Cohen. Among Cohen’s contributions to mathematics is finding the answer to the Continuum Hypothesis questioning its validity. Algebraic geometry also came into existence. Algebraic geometry was able to decode mathematics’ hardest equations such as Fermat’s Last Theorem. Julia Robinson and Sophia Covaleskia were among the female mathematicians that I have known from this episode and women in the realm of mathematics were rare.

            Hilbert’s 23 mathematical problems have become the foundation for the inquisitive minds of modern mathematicians. Other problems have led to discovery of answers while some problems have left to uncertainty such as the Riemann’s hypothesis where no one has ever provided an answer to it. The Clay Mathematics Institute would give a stunning US $1,000,000 to anyone who can provide a solution to the Riemann hypothesis. (So better get your pen and tons of papers and try to find the solution. :D)

            Among the four episodes, this was the most difficult for me to comprehend. The concept of infinity has led me to the infinity of uncertainty. Yet, I appreciate Marcus du Sautoy on his work to reach the people and see into another dimension of mathematics. Sadly, I am going to miss this series starting from the Egyptians up to the modern 21^st century mathematics. We owe too much to these people who devoted their time to make our lives easier.