Then, Now, and Forever

So, it has come to me that The Story of Maths has ended and, of course, I won't say goodbye to it without reviewing the last episode entitled 'To Infinity and Beyond' (Buzz Lightyear, is that you?).

The last episode opened with David Hilbert presenting the 'twenty-three most important problems for mathematicians to crack' that became the foundation of 20th century mathematics. His first problem was centered on Georg Cantor's work, the first person to understand and explain infinity and developed the Continuum Hypothesis. A contemporary by the name of Henri Poincaré, who believed in Cantor's ideas, participated and won in a competition proving if the solar system would continue to work like clockwork in the future. His idea never did answer the objective of the competition but his techniques indirectly led to his Chaos Theory. Relating to Poincaré, a Russian mathematician named Grigori Perelman was able to solve a problem that even its discoverer could not fathom. This problem was the Poincaré's conjecture. Another one who was influenced by Cantor would be Paul Cohen; though, that would take numbers of years later.

David Hilbert had created an abstract approach of mathematics and believed that maths is a language powerful enough to find solution to his twenty-three problems. But, his belief was shattered when an Austrian mathematician brought uncertainty to the world of maths. His name was Kurt Gödel and he developed the Incompleteness Theory. Another one of Hilbert's problem, specifically the 10th problem, became the lifework of Julia Robinson, the creator of the Robinson Hypothesis. She was unable to find an answer and this gave Yuri Matiyasevich bring closure to her work.

The last part focused on the idea of Évariste Galois that maths is a study of structure and his application of geometry to analyze equations gave path to the introduction of Algebraic Geometry by André Weil. He and Alexander Grothendieck contributed to the conception of the influential Nicolas Bourbaki, pseudonym for French mathematicians who wrote accounts of the 20th century maths.

The documentary The Story of Maths unveils the birth of mathematics from the ancient times, its flourish in the Age of Enlightenment, and its continuous development in the modern era. Not to be overlooked, the documentary also presented the ups and downs of maths and the persons responsible to the wonder that is maths. With new concepts and ideas being developed with the flourish of maths, there are still problems unanswered. You never know, the person who would be able to unriddle Hilbert's eighth problem, the Holy Grail of the world of maths, is someone among us.