Of infinite patterns: A movie review on the Story of Math's "To infinity and beyond'

by: Kissel Cablayda

The past three episodes presented a long history of mathematics. But the fourth episode, “To infinity and beyond”, finishes the story through looking at the current status of mathematics. It clearly presents the more complex and abstract side of math. In this last episode, Professor Marcus du Sautoy emphasizes David Hilbert’s twenty eight mathematical problems and several mathematicians who successfully solved some of Hilbert’s mathematical problems.

In the opening part, du Sautoy explores the first mathematical problem, the true concept of infinity. He introduced the first person to understand it, Georg Cantor. Du Sautoy then connected it to the continuum hypothesis which Cantor cannot solve. He also introduced Henri Poincare, the leading mathematician of his time, who successfully made a successive approximation of the stability of orbiting planets. Although this work was not successful enough, his mistake surprisingly led him to a more important concept, the Chaos theory. A theory stating that randomly small changes of things in initial conditions can be expanded over time. Another great mathematician, Leonard Oyler, successfully solved the problem of Topology, also known as bendy geometry. This led to another problem, called Poincare conjecture. It was recently solved by a Russian mathematician, Grigori Perelman.

Du Sautoy then mentioned the achievements of David Hilbert, such as the Hilbert space, classification, inequality and several Hilbert theorems. But he emphasized his early work on equation, creating a new style, a more abstract or philosophical mathematics. He was known for his statement on “logical systems that are true but cannot be proved”. Kurt Godel then successfully changed Hilbert’s statement into a statement of mathematics.

And as the Second World War rises, the history of mathematics began to develop in a fresher setting, known as America. Mathematician from the European countries, who fled to the new world, continue to make history in mathematics. One of them is John Neumann who developed the Game theory. Another teenager and a mathematician, Paul Cohen solved Hilbert’s first hypothesis, also known as Cantor’s continuum hypothesis. A significant mathematician, Julia Robinson, made history when she was proclaimed as the first female president of the American Mathematical Society. And together with another Russian mathematician, Yuri Matiyasevich, they tried to solve the Robinson’s hypothesis, also known as Hilberts’ 10^th problem.

Mathematicians like Galois, who discovered new techniques to be able to tell whether certain equation could be solved; Nicholas Bourbaki, a group of mathematician led by Andre Weil; and Alexander Grothendieck, who solved hidden structures underneath mathematics, continued to make great history in the story of math.

One good thing about this episode is that the audio is the most important aspect in understanding the narration. The audience can still learn from the documentary while listening to the narrator, not looking at the video and doing other tasks. Like the past three episodes, the images or visuals are less useful compared to the audio. One can look up from time to time when du Sautoy tries to show demonstrations or examples of an equation.

The episode is indeed a good examination of the mathematical innovations prospered during the twentieth century. Du Sautoy raises a good point when he gave his own meaning of mathematics, that it is “a quest or search for patterns”. This clears out the common idea that math is only a study of numbers. Hence, he successfully emphasized that there are deeper understandings that lay behind the general notion of mathematics, and that it has long been connected to our lives and culture, trying to make sense of our world through searching common patterns, with proving and precision.