To Infinity and Beyond!

BBC Story of Maths part 4                                                                                                                  To Infinity and Beyond

            “Mathematics is about solving problems and it’s the great unsolved problems that make it really alive”

            The final episode is about the great unsolved problems that troubled mathematicians in the 20^th century. In a congress in 1900, David Hilbert, a young German mathematician, posed 23 most important problems that mathematicians still needed to crack. Those problems would be f great help in defining the math in modern age. 

            The first problem listed by Hilbert was George Cantor’s “Continuum Hypothesis” in dealing with infinities. Next was Henri Poincaré's, topological problem, the Poincaré conjection, that dealt with all the possible shapes in a 3D universe which he cannot solve. Hilbert’s own problems and theories which he was not able to prove were also in the list. Hilbert believed that math is a universal language that is powerful enough to unlock all truths and solve all 23 problems. Kurt Godell shattered his belief by saying “This statement cannot be proved” and by formulating the “Incompleteness Theorem” which states that in any logical systems in math, there would be statements about numbers which are true but cannot be proved.

            Godell influenced American mathematics a lot. In 1950s, a young American mathematician, Paul Cohen, took up the challenge of Cantor's Continuum Hypothesis. He found that there existed two equally consistent mathematical worlds. Some believed the hypothesis was true while others thought it was not.

Another problem in Hilbert’s list was the Riemann’s hypothesis which is still unsolved until now. Another problem stated was, if there was some universal method that could tell whether any equation had whole number solutions or not. Julia Robinson formulated the Robinson hypothesis, which states that there is no universal method to solve equations using specific set of numbers. The final section of the movie discussed about works of great mathematicians in the fields of number theory, algebra, topology and geometry.

There was a part in the movie where in de Sautoy read a book saying “If we wish to foresee the future of mathematics, our proper course is to study its history”. He was indeed in the right direction in making the Story of Maths.

Up until now, there are still some unsolved problems in Hilbert’s list. But like what he said, it’s the unsolved problems that make mathematics alive. And if  we must know, then we will know.