CASE Maths Seminar: "Cantor's Paradise" 

By Kuba Hoque, Year 12

On Thursday 5th November, the brilliant Professor Thomas Ward presented a thought-provoking seminar to Sixth Form students on the works of the celebrated and groundbreaking Russian mathematician Georg Ferdinand Ludwig Philipp Cantor (1845-1918). 

He is well known for his pivotal contributions to the concepts of cardinal (used to represent the size of a set) and ordinal (used to denote order within a set) numbers, information we had to research prior to the seminar. However, his sheer expertise in the subject of numerical sets was emphasised to all in attendance; the concept of one-to-one correspondences, which Cantor established, was a landmark mathematical discovery with a profound impact on our world (direct translation or ISBN numbers would be a mere fantasy without these discoveries). 

The main proofs written by Cantor that were covered in the seminar were that any set could be countable if a 1:1 correspondence could be formed with the natural numbers set – numbers used for counting – a key principle used to organise larger databases, and that for any set, the cardinality of the set of subsets would be greater than the cardinality of the original set: 

|A| < |2^A| 

Overall, the seminar was highly interesting and challenged me and other students to deepen our knowledge on numerical sets and consider how complex mathematical theorems can shape our daily lives. As David Hilbert once remarked: "From the paradise which Cantor has created shall no one expel us!”