Axiomatic set theory beyond the continuum hypothesis - Neo, Chee Heng (Nanyang Technological University, 2022)
There exist mathematical statements that can neither be proven nor disproven, collectively referred to as independent statements. This phenomenon is fundamentally different from problems that have yet to be solved, as independent statements can never be decided to be true or false. To observe what exactly causes this would require an understanding of the underlying axiomatic system and assumptions that one is working with. It is thus a meaningful mathematical endeavour to study these statements in detail, and gain insights into what makes them independent.