From: mk_thisisit
Professor Dawid Kielak, a mathematician at the University of Oxford, identifies the theorem on fibration as his most significant mathematical statement and greatest discovery to date [00:00:41], [00:01:40], [00:01:59]. This achievement, alongside his work on the “symmetry of all symmetries,” was a major factor in him receiving the Whitehead Prize [00:05:27], [00:06:04]. His work on this theorem also contributed to his professorship at Oxford [00:03:57].
Conceptual Foundation
The theorem on fibration seeks a way to understand the world similar to how Einstein viewed it [00:02:06], [00:02:09]. Einstein recognized that we live in a four-dimensional space, but we perceive ourselves as three-dimensional beings whose world changes over time, as time plays a distinct role [00:02:12], [00:02:22], [00:02:27].
Mathematically, this concept is described using the formulation “fiberization on a circle” [00:02:30], [00:02:34]. It posits that four-dimensional space-time “fiberizes over a circle,” meaning it can be understood as a one-dimensionally lower space that dynamically changes in time [00:02:39], [00:02:41], [00:02:44], [00:02:56].
The Core Problem and Kielak’s Contribution
Professor Kielak’s specific interest lies in determining whether a given space “fiberizes over a circle” and if it can be understood as a simpler system changing dynamically in time [00:02:47], [00:02:50], [00:02:54]. He discovered that this can be determined by examining certain algebraic properties of the space [00:03:02], [00:03:06].
His method involves “squeezing out” invariants (numbers or objects) from the space and analyzing them [00:03:09], [00:03:12], [00:03:16]. For example, if a specific invariant number is zero, the space will fiberize; if it’s not zero, it won’t [00:03:20], [00:03:22], [00:03:25], [00:03:26].
Kielak arrived at this theorem by generalizing an existing proof for a very specific case of a similar theorem [00:03:32], [00:03:40], [00:03:43]. While the original proof was approached by a topologist, Kielak, being more of an algebraist, recognized how to apply the underlying algebra to make the theorem general [00:03:50], [00:03:51], [00:03:55], [00:03:57].
Practical Applications
Currently, there are no immediate, everyday practical applications for this specific theorem [00:04:19], [00:04:23], [00:04:25]. Kielak draws a parallel to Newton’s invention of differential calculus, whose applications took centuries to emerge and now underpin nearly all science [00:04:30], [00:04:32], [00:04:35], [00:04:37]. He also references Alan Turing’s work on computation, which eventually led to practical machines used for complex calculations like particle collisions and nuclear reactions [00:04:49], [00:04:51], [00:04:53], [00:04:55], [00:04:57], [00:04:59]. While not claiming his work will have such a broad impact, he emphasizes that the long-term utility of fundamental mathematical discoveries is often unforeseen [00:04:45], [00:04:47], [00:05:06].