Hard to test (speculative) and hard to falsify subjects...

The extent to which a question gets settled on a given time scale in some academic disciplines is much less than others.

E.g. in the mid 19th C, Darwin presented a truly radical view of how various species of plants and animals evolved from other ones. This suggested e.g. that humans must share common ancestors with the great apes. This meant one must find the missing link between apes and humans. This in turn involved (a) finding sufficiently many fossils which could be candidates for the missing links, (b) gather evidence to establish that these candidate fossils are the missing links. Though this could not be done right away, we have now (over a period of 150+ years) gathered enough evidence to convince ourselves that humans indeed shared ancestors with apes.

Within physics

Within physics, questions in astrophysics/astronomy are harder to decisively settle than in e.g. material science. But even by these standards, the following subjects are extremely speculative:

(1) String theory and other theories of QG,
(2) BH physics, QFT in CST, semi-classical gravity etc,
(3) Early universe: Baryon-Asymmetry in the Universe, inflation(or, alternatives to inflation),
(4) Dark matter: though specific models can be ruled out, how to falsify the entire paradigm;
(5) BSM particle phenomenology: unless new physics is found;

Outside of theoretical physics

(1) Ancient history (including pre-history);
(2) The origin of life;
(3) the origin of human language;

My own research: