you probably need fundamental mathematical insights, and it's damn hard to predict those.

We can still try. As it happens, a perfectly relevant paper was just released: "On the distribution of time-to-proof of mathematical conjectures"

What is the productivity of Science? Can we measure an evolution of the production of mathematicians over history? Can we predict the waiting time till the proof of a challenging conjecture such as the P-versus-NP problem? Motivated by these questions, we revisit a suggestion published recently and debated in the "New Scientist" that the historical distribution of time-to-proof's, i.e., of waiting times between formulation of a mathematical conjecture and its proof, can be quantified and gives meaningful insights in the future development of still open conjectures. We find however evidence that the mathematical process of creation is too much non-stationary, with too little data and constraints, to allow for a meaningful conclusion. In particular, the approximate unsteady exponential growth of human population, and arguably that of mathematicians, essentially hides the true distribution. Another issue is the incompleteness of the dataset available. In conclusion we cannot really reject the simplest model of an exponential rate of conjecture proof with a rate of 0.01/year for the dataset that we have studied, translating into an average waiting time to proof of 100 years. We hope that the presented methodology, combining the mathematics of recurrent processes, linking proved and still open conjectures, with different empirical constraints, will be useful for other similar investigations probing the productivity associated with mankind growth and creativity.

They took the 144 from the Wikipedia list of conjectures; their population covariate is just an exponential equation they borrowed from somewhere. Regardless, they turn in the result one would basically expect: a constant chance of solving a problem in each time period. (In turn, this and the correlation with population suggests to me that solving conjectures is more parallel than serial: delays are related more to how much mathematical effort is being devoted to each problem.)