Gell-Mann and others came out with quarks around 1964, which were extremely useful in organizing our understanding, but of limited use in computing particle masses!
You need quantum chromodynamics (QCD), invented around 1973, to understand how quarks interact and have a chance at computing the masses of the particles they form.
But even with QCD it's incredibly hard to do the computations! So even now, many things remain mysterious -- and those who love this subject have lots left to do.
For example the lightest spin-1/2 excited state of the proton, the N(1440)⁺, has a mysteriously low mass. It defies simple explanation! It's called the 'Roper resonance' after the guy who found it in 1964, and people have been struggling with it ever since:
https://en.wikipedia.org/wiki/Roper_resonance
For the epic quest to understand the Roper resonance, read this:
• Volker D. Burkert, Craig D. Roberts ,Roper resonance -- solution to the fifty year puzzle, https://arxiv.org/abs/1710.02549
"This is a prodigious task, but a ten-year international effort, drawing together experimentalists and theorists, has presented a solution to the puzzle."
But don't bet on it being the final word!
This physics of particles made of quarks -- called 'hadron physics' -- is in some ways a lot like nuclear physics, or chemistry. The underlying laws are known. Applying them can be very hard. You wind up needing supercomputers, physics intuition, and rules of thumb.
But nuclear physics is less useful than chemistry, and hadron physics is even less useful. So past a certain point you do it, if at all, for love.
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