I don‘t quite understand why we think humans can survive staying on moon bases or trips to Mars before the problem of cosmic radiation is solved. Going on a trip to Mars and back makes you prone to dying from cancer. Mars doesn‘t have a magnetic field that would shield inhabitants from being bombarded by high-energy particles. How are we going to deal with this?
We know how to shield from radiation, there is no mystery there, just put matter in btween the source and the passengers. It's not easy, but the physics are well understood.
Besides, how do the astronauts on the ISS deal with radiation? Is the ISS somehow better protected near earth than in deep space?
Yes, the ISS has some protection from being in low Earth orbit. But the rate of cosmic ray strikes is still high enough to pose a health risk, so the areas on ISS where astronauts spend most of their time have additional shielding. The material most often used for shielding is polyethylene because it performs better in terms of secondary emissions - heavy elements like lead emit showers of secondary particles when struck by cosmic rays and have to be very thick to contain the secondaries, which is far too heavy to put into space.
Once away from low Earth orbit the shielding on a spacecraft becomes very expensive in terms of size and weight, even when it is the lighter weight polyethylene material.
The problem will be solved in time, and in the meantime, we can solve other problems (like in-situ resource utilization, closed-loop habitation, etc.) in parallel.
> How are we going to deal with this?
I don't have an answer for the journey to Mars itself (and I'm also not sure if there's a consensus on how big a danger would such trip pose) - but you'll definitely want to keep the fuel between the passengers and the Sun. It would likely also be wise to pad the whole vehicle with some dense material - but to do that, you'd really want to have some sort of manufacturing capability in cislunar space, to avoid having to lift all that mass upwell.
As for bases on Moon and/or Mars, the best solution is probably to dig in - find a cave or make a tunnel, set up there, and develop underground. Ground is a very good radiation shield.
