It is simply impossible to get a handle on modern science, even at fairly basic levels, without a good understanding of mathematics
These sound like "fairly basic levels" for a postdoctorate student, rather than a layperson. I find it difficult to believe that cell division, or sublimation, or even gravity, can be better explained using chalk and algebra than by our much-derided friend the "infographic" or by any kind of decent animation, perhaps with interactive elements to assist understanding. There is just tons of potential there.
But yes, my question lacked clarity on this point. I do not want to understand "complex ideas" completely, just to grasp the basics. I want basic things to click in ways they haven't done so far. I'm not a scientist and never will be (I studied history), I just want to be a little less dumb. Just a little.