There is a huge difference between knowing something and acting on it. Science is concerned with accumulating and understanding observations of the physical world. That understanding alone solves no problems. Individual people have to act on that understanding for it to help solve problems. For instance, science has found that regular exercise can lower your risk of heart disease. Knowing this fact is interesting, but it will do nothing for your personal heath unless you act on it and actually exercise. And that's the hard part. Reading an article about exercise is easy. Getting into an actual routine of regular exercise is harder. In this sense, science really solves no problems at all. Problems are only solved when people take the knowledge (or tool, or pill, or whatever) provided by science and use it. In fact, many of humanity's biggest problems are caused by lack of action, and not lack of knowledge.
Take world hunger, for example. There is currently enough food produced on the earth every year to comfortably feed every single person. The world produces about 700 trillion grams of rice each year. With seven billion people on the planet, 365 days in the year, and about 40 grams per typical serving of rice, there is enough rice on the planet to feed every single last person seven servings of rice every day. And this is just rice. Similar numbers hold up for wheat, corn, meat, etc. Science has done an amazing job in the last 50 years of making farms productive. And yet, millions of people in the world still suffer starvation. Why? Because of actions. If all it took was science to solve problems, no one would go hungry anymore because there is enough food. We could fill books with the analysis of human actions that cause world hunger if we wanted to, but let's just focus on a few factors to illustrate the point. A large portion of the world's food is simply wasted by lazy humans. People in affluent countries buy more food than they need, so that much of their food goes rotten and must be tossed before it is eaten. Or they pile more food on their plate than they could possibly eat and much of the food ends up in the trash. Another major factor is corrupt or incompetent governments who hoard food among a select few, poorly distribute food, or refuse to adopt modern agricultural methods. Tyrants sometimes even use forced hunger as a way to subdue the masses or punish opponents. Science can make an acre of farmland amazingly productive, but it can't force a dictator to give back the food he has stolen from his people.