Answer:
Science can not solve all of our problems. While scientific understanding can help battle things like disease, hunger, and poverty when applied properly, it does not do so completely and automatically. Furthermore, there are many areas of life where science can have little impact. Let us look at some of the reasons why this is so.
First of all, 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.
Many of the "problems" that are discussed in the political sphere are not really problems at all in the scientific sense. They are simply a clash of human wants: one large faction wants one thing and the other faction wants something else. No one is really "right" in the scientific sense in such cases (although, fervent partisans are usually convinced they are always right and their opponents are always wrong). For instance, is it better to let the free market run a nation's healthcare system or should the government take over? The answer to this question really depends on how you define "better", which depends entirely on what you personally want. To people that want freedom above all else, "better" will mean letting the free market provide healthcare. To humans that want a uniform system that won't let people fall through the cracks, "better" may mean centralized medicine. The point is that neither side of the debate is "better" in a scientific sense, so science can never solve this problem. Science can save more lives through medical breakthroughs, and can even streamline the healthcare bureaucracy, but it can't find out if government-run or market-run healthcare is better, because "better" is so subjective. The same situation exists for many "problems" debated in the political sphere. For this reason, scientists do not make good political leaders. The role of political leaders is to ascertain and carry out the wants of the people, which science is fundamentally not equipped to do.
Lastly, many areas of life are simply too non-physical to be satisfactorily addressed by science. Love, hate, relationships, poetry, art, music, literature, and spirituality are all outside the realm of science. Any problems that arise in these areas cannot be completely solved by science.
