Why do we do Science?

I have been asked several questions revolving about the usefulness of research: why do you do research in mathematics, computers can do the calculations? or why do you do research in computer science, is it to build faster computers? or what is the use of doing all these complicated calculations, is there any application you can make money of?
At some point I used to answer that there is nothing more useful than something that seems useless like a new mathematical theory. My argument was that things that are immediately useful are only useful immediately, while things for which we do not see any immediate application may very well turn out to lead to entirely new technologies in the long run. As an example, take the complex numbers. When they were invented, they were considered as a nice creation of the mind, as something only some mathematicians understood, but as something that would never have any application in the real world. Centuries later they are at the basis of many fields of technology we could hardly live without such as signal processing or electronics.
Unfortunately, it is not easy to predict which of the many mathematical works that are done today will be most useful in a few centuries. There is thus potentially a lot of wasted effort.
Another thing I used to say is the following: it is more fruitful to build a theory that explains several phenomena than to solve a specific problem (this is the difference between science and engineering).
A quote which I like is : "There is nothing so practical as a good theory". It is originally from Kurt Lewin (although some ML people think it is due to Vapnik because it is often used by him).

Anyway, instead of trying to justify scientific research, it is probably more interesting to think about how this research should be conducted and in particular what should be the motivations of someone doing so.
I recently found some interesting answers in the following quotes from Albert Einstein (taken from "The Einstein-Besso Manuscript", Scriptura, Aristophil 2005):

1. "My scientific work is motivated by an irresistible longing to understand the secrets of Nature and by no other feelings. My love for justice and the striving to contribute toward the improvement of human conditions are quite independent from my scientific interests."
2. "The important thing is not to stop questioning. Curiosity has its own reason for existing. One cannot help but be in awe when he contemplates the mysteries of eternity, of life, of the marvelous structure of reality. It is enough if one tries merely to comprehend a little of this mystery every day. Never lose a holy curiosity.
3. "To be sure, it is not the fruits of scientific research that elevate a man an enrich his nature, but the urge to understand, the intellectual work, creative or receptive."
4. "Where the world ceases to be the scene of our personal hopes and wishes, where we face it as free beings admiring, asking and observing, there we enter the realm of Art and Science."
5. "The most beautiful thing we can experience is the mysterious. It is the source of all true art and science, who can no longer pause to wonder and stand rapt in awe is as good as dead: his eyes are closed."
6. "After a certain high level of technical skill is achieved, science and art tend to coalesce in aesthetics, plasticity, and form. The greatest scientists are always artists as well.
7. "It is my inner conviction that the development of science seeks in the main to satisfy the longing for pure knowledge."

So as a conclusion, the main motivation is the curiosity or the desire to understand, there should be no other. This is probably a bit idealistic, but what is life without a bit of idealism?

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