So, when Poincaré says that "most men do not love to think" he is only stating the obvious. There is no implied condemnation. Human society does not want or need everyone to be a scientist, philosopher or politician, but someone has to perform these roles in order for a civilized life to even be possible.
Poincaré believes that to ask what is the value of science is analogous to asking what is the value of truth, or what is the value of beauty? You either feel the necessity of these things in your life or you do not.
"The things which seem to us beautiful are those which best adapt themselves to our intelligence."And, in fact, Poincaré believes that the love of truth is essentially the same as the love of beauty, because the study of nature reveals a fundamental order or harmony that is intrinsic to beauty. Like Pythagoras, Poincaré believes that rationality and beauty are symbiotic aspects of nature. That is to say, both are necessary in order for either one to exist. This arrangement is eminently practical because human society (as well as nature) requires order, and order is always preferable to chaos.
Regarding Tolstoy's desire to help mankind, Poincaré has no objection:
"For my part, it need scarce be said, I could never be content with either the one or the other ideal; I want neither that plutocracy grasping and mean, nor that democracy goody and mediocre, occupied solely in turning the other cheek, where would dwell sages without curiosity, who, shunning excess, would not die of disease, but would surely die of ennui. But that is a matter of taste and is not what I wish to discuss."The role of science is simply to reveal the mysteries that God or nature have created. Again, there are other roles for people to play who lack the means or will to investigate nature. There need be no hostility between men of science and men of the cloth. But their respective areas of enquiry must necessarily lead in different directions...
"The search for truth should be the goal of our activities; it is the sole end worthy of them. Doubtless we should first bend our efforts to assuage human suffering, but why? Not to suffer is a negative ideal more surely attained by the annihilation of the world. If we wish more and more to free man from material cares, it is that he may be able to employ the liberty obtained in the study and contemplation of truth."Where this truth finally leads us is not for Poincaré to judge.
Is science harmful to mankind? Possibly. If the knowledge that science makes available to us is put to bad use then it can, and often does, lead to human suffering. But this is nothing more than to acknowledge the fallibility of man. Is religion harmful to mankind? Sometimes, when it leads to persecutions by Grand Inquisitors. Name anything that, in the wrong hands, cannot be put to a bad purpose. Science claims neutrality as to the moral ends for which knowledge (or truth) is used. For better or worse, civilization moves ahead. Progress will follow as long as men seek truth, and refuse to accept bogus theories or knuckle under to the frail illusions of the past.