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What is the purpose of science?

The failure of modern science to solve all major problems

It can be observed that the arrival of modern science and the subsequent technological explosion have not provided solutions commensurate with expectations regarding major individual and collective problems. Science primarily deals with highly specialized questions whose implications in our lives are minimal and seems to produce almost as many calamities (ecology, weapons of mass destruction) as solutions.

Cause of the failure

The phrase by Rabelais 'Science without conscience is but ruin of the soul' in his Pantagruel illustrates the problem: what is envisioned is an individual framing (personal conscience) of science rather than a collective framing (social organization).
What is truly lacking is an effective social organization such as the one described in the book From Capital to Reason. Neither liberal democracy, nor communism, nor autocracy, are social organizations effective enough to channel the powerful tool that is science.
A more helpful metaphor would therefore be to present science as an engine and social organization as the steering wheel.

Utility of modern science for problem-solving

Addressing a problem requires following this process:
1. Recognize the problem.
2. Conduct a serious analysis.
3. Develop a solution, often partial.
4. Implement it.
Without even mentioning its great utility at the analysis stage, science is of major importance for developing a solution. It is so true that as soon as one regularly practices the serious method of problem-solving, it becomes apparent that what is possible at the solution level is often largely determined by available technologies, which leads to an interest in science.

Further exploration

Regarding the mismatch between scientific subjects and our fundamental problems:
The conference Should we continue scientific research? by Alexandre Grothendieck at CERN in 1972
The statements by Matthieu Ricard in the first chapter (From scientific research to spiritual quest) of the book The Monk and the Philosopher.

Regarding social regulation of sciences and technologies, see the Amish approach of adopting only a subset of technological inventions. We have chosen the approach of an indispensable search for minimalism, which constitutes one of the three pillars of our answer to the question 'How to succeed in life?'.