This was the title C. P. Snow's controversial 1959 lecture concerning the social division between cultures of sciences and the liberal arts: the former he calls the scientists, and the latter the literary intellectuals.
Given Snow's academic background, it is easy to see where he draws this distinction from, but he extends his argument to speak for the population in general, as the problems perpetuate through government (and other means) society at large (it is Western society really of which he speaks, with some of the trends being most clear in Britain). The main problems he cites are those of misunderstanding each other (due to a small body of common knowledge), and a difference in attitude to how society should develop.
Snow gives a particularly incisive example of the first, acknowledging that whilst scientists may have a poor grasp of Dickens, the literary intellectuals have an even narrower grasp of science:
    Once or twice I have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: Have you ever read a work of Shakespere's?
    I now believe that if I had asked an even simpler question - such as, What do you mean by mass, or acceleration, which is the scientific equivalent of saying, Can you read? - not more that one in ten of the highly educated would have felt I spoke the same language.
In the second case, he puts forward the claim that the scientifically minded are much more ready to accept progress (implicitly for good, which he terms 'scientific morallity') than the literary intellectuals, who would rather accept the present stae of human affairs. This disagreement is claimed to be the main factor obstructing what he terms as the 'scientific revolution'.

Snow's main prescribed course of action is the rethink the education process so as to broaden the level of interaction between the two cultures, and do this whilst reducing the level of exclusive specialisation to any one subject in particular (which at the time was most accute in Britain).

That was in 1959. Since its delivery, the lecture has received much praise, although quite understandably there has also been a substantial backlash from precisely those people termed 'literary intellecuals' who were not shown up in their best light. Also, there were other complaints about the use of the term 'cuture', and why only two such are mentioned. The lecture has certainly has some effect on education, even if perhaps in small measures such as the British Government's recent introduction of a broader range of subjects to be taught at A level.
Another question that occurs to me is that of who should be entitled to decide what is culture and what is not. A good example of this comes from the art world, whose critics are firmly secured in the literary culture: the works of M.C. Escher are largely ignored by these people (having little in terms of themes which interst them), and so rarely feature in serious catalogues of twentieth century art. However, the appeal of Escher's works is the scientific culture is more or less universal (having themes relevant in many branches of science and mathematics).

The lecture was published in essay form by the Cambridge University Press and has been reprinted thirty three times to date.