I think the monetary theory subjacent to most keynesians finally made click in my head

Diary!

I cannot stop thinking that according to Keynes, economic problems seem to stem from demand problems ...

I would imagine that one can conceive demand in a nominal way. ...

See my diary Keynes and the monetarization of economics (July 16th, 2006) for Keynes' discussion of real vs. nominal quantities and why he decides to measure labour in nominal wage terms and output in nominal money terms:

Nevertheless these difficulties are rightly regarded as 'conundrums'. They are 'purely theoretical' in the sense that they never perplex, or indeed enter in any way into, business decisions and have no relevance in the causal sequence of economic events, which are clear-cut and determinate in spite of the quantitative indeterminacy of  these concepts. It is natural, therefore, to conclude that they not only lack precision but are unnecessary. Obviously our quantitative analysis must be expressed without using any quantitatively vague expressions. And, indeed, as soon as one makes the attempt, it becomes clear, as I hope to show, that one can get on much better without them.

...

In dealing with the theory of employment I propose, therefore, to make use of only two fundamental units of quantity, namely, quantities of money-value and quantities of employment. The first of these is strictly homogeneous, and the second can be made so. For, in so far as different grades and kinds of labour and salaried assistance enjoy a more or less fixed relative remuneration, the quantity of employment can be sufficiently defined for our purpose by taking an hour's employment of special labour in proportion to its remuneration; i.e. an hour of special labour remunerated at double ordinary rates will count as two units. We shall call the unit in which the quantity of employment the labour-unit; and the money-wage of a labour-unit we shall call the wage-unit.

...

It is my belief that much unnecessary perplexity can be avoided if we limit ourselves strictly to the two units, money and labour, when we are dealingg with behaviour of the economic system as a whole; reserving the use of units of particular outputs and eqquipments to the occasions when we are analysing the output of individual firms or industries in isolation; and the use of vague concepts, such as the quantity of output as a whole, the quantity of capital equipment as a whole and the general level of prices, to the occasions  when we are attempting some historical comparison which is within certain (perhaps fairly wide) limis avowedly imprecise and approximate.

Maybe it's because Keynes was a mathematician by training that he didn't need to make apologies for writing economics without making apologies for not using too much mathematics.

If you are not convinced, try it on someone who has not been entirely debauched by economics. — Piero Sraffa