Many thanks, Susiedqq and Anglika, for your replies.
First of all, it was my mistake not to underline I did not have school essays on mind but those others, which are published or spread among possible audience in any other way.
I don't have any particular topic on my mind; for the sake of simplicity let's limit ourselves to science.
I see it that in any case there's some viewpoint of the author; without this an essay becomes a different kind of prose, losing one of its most important features. Can it, then, be purely objective?
It can be both short and long (the latter not agreeing with what I found in some dictionaries), but not too short. I don't think a piece of 200 words could be called an essay, but one very long, say of 40 000 words, could.
It can be both formal and informal, of course, though if this is science the essay is to be about, the level of informality should be limited. Slang, for example, should be avoided though in particular situations (e.g., in examples?) it might enhance the writing by adding some unexpected value, making it more lively and intriguing. I don't think that the language should be of too high register, calling for the use of seventeen or so technical dictionaries; it should rather be understandable and clear, with energy or peace, depending on the topic; and it should flow smoothly like the Athabasca river, though its contents should be more clear and transparent.
And the topic. I don't think it should be written like a science article, since then it would be an article, not an essay. It should not offer some novel technical solutions or the like, which does not mean it must not be novel or touch upon anything that is unknown to the audience. I rather see it as an critical or discussion piece of writing, in which the author shows what he or she thinks about the topic. The author may also present some new viewpoints on or understandings of a particular problem, criticizing other (old or relatively new, recently brought to light) approaches toward the problem, proposing something new, or both.
How the author attacks the above issues--plus a number of others, including how it is written and organized--constitutes the heart of an essay. In my eyes an essay must be pleasant in reading, must call for the readers' thinking, and most of all must be interesting. I do believe that a well-written, lively essay on less interesting topic can be much better than that which deals with a hot topic, but does not have this flow I would expect from it. Hence this is rather how one attacks the essay which gives it life and power (which should not be understood as the hummer power, but rather as a power of getting into the readers' minds and hearts), and not necessarily the topic it describes. Of course, both these features, that is hot topic and the powerful writing, would create a great essay.
That's how I see it. Do you agree with me or have any other viewpoints or ideas?
Thanks,
Nyggus
PS: Is my reply not an essay?
PPS: Let it be a lesson that Nyggus should not be asked any questions. Long replies is what should be expected then.
What is an essay? 
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