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With LaTeX, I know you can put pictures in the documents, use different fonts, ... and practically do whatever you want (except the fact that your document must have a predefined style, imposed by the macro packages you are using); instead, in TeX, you are absolutely free to dispose thing in the page as you like. But, in TeX, it seems (at least according to me) that you can't do things you can do with LaTeX, e.g., putting pictures in the pages. Is this the truth or is that I'm ignorant in it?

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You can do everything in TeX, but not necessarily as easily as in LaTeX, to the extent that there are packages that depend on LaTeX. But LaTeX is simply a set of macros built on top of TeX, so in principle you can do anything in TeX that LaTeX can do. See also Reasons to use plain TeX and Why do some people still use TeX instead of LaTeX? – Alan Munn Dec 26 '13 at 20:00
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I have another question: Can you do everything you want in ConTeXt? Because of it's monolithic nature, hence if there are really things that are impossible to perform in ConTeXt with that extent of easiness as in LaTeX? – pashazz Dec 26 '13 at 20:06
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TeX is a Turing complete programming language. So yes. It can. – m0nhawk Dec 26 '13 at 20:07
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tex.stackexchange.com/questions/63789/… (edit: I know this is not exactly what you're looking for, but if you look at graphics.sty and miniltx.tex, you will find that everything boils down to the primitive commands.) – Sean Allred Dec 26 '13 at 20:13
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"before latex" there were macro files similar to latex packages that provided facilities for such things as including pictures. one such was boxedeps.tex. it's not included in tex live, but it's still there on ctan. i can confirm that it got a good workout before it was superseded. – barbara beeton Dec 26 '13 at 21:16

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You are asking the wrong question. The real question is whether you can do in LaTeX all you can do in TeX? LaTeX is a set of TeX macros created by Leslie Lamport with the idea that a typical TeX user is not an expert in Typography and even if she/he was, her/his primary concern should be the document content—not the format. On another hand, TeX is a complete typesetting engine/language which is created to enable inexpensive production of relatively high quality documents in Typographical sense. Both TeX and LaTeX have completely succeeded in completing original goals. While arguably you can produce documents of better typographical quality with hot metal typesetting (deep typesetting) and Phototypesetting, with TeX you can do almost as good for the tiny fraction of the price. While TeX is typographic system, it has not removed the need for a typographer—a professional who is suppose to edit the document layout according to rules of typography. LaTeX has also accomplished its original goal and removed the need for a professional typographer for the creation of large classes of documents at least in practice. No Mathematics department and few if any publishers now have typographers on their payroll. I concede that typographic quality of typical LaTeX document is debatable.

Now going to your original question—if your goal is to create a generic mathematics article it would be quite foolish that you use TeX as it would require that you essentially re-implement certain parts of LaTeX. It is not impossible though. If your goal is to create a truly unique document you would be foolish to use LaTeX as you would have to fight pre-built document classes and you could still fail. Even something as simple as creating a documents with the letter of arbitrary size is non-trivial in LaTeX and involves use of third party packages.

I would also like to bring to your attention ConTeXt which was created to easy the use of TeX in a radically different way than LaTeX. ConTeXt is not trying to tell you how your document should look like. It expected that you are an expert in typography. It just makes it easy to create stunning documents in the fraction of time it would take it with TeX by a heavy use of key value parameters. Note that unlike LaTeX which requires tons of third party packages for a document of relatively modest complexity, ConTeXt is self contained. Everything you need is already in the "core" ConTeXt.

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I'm close to giving -1 for this: "If your goal is to create a truly unique document ou would be foolish to use LaTeX" You would be foolish not to use LaTeX, as a good example, take beamer presentations: beamer works in LaTeX, and makes something completely different, and you can modify everything in LaTeX, as you can in plain-TeX. "LaTeX has also accomplished its original goal and removed the need for a professional typographer" Circa 9 in 10 university lecture notes done in LaTeX are a typographical disaster, with scientific articles, the ratio would be around 1 in 2. – yo' Dec 27 '13 at 9:22
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@tohecz -- having in the past been forced (a management decision above my level) to produce some "unusual" documents in latex rather than plain tex, i can assure you that there are certain kinds of documents that can be produced that way only by essentially undoing most latex conventions. of course, this does require competence in both plain tex and latex macro coding. prerequisite, though, is to first determine what the user interface should be, and then decide what that is best built on. the end user should never see the "bare" macro coding. – barbara beeton Dec 27 '13 at 13:48
    
@tohecz Beamer is really bad example. It is a presentation class. I am not talking about customizing presentation class I am talking about truly unique document. The LaTeX has accomplished the goal. How many Mathematics departments or for that matter publishing companies now employee professional typographers? One of major complains regarding current publishing model is that most people see no added value from publisher because most publishers just take your LaTeX code and publish without serious typographic editing. Whether the product is really that good is subject to debate. – Predrag Punosevac Dec 27 '13 at 16:29
    
Most publishers? Maybe most publishers of mathematics-heavy documents, but most publishers in general, including most publishers of scholarly works in the humanities, certainly do not use any form of TeX. (Whether they also do or do not employ what we would consider professional typographers is another question entirely.) – jon Dec 27 '13 at 17:26
    
@jon I do not want to be rude but please check tex.stackexchange.com/questions/40720/latex-in-industry/… before trying to educate me. – Predrag Punosevac Dec 28 '13 at 0:40

Yes, whatever can be done in LaTeX can be of course done in Plain TeX. If your aim is to write a simple paper using Computer Modern and seven bit fonts, or a novel in English without fancy graphics, Plain TeX is maybe the best tool. If you'd like to add support for UTF-8 encoding, you can use Plain XeTeX or LuaTeX, so you can also change fonts rather easily. That's all. Graphics are not really a problem, because PGF and TikZ run also over Plain.

Would you try starting a critical edition work with Plain TeX? Would you implement code listings with syntax coloring? Multiple indices, automatic cross references and numbering, multiple tables of contents? These must be implemented anew. What about commented bibliographies split by chapter? No, biblatex doesn't run over Plain and there's no interface to Biber available.

You're starting from a false premise and, as you probably know, ex falso quodlibet sequitur

except the fact that your document must have a predefined style, imposed by the macro packages you are using

This statement is untrue: with a document class such as memoir you can rather easily change every small detail of the output format and have at your disposal the hundreds of LaTeX packages. There are scores of other LaTeX class files that can even be customized at will.

Suppose you want to write a program for number crunching. Well, you have C, don't you? If you follow your idea, you wouldn't link to Octave, PARI-GP or other programs that would force you to use their API.

LaTeX is like a big set of libraries built over the basic TeX language. Using it poses no limits to your freedom. But it avoids having to reinvent hot water.

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Yes, I almost agree with all what you've "said". But, about multiple indices, automatic cross references and numbering, ... well, I'm not not really interested in: I hate books or documents in which there are lots of numbers (for example where there are expressions like "Theorem 5.2.4 is a direct consequence of both theorem 3.2.1 and 4.5.4"), they are too frustrating! I'd like documents were the simplest possible. An example of document style that I like is the following: books.google.it/… – User Dec 27 '13 at 18:18
    
And as I know from its author, it has all been typesetted using Plain TeX. Try have a look at it and say me what you think about :) (By the way, it is the best book I've ever seen, both for the way it has been typesetted and the well organized content) – User Dec 27 '13 at 18:22
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@Matteo The book is typeset with AMS-TeX or, more probably, with LAMS-TeX, which was a format that added support for math displays (and is available for LaTeX as amsmath). There should be little problems in producing it with memoir (barring the ridiculous font for the chapter numbers). – egreg Dec 27 '13 at 18:30
    
In addition to what you've said about programming languages: I think I would have never appreciate the beauty of OOP programming (for example with java), if before I hadn't learnt C language and its structured and imperative way of programming. So maybe it's better to start from the basic (TeX) and then some day switch to someting more advanced (LaTeX) so that I will get the most out of the last. – User Dec 27 '13 at 18:31
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@Matteo Plain is a format, similarly to LaTeX just much "simpler". What you likely mean by "TeX itself" is the TeX code ;) – yo' Dec 27 '13 at 23:17

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