> the sentence "a monad is a monoid in the category of endofunctors" is pretty much impossible to represent in a script like egyptian heiroglyphics or this one

单子是自函子范畴中的幺半群

It bears remembering that spoken language existed long before written language, and written language developed as a form of encoding spoken language. Purely pictorial communication utilises a small number of large symbols that make it clear what is being conveyed from pictures alone, but the language depicted is too complex and abstracted to be purely pictorial; it uses a great number of small symbols, and you cannot understand what it is trying to convey merely by looking at it as a series of pictures. For a reader to understand what is written there would require understanding the relation of symbols to spoken language.

This is a line of thinking that's very common amongst people who only speak languages that use alphabets but it's not remotely true. Egypt became one of the greatest empires ever with hieroglyphs and those evolved into a phonetic writing system. Chinese and Japanese of course function and they evolved from pictographs. A pictograph is only limiting if a character that resembles a dog can only carry the meaning of a dog and nothing else. But that's not the case in any language. They all evolved to use the symbol of a dog, or any given character, to carry other meanings.

The very first letter in your example sentence started as an ox 𓃾 then via 𐤀 α etc. turned into a https://en.wikipedia.org/wiki/A#:~:text=1-,History,a – but even in the hieroglyphics it was used to represent the sound (the sound of the start of the word for ox), not literal oxes. The road towards more abstract / less pictorial systems was created for speed and ease of writing, not in order to represent more abstract thought. (Note also how alphabets are changed by the implements used to write them, e.g. runes for knife-on-wood, wedge incisions for clay tablets, square capitals on stone – this too was a pressure from ease of writing, nothing to do with representing more complex ideas.)

While the proto-writing systems are based on pictograms, both the Sumenrian cuneiforms and the Egyptian hieroglyphic (used for inscriptions on stone) and hieratic (use for writing with a reed brush on papyrus) have made the transition towards having phonetic symbols, used together with ideograms.

Using the phonetic sign subsets of the Egyptian and Sumerian scripts, it was possible to write any sentence that could be spoken in their languages.

This was the most important advance in writing and both in Mesopotamia and in Egypt there is evidence about this transition from an earlier writing system that could write only a subset of the words of a language, so it could not be used to write arbitrary sentences, but only things like lists of objects with their amounts and owners, like needed for accounting, to a writing system that added phonetic symbols for writing any words that did not have their own symbol.

I cannot read the paywalled article, but it seems that now there is evidence that also the Proto-Elamite writing system has also passed around the same time through this transition from having only symbols for certain words to having phonetic symbols too, e.g. for syllables, which can be used to write arbitrary words and sentences.

Before phonetic symbols began to be used, we cannot know the language spoken by the users of a proto-writing system.

While in Egypt there is little doubt that the first users of writing spoke some kind of Old Egyptian, in Mesopotamia there is doubt the users of the first proto-cuneiform writing system spoke Sumerian. However, by the time when phonetic cuneiform signs were introduced, the language of the writers was Sumerian.

In the territory later known as Elam (in the West of present Iran), it is not known what language was spoken by the users of the Proto-Elamite writing system. It could have been an ancestor of the Elamite language spoken a millennium later, or it could have been a completely different language. Elamite is not related to the Indo-European languages that spread much later in that territory, like Old Persian.

I am sorry but this like saying that "chinese cannot represent abstract notions" because "picture" .

In middle egyptian (the language you probably assume) "pictures" are just syllables. They are phonetic, not semantic, in the same way letter of modern language correspond to sounds, not meanings.

Egyptians had no problem expressinyg conplex concepts and they also had cursive writing, which is much easier to write.

It does look complex. These are not mere pictographs but a refined and codified system of representing ideas.

By the way, Chinese uses a modern example of such a script and succeeds in representing such concepts.