Non-native speaker here. What is wrong with this sentence and how would you improve it?

There is nothing wrong with it. Rather question the judgment of someone who has used the words "witting skills".

Remove it. If you've stated your goal, that should be clear. There is no reason to state that you've stated your goal.

There are undertones here. What the section really says is that mathematical intuition has different aspects that are very distinct, and that a discussion of some of these will follow. Which ones these are and why these were chosen will be discussed in Section 1.

The task of the editor is never to impose their style upon the author. There are different writing styles even in academic writing, a wordy one, one that chooses outrageous words, a very terse one, and the awful MBA-style kind.

What's worst is an editor that sees a sentence that he does not understand, and edits that, thinking it's just style but completely changes the meaning.

The editors job is to improve the writing by making it easier for the intended audience to read and comprehend.

In this case, the sentence can be easily worked into the preceding sentence which it echos - by changing the place holder clause "The first order of business is.." to "The aim of section one is..".

That version loses the emphasis on recognizing that there are distinct aspects of mathematical intuition. Congratulations! You successfully changed the meaning of the sentence! The intended audience is mathematicians and philosophers, these people can be expected to have full grasp of the English language and to engage with the paper.

I once was working with a horrible boss like that. I'd write a draft of the paper, she would not understand subject or prose and change some sentences into something else, based on her limited understanding of the subject and the prose. It was excruciating. You'd read her draft full of MBA-speak and couldn't make out the meaning of some of it!

First off all, the meaning is equivalent and this sentence is completely unnecessary. Repeating your intents in sequential lines doesn't add meaning.

"The first order of business will be" is a placeholder used in speech, to me it has the equivalent meaning of "Uhm, I will be". Care to elaborate further on what you think the special emphasis of this phrase is in this context?

>Congratulations!

Not to edit your style bro, but the condescension is a bit much. Seems like you have just soured on editors due to some bad personal experiences. Editing is suppose to be a two way conversation in which the editor marks up all possible errors and you accept the changes that you think add clarity or just rewrite it yourself knowing that your previous version was unclear to at least 1 person.

That said, I don't really see the grey area in this case.

I hate to say it but I don't know grammar rules well enough to explain it. The best I can offer is something that sounds better to me. First example is the paper, second example is one possible rewrite:

"The first order of business will be to draw some distinctions between these notions and pick an appropriate focus for our present inquiry. That is the aim of section 1."

"Section 1 draws distinctions between these notions, one of which will be the focus of our inquiry."

You're probably mostly objecting to the passive voice, which is a reasonable stand to take in scientific writing. He uses passive voice three times in these two sentences alone.

Using "to be" isn't necessarily the passive voice. The author doesn't use the passive voice in those sentences.

http://writingcenter.unc.edu/handouts/passive-voice/

You're absolutely right, I misread those.

Passive voice would be "to be drawn", "to be read", etc.

Thank you.

It's always either redundant or indicative of a problem elsewhere. Either section 1 has a title/thesis that makes it obvious what it's about and so the restatement is unnecessary, or you need to say it because you haven't already made it obvious. Instead of saying "This is the aim of section 1", just make the point of the section apparent.

This is a class of stylistic issue that's common in professional writing by those new to it and usually stems from a lack of confidence in the topic or in one's self.

Giving "overview of the rest of the paper" that points out what will be happening in future sections is quite common in academic literature - there are better ways to phrase it (and many people writing academic papers, myself included, try to word it so that it does not sound that silly), but this wording (even if grammatically quite clumsy) sounds pretty standard to me - I would not overthink it as a "lack of confidence".

> The problem here seems to be witting skills.

Heheheh... ;-)