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My question is about the place of to+infinitive in some sentences.

For example,

1- Before I went on holiday for a week, I was really eager to study at mathematics.

I know this is correct.

How about the following one I am just trying to give more emphasise to?

2- To study at mathematics, I was really eager before I went on holiday for a week.

I know 2 is not natural, however, I am just curious if it is grammatically correct and gives the right meaning still.

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  • Related: english.stackexchange.com/a/177461/216106
    – Davo
    Commented Aug 23, 2019 at 12:28
  • 1
    As a native US English speaker, I can't tell the intent of either sentence. I would remove "at" from both sentences (perhaps that's a British construct)? Are you eager to study math before holiday, or during holiday? That's what's not clear. Perhaps, "I was quite eager to study mathematics before going on holiday for a week." Or, "I was quite eager to study mathematics while on holiday for a week." Different meanings, though.
    – Edward Barnard
    Commented Aug 27, 2019 at 21:53

2 Answers 2

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Removing the superfluous "at" leaves:

1A Before I went on holiday for a week, I was really eager to study mathematics.

This is grammatically correct, but ambiguous. It could mean that the spark was eager to study math before s/he went on holiday, but was somehow disenchanted during the week and no longer eager after it. Or it could mean that the speaker was eager to study during the holiday, or to study before the holiday started. Additional context would probably make the meaning clear.

The construction

2A To study mathematics, I was really eager

Is unusual, indeed unnatural. It sounds archaic or affected, because of the placement of the verb phrase "To study mathematics" before "I was really eager" (I would not call it wrong, but it will cause raised eyebrows every time.) The obvious revision is:

2B I was really eager to study mathematics before I went on holiday for a week.

This has much the same meaning as 1A, but emphasizes the desire to study, while 1A emphasizes the holiday. It also has the same ambiguity as 1A.

Some verbs naturally take "at" after the to-form, (or in the present) such as "play".

He seemed to play at mathematics, rather than to seriously study it.

Others do not, such as "study". Such forms as "work at" and "fail at" seem natural, while for example "feel at" does not.

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Sentence 2 neither sounds natural nor is it grammatically correct.

(Ignoring to fact that you used "to study", the word "study" doesn't collocate with "at".)

You can sometimes treat the to-verb like a noun in these cases.

To play is to have fun.
To learn is to take in information.

You may notice that both the subject and object in my 2 examples above are to-verb. To be honest, it's hard for me to think of a sentence where the subject is a to-verb but the object isn't, so I think that's usually the correct form.

In your example #2, if you change it to:

Studying mathematics, I was really eager before I went on holiday for a week.

..., that would be grammatically correct but has a different meaning. It would mean:

I was really eager before I went on holiday for a week because I study mathematics.

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