As others said, this is a matter of style of convention and taste.

Compare these two abstracts:

Does every compact Hausdorff space admit a compatible metric? In this work we show that the answer is positive exactly in the case where the space is second-countable.

And

We show that a compact Hausdorff space admits a compatible metric if and only if it is second-countable.

Both have the same content, but only one of them feels like it actually invites you to read the paper. It starts by asking you a question, which to some extent is intriguing, and then provides you with a complete answer.

Papers should be something that is read by people. As such, the writing style can, and even should, be not entirely dry. I'm not saying that you should go overboard with elaborate writing and story telling devices. But sprucing up your writing a little bit using questions or explanations is a good thing, it can help to make your paper much more palatable.

As for your friend's comment? Well. If he can judge the content of a paper by the first sentence of the abstract, I'm sure that he can skip the abstract altogether and just judge a paper by the title. I mean, why waste time reading two sentences?

As others said, this is a matter of style of convention and taste.

Compare these two abstracts:

Does every compact Hausdorff space admit a compatible metric? In this work we show that the answer is positive exactly in the case where the space is second-countable.

And

We show that a compact Hausdorff space admits a compatible metric if and only if it is second-countable.

Both have the same content, but only one of them feels like it actually invites you to read the paper. It starts by asking you a question, which to some extent is intriguing, and then provides you with a complete answer.

Papers should be something that is read by people. As such, the writing style should not be dry. I'm not saying that you should go overboard with elaborate writing and storytelling devices, but sprucing up your writing a little bit using questions or explanations is a good thing; it can help to make your paper much more palatable.

As for your friend's comment? Well, if he can judge the content of a paper by the first sentence of the abstract, I'm sure that he can skip the abstract altogether and just judge a paper by the title. I mean, why waste time reading two sentences?

As others said, this is a matter of style of convention and taste.

Compare these two abstracts:

Does every compact Hausdorff space admit a compatible metric? In this work we show that the answer is positive exactly in the case where the space is second-countable.

And

We show that a compact Hausdorff space admits a compatible metric if and only if it is second-countable.

Both have the same content, but only one of them feels like it actually invites you to read the paper. It starts by asking you a question, which to some extent is intriguing, and then provides you with a complete answer.

Papers should be something that is read by people. As such, the writing style can, and even should, be not entirely dry. I'm not saying that you should go overboard with prosaic writing and story telling devices. But sprucing up your writing a little bit using questions or explanations is a good thing, it can help to make your paper much more palatable.

As for your friend's comment? Well. If he can judge the content of a paper by the first sentence of the abstract, I'm sure that he can skip the abstract altogether and just judge a paper by the title. I mean, why waste time reading two sentences?

As others said, this is a matter of style of convention and taste.

Compare these two abstracts:

Does every compact Hausdorff space admit a compatible metric? In this work we show that the answer is positive exactly in the case where the space is second-countable.

And

We show that a compact Hausdorff space admits a compatible metric if and only if it is second-countable.

Both have the same content, but only one of them feels like it actually invites you to read the paper. It starts by asking you a question, which to some extent is intriguing, and then provides you with a complete answer.

Papers should be something that is read by people. As such, the writing style can, and even should, be not entirely dry. I'm not saying that you should go overboard with elaborate writing and story telling devices. But sprucing up your writing a little bit using questions or explanations is a good thing, it can help to make your paper much more palatable.

As for your friend's comment? Well. If he can judge the content of a paper by the first sentence of the abstract, I'm sure that he can skip the abstract altogether and just judge a paper by the title. I mean, why waste time reading two sentences?