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This is related to the following questions, 1, 2.

In many papers in mathematics, I often see the following constructions.

Similar to [1], we have that 2+ax = 3y.

Similar to Equation 2.3, we note that ax = by for non-negative integers a and b.

By straightforward calculations similar to Equation 2.2, p=np.

To be clear, the authors usually mean to say a lengthy calculation is identical to the procedure used to arrive at an equation earlier in the paper in the case of the second and third example, or in a cited source in the first example.

After reading the aforementioned related questions and related discussion elsewhere, I still do not understand whether or not these examples should be written as "similar" or "similarly".

Based on 1, I suspect that the correct choice is similarly, however I am experiencing cognitive dissonance because I rarely see these sentences written like this. After consulting with others I consider fairly well versed in English, they all agree that "Similarly" sounds strange in all three of these contexts too.

The argument I am faced with is whether we should use the adverb, similarly, by essentially implicitly encapsulating the entire process to arrive at a new equation as the verb; or whether we should use the adjective, similar, to suggest that the equation or citation are similar to our equation, but leave us with the ambiguity illustrated in user curious-proofreader's Tokyo example found in 2.

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    You could build a cathedral which is similar to cathedrals in France, but you could also build a cathedral similarly to how they were built in France. Does that make sense? One is modifying a noun, the other a verb. Similar cathedrals were similarly built.
    – tchrist
    Jul 31, 2017 at 2:27
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    "Similar to" is adjectival, and so "Similar to [1], we" means literally that "we are similar to [1]." Surely not the intended meaning."Similarly to [noun]" sounds quite unidiomatic to my ears. Are these math papers you see written by native English speakers? More idiomatic to my ears is, for example, the adverbial phrase "as in." In fact, an Ngram comparison for A. "as in equation" vs. B. "similarly to equation" shows version A to be about 100 times more common. And these are examples in science textbooks, not informal language. So, as in Question 2 linked above, I also here suggest "as in." Jul 31, 2017 at 6:55
  • @curious-proofreader Due to the fact that similarity is a common mathematical property between two objects, there are further incentives for mathematicians to avoid using it in this manner. Out of interest, I checked around 30 peer reviewed articles papers since reading your comment and from my small sample, use of similar or similarly seemed overwhelmingly more popular. Nevertheless, I see your point and I will follow your suggestion. Thank you.
    – Echan
    Jul 31, 2017 at 8:25
  • Does this answer your question? similar to or similarly to
    – alphabet
    Mar 5, 2023 at 22:56
  • Mathematicians, like all professionals, have their own speech and writing conventions, and are not covered by grammar school rules -- particularly not when dealing with anything as contentious as adverbial usage. They are correct because they were published. If you want to demonstrate correct usage for the authors, publish your own math article. Mar 10, 2023 at 20:08

2 Answers 2

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If the preceding sentence is indicative of the example or object of comparison, 'similarly' sounds better. If the example was referenced prior to the preceding sentence, 'similar to' is necessary to establish connection.

Example 1: 5(x)=10. Similarly, 6(x)=12.

Example 2: Spaghetti is a versatile pasta. It can be incorporated into many different types of dishes and cooked in multiple ways. Choosing the perfect pasta for your dish boils down to personal preference. Similar to spaghetti, linguini noodles are long and thin and adaptable to a variety of dishes.

Now, try interchanging 'similarly' and 'similar to' in the examples.

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    This is true as far as it goes, but would benefit from an explanation of the underlying grammar, such as is provided in the comments: "similar" is an adjective and "similarly" an adverb, and they modify different things.
    – Stuart F
    Apr 10, 2023 at 11:09
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There is a difference between using "similarly to" and "similar to". "Similarly to" modifies the verb while "similar to" modifies the noun. For example, let's use @tchrist's examples in the comments:

You could build a cathedral which is similar to cathedrals in France...

...but you could also build a cathedral similarly to how they were built in France.

Additionally, as an AmE speaker, I find "similarly to [1],..." unidiomatic to my ears. "Similar to" sounds a lot better.

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