Please take a look at the two sentences below which I quoted from http://www.cacr.caltech.edu/~sean/projects/stlib/html/numerical/numerical_random_poisson.htm.

"I have adapted some methods from various random number packages. Each of them are hybrid methods."

Isn't the second sentence gramatically wrong for using 'are'? If it is not, please explain.

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Yes, grammatically it should read 'each of them is' or 'all of them are'. Mathematicians are not the best writers.
'Each of them are hybrid methods' sounds less formal, but both variants are correct. You may as well see a slight difference in the meaning: 'Each of them is a hybrid method = Every method is a hybrid one' and 'Each of them are hybrid methods = All of them are hybrid methods'.
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No, sorry, both variants are not correct.
It has nothing to do with formality or meaning.

Each is singular and takes a singular verb. Period. End of story.

The writer has gone astray because in English the verb nearly always follows immediately after the subject. In this case, the pronoun closest to the verb-them-is plural, so the writer has made the mistake of thinking that the subject is plural. However, the subject of an English sentence can never be inside a prepositional phrase (of them.)

Think about it this way. Which is correct?
Each peach is ripe.
Each peach are ripe.

Retired ESL teacher.
Hello, Andelie-- and welcome to English Forums.

Could you please supply us with an authoritative reference for 'each of them are' being 'less formal but correct'? As far as I know, 'each are' is not yet acceptable.
Dear Mister Micawber,

I believe the only time we can use the structure 'each are' is when we place a plural object before each as in "They each are ..."

In the case I questioned earlier, I believe that 'Each' is the subject of the sentence; thus, the verb has to be singular.

I thank you for your support.
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I wrote it basing on my experience with Americans, who used 'are' very often. Maybe it was wrong of me to say 'less formal'. What one often hears, is not always correct (like 'We don't need no education Emotion: smile'). You can google 'each of them are' or 'each of them have', but of course, as I said, colloquial speech isn't a good source to learn from. I also found this link:


The verb after each of is usually singular, but it can be plural in an informal style.
  • Each of us has problems. (More formal)
  • Each of us have problems. (More informal)
However, I don't think one website can prove anything. I'm sorry for my 'less formal'. Couldn't find the appropriate word to describe the construction which is wrong, but used quite often.
Oh, I think that's about right-- it's just a matter of where you try to use the 'informal' form. In conversation, of course many native speakers do-- me, too, I think. Proximal concord ('...us have...') is a strong draw in the spoken word, which emerges linearly from our mouths.

But for business letters, formal speeches, essays and reports: 'too informal'.

(By the way, the word I use for 'very informal but not substandard' is 'casual'.)
Mister MicawberMathematicians are not the best writers
Emotion: rofl

I see that the question has been more than adequately answered. I can't contribute anything more than a smiley after the comment about mathematicians and English.
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