is this grammar correct?

jacob my best friend belives that he is as smart as i am

If you put capital letters and commas in the right place and double-check all the spelling ... maybe.

Let us know how you'd rewrite this.

No, the grammar in the sentence you provided is not correct. Here's the corrected version:

"Jacob, my best friend, believes that he is as smart as I am."

To explain the correction:
1. Jacob, as a proper noun, should be capitalized.
2. Commas should be placed before and after the phrase "my best friend" to set it apart as additional information.
3. The pronoun "I" should be capitalized because it functions as the subject in the second clause of the sentence.

By following these rules, the sentence becomes grammatically correct.