Moving the adverb immediately in front of the verb instead of the sentence eliminates the ambiguity, and also produces a structure that sounds like something a native speaker of English, and not a Martian, might generate **:

"Students who rigorously study physics learn math".

Incidentally, the assertion that in the sentence

"Rigorously, students who study physics learn math",

'rigorously' unambiguously modifies 'learn' and not 'study', is incorrect.

It doesn't modify either of those verbs (unambiguously or otherwise), because very few native speakers with normal cognitive abilities exist who would ever think of uttering (or writing) such a barbarism.

** Though the Martian would at least deserve some credit for effort.

Moving the adverb immediately in front of the verb instead of the sentence eliminates the ambiguity, and also produces a structure that sounds like something a native speaker of English, and not a Martian, might generate **:

"Students who rigorously study physics learn math".

Incidentally, the assertion that in the sentence

"Rigorously, students who study physics learn math",

'rigorously' unambiguously modifies 'learn' and not 'study', is incorrect.

It doesn't modify either of those verbs (unambiguously or otherwise), because very few native speakers with normal cognitive abilities exist who would ever think of uttering (or writing) such a barbarism. Insofar as it can be said to modify anything at all, it modifies the entire sentence.

** Though the Martian would at least deserve some credit for effort.

Moving the adverb immediately in front of the verb instead of the sentence eliminates the ambiguity, and also produces a structure that sounds like something a native speaker of English, and not a Martian, might generate **:

"Students who rigorously study physics learn math".

Incidentally, the assertion that in the sentence

"Rigorously, students who study physics learn math",

'rigorously' unambiguously modifies 'learn' and not 'study', is incorrect.

It doesn't modify either of those verbs (unambiguously or otherwise), because very few native speakers with normal cognitive abilities exist who would ever think of uttering (or writing) such a barbarism.

** Though they would at least deserve some credit for effort.

Moving the adverb immediately in front of the verb instead of the sentence eliminates the ambiguity, and also produces a structure that sounds like something a native speaker of English, and not a Martian, might generate **:

"Students who rigorously study physics learn math".

Incidentally, the assertion that in the sentence

"Rigorously, students who study physics learn math",

'rigorously' unambiguously modifies 'learn' and not 'study', is incorrect.

It doesn't modify either of those verbs (unambiguously or otherwise), because very few native speakers with normal cognitive abilities exist who would ever think of uttering (or writing) such a barbarism.

** Though the Martian would at least deserve some credit for effort.