Ranked among great mathematical scientists

[RonPurewal]

Correct; the initial modifier should have a close relationship to the entire sentence that follows, not just to the subject.

Good eye.

[whereisraihan]

Thank you very much, Ron.
We are very lucky to get great expert like you

[tim]

We are very lucky indeed!

[aflaamM589]

Hello Ron,
I think C is not even a sentence.
Can you confirm?
al-Haytham,born in Iraq in 965 C.E., and who experimented extensively with light and vision, thereby laid the foundation for modern optics and also for the notion that science should be based on not only experiment but also
Leaves us with
al-Haytham thereby laid the foundation for modern optics and also for the notion that science should be based on not only experiment but also
Is presence of thereby in this location acceptable?
Thanks in anticipation
Have a nice day

[RonPurewal]

there's nothing intrinsically wrong with having "thereby" there, if it's justified by something in the modifier(s).

for an analogous example, consider the use of "also" in the correct answer to this one:
https://www.manhattanprep.com/gmat/foru ... t3170.html
in that sentence ^^ you need the content of the modifiers for "also" to make sense—but that's ok, because the modifiers are there. (:

__

in any case, it should be clear enough that the two colored parts are non-parallel; there's no reason to over-think this.

that yellow... my eyes!

[aflaamM589]

Thanks for the explanation.
and apologies for inappropriate color, have edited it .
God bless ya

[RonPurewal]

you're welcome. no problem about the color—just keep readability in mind please (including on tablets, where it can be difficult or impossible to highlight things).