: Questions on two sentences on a cover letter I am writing a cover letter - an excrutiating process. There are two sentences I am quite unsure about. The first one: I hold a math Ph.D.

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Your question 1 is too long, but where you should break it is not where you broke it. The information about the professor is a sidenote and is a parenthetical remark if ever I saw one.

Also, you can't "carry out" a degree, and "I hold a degree that was earned" is verbose; "I earned my degree" would be more concise.

So my suggestion is:

I earned my math Ph.D. from xxx in a research group headed by yyy. (yyy is a recipient of the Fields Medal, the “Nobel Prize of Mathematics.")

Note correct spelling of "recipient" which was misspelled in your original.

On to your second problem sentence.

I believe that the advertised post is an outstanding opportunity to contribute to, and further develop my career in, governmental policy planing and analysis.

My issue with this sentence is that it focuses on what you would get out of the position, not what you would give to the position. It also seems tentative due to the "I believe" at the beginning. So I would simply say:

The advertised post is an excellent fit for my background, skills, and career goals, and I am certain I can make a valuable contribution to the project.

Of course, it is difficult to give advice at the sentence level without the advantage of the context in which the sentences appear. My rewrites may well not fit in with the tone of the rest of your letter.

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Some people do not like it if you begin your letter with "I". They think you are ego-centric and they do not want to work with these kind of people. I contrarily think starting a cover letter with "I" is pretty straight forward, but again, that's maybe just me.
The sentence is presumptuous (BTW: use a spell checker and a native speaker if you aren't one). Skip the "Nobel Prize" stuff. Either the people know the Fields Metal or they google it (unlikely) or they just don't care. You would only help the googling guys and I don't think it's worth it.
Do you mean "planing" or "planning"?
"believe" is a word I would try to avoid. It always provokes the "why don't you know" reaction. Use "Your advertised position is an ...".
You do not want to develop your career, you want to develop yourself and your abilities. I also wouldn't use both verbs "contribute" and "develop"; pick one. You can still add another sentence like "contribute to your team/success" or nonsense like that if you really want.

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