Is it permissible for a woman to uncover her face in order to seek knowledge?

Firstly: 

The hadeeth “The difference of opinion among the fuqaha’ of
my ummah is a mercy” is a fabricated hadeeth, as it says in Asraar
al-Marfoo’ah, 506 and Tanzeeh al-Sharee’ah, 2/402. 

Shaykh al-Albaani said of this hadeeth in al-Silsilah
al-Da’eefah wa’l-Mawdoo’ah (hadeeth no. 57): It has no basis, and the
muhaddithoon (scholars of hadeeth) tried hard to find an isnaad for it but
without success. 

Al-Manaawi narrated that al-Subki said: It is not known to
the muhaddithoon, and I could not find any isnaad for it, whether saheeh,
da’eef or mawdoo’. This was confirmed by Zakariya al-Ansaari in his
commentary on Tafseer al-Baydaawi. 

End quote 

It is not permissible for
a woman to uncover her face in front of non-mahram men, except in cases of
necessity, such as a medical doctor when no female doctor is available, so
long as she is not alone with him (khulwah), or when proposing marriage, or
when bearing witness in front of a qaadi (judge). In the cases mentioned
above, it should be limited only to that which is necessary, and no more
than that. 

A woman’s hijab and niqab do not pose an obstacle to her
seeking knowledge. It is not correct to believe that there is a
contradiction between covering and seeking knowledge. May Allaah never bless
knowledge that is only acquired by means of sin and women neglecting
modesty. Women who wear hijab and are covered have reached the highest
levels of knowledge and have earned degrees and certificates without mixing
with men or uncovering their faces, whilst we see many of those who fail to
acquire knowledge wearing the minimum of clothing on their bodies. Since
when does neglecting modesty bring knowledge and hijab prevent it? 

Covering the face is obligatory for Muslim women who have
reached the age of adolescence. In the answer to question no.
12525 you will find an explanation
that the face is ‘awrah. 

We have discussed the evidence that it is obligatory to cover
the face in the answer to question no.
21134, 21536 and
11774. 

The view that it is permissible for women to uncover their
faces in order to seek knowledge is not correct. 

We ask Allaah to help you to do that which pleases Him, and
to reward you greatly for your question and your efforts to learn. Our
advice to you is to keep away from dubious places where mixing takes place.
We give you the glad tidings from the Prophet (peace and blessings of
Allaah be upon him) who said: “Whoever gives up a thing for the sake of
Allaah, Allaah will compensate him with something better than it.” So seek
the help of Allaah and be patient. The first Muslim women gave up their
(former) religion, their husbands and their homelands in order to enter
Islam, and this move from being uncovered to wearing hijab is insignificant
in comparison to what those women did. Be sure that you will find
encouragement from your veiled sisters who will make that transition easier
for you. Do not pay any attention to the obstacles put in your way by evil
and corrupt people, women and men alike, for they do not wish you well and
they do not want you to be happy or be rewarded, nor do they know the true
path to happiness and reward. 

And Allaah knows best.