Of course it is possible to reach excellence in Mathematics for a blind person: Lev Pontriaguin blinded before studying math at the university. 

BUT I think you are also asking if it is a serious handicap. I think the answer is yes, it is.

Another interesting question is if we can develop learning and teaching maths without using visual tools. I don't know the answer.

Of course it is possible to reach excellence in Mathematics for a blind person: Lev Pontriaguin blinded before studying math at the university. 

BUT I think you are also asking if it is a serious handicap. I think the answer is yes, it is.

Another interesting question is if we can develop learning and teaching maths without using visual tools. I don't know the answer.

Thank Prof. Carriegos for the information.

Blindness is certainly a serious obstacle when studying geometry but it is not so when studying probability.  There is also a reason for many mathematicians not to illustrate their thinking with figures: sometimes such figures can be misleading and quite often they suggest too much, thus eliminating solutions other than widely/intuitively known.

Dear Alfred, I tell you my experience 

In 1993 there was one of my students blind, in the third year of Licence (graduate level),  I gave them a course in Abstract Algebra and Algebraic number theory. She was the first in her section. The problem was: I should pronounce every thing, because she only listen, sometimes I forgot that and she remaindered me.

In the exam, I dictated it, she wrote it in Braille, and in the end of the exam, she dictated her answer written in Braille and I wrote it as she spelled.  That student now is a doctor in one of French universities,  what she does, how she teach? Really I don't know

Yes because we have one that has just graduated in my university

This is an excellent question.    In addition to the helpful observations that have already been made, there is a bit more that can be added.   This is a followup to the AMS Notices article on blind mathematicians cited by @George Stoica.

There are quite a examples of those who were blind and have succeeded in Mathematics.   Here are a couple.

Lev Pontryagin was a very prominent blind mathematician. Apparently, his mother taught him mathematics from an early age and he was able to pick up the subject quite quickly.

https://www.quora.com/Are-there-any-blind-mathematicians

Larry Wos:  Wos quickly learned that Chicago's math department "wasn't about numbers. It was about abstract mathematics. Groups and rings and fields and topological spaces and set theory." Being blind placed Wos further into uncharted territory. "They didn't even have a good Braille code for mathematics. So we invented our own. And I got through. I got great grades."

Two professors, in particular, took a liking to him: Paul Halmos and I.J. Kaplansky, "who will probably go down in the history of mathematics as one of the century's greatest," says Wos. Both challenged him to use the mental gifts he'd previously taken for granted.

http://www.mcs.anl.gov/~wos/uofc-bio.html

Thanks to everyone to me it's an eye opener. 

This will enable motivate my students the more.

I remember in Mex-Math Faculty, at Moscow State University "Lomonosov", there were several blind students and they did well.

I worked for three years in a school for the blind. I taught drawing. For the children's understanding, I made 3D geometric figures. After tactile-kinesthetic exploring  a pyramid, a girl asked me: "Can you do something so that I can feel the axes, too? Height, diagonals ..." I made them of wire. She said: "Ok, now I know how to solve the problem of geometry." So I came to help the children perform in geometry problems.

I worked a lot with a Maths teacher. That girl graduated in mathematics. I lost touch with her, otherwise I would have asked her how she has done in college. I just know that she had good results.

Can a blind person study mathematics at the university level?

Yes they can - you can refer to this link for an example:

https://nfb.org/images/nfb/publications/bm/bm12/bm1207/bm120702.htm

Following links also show how the blind people are learning mathematics:

https://www.youtube.com/watch?v=OqutQqLMVN4

https://www.youtube.com/watch?v=vfg8J_8ZPIs

https://www.youtube.com/watch?v=Uk31xOMGSWM

https://www.youtube.com/watch?v=hSdoj3UM0Dk

Beside mathematics, blind people also can do software programming - see this link also:

http://www.windowscentral.com/blind-microsoft-developer-has-created-app-help-him-see-world

hi

Unfortunately, I think they can not - it is rather unnecessary effort, such as painting images by blind persons. But they paint - and as long as they enjoy it, let them do it.

yes, they can. my friend got a blind son, he was blind since 16. he went to normal University, graduated as LLB law degree 1st class student in 2016. Today, he is doing his internship at law firm. it is possible, with great faith, comes great success, by God's will, blind people will succeed. It is the strong determination and faith inside the blind people heart, that determine their destination.