Here is a link to Fermat's last Theorem:

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html

Here is the link to show that a computer verified Wiles' proof:

http://www.cs.rug.nl/~wim/fermat/wilesEnglish.html

Here is a connection between proof theory and programming:

http://www.ercim.org/publication/Ercim_News/enw23/galmiche.html