Characters might be flat or round, static or dynamic, but in 1984, Syme plays a specific role.
In my opinion, Syme is a foil to Winston. A foil is a character intended to help show a main character's traits by being opposite in many ways. While Winston is just your average guy, Syme is depicted as rather intelligent. This intelligence further demonstrates that intellect is not valued in this society, because Winston knows that Syme will ultimately die. This discrepancy in how each man reveals his thoughts makes readers empathize even more with Winston. Readers want him to keep living to keep the story alive and hopefully watch him overthrow Big Brother.
Other differences that help show contrast include devotion to Big Brother, level of excitement for the Party, and level of directness in communication. Winston knows to be quiet about his thoughts, whereas Syme blurts out his every idea. Syme clearly loves Big Brother, while Winston wants to take him down.
This contrast also develops readers' eventual disappointment in Winston. Readers realize he does not have all it takes because they have seen more intelligent characters, like Syme.