What is the symbolic significance of 2+2=5 in the novel?

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The illogical math problem symbolically represents the Party's control over reality, which is a primary aspect of their totalitarian regime. The Party employs various means of oppressing and manipulating the population, and reality control is one of the most significant ways they maintain complete authority over the dystopian society.

The Party successfully controls reality by continually revising, destroying, and fabricating historical records in order to make the Party seem omniscient. The Party members are also required to practice doublethink, which is the ability to hold two completely contradictory thoughts simultaneously while believing both of them to be true. The wide use of paradoxes and strict control over language is another means of reality control. From the Party's perspective, completely orthodox, obedient Party members can firmly believe that two plus two equals five. By believing this illogical math problem, the citizen has allowed the Party to successfully form and manipulate their reality. Winston Smith is not one of the Party members who believe this lie, writing,

Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. (Orwell, 103)

Overall, the illogical math problem symbolically represents the Party's control over reality and is used as a gauge to assess a Party member's orthodoxy.

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To me, the only meaning of this is that it symbolizes just how completely the Party has changed people.  We know that the Party is trying hard to be the only source of reality.  It tells people things like "War is Peace" and expects them to believe it.  It changes the past (like what Winston does) so that people cannot have any idea of what happened other than what the Party says.

To me, the equation you mention is sort of the ultimate example of the Party controlling people.  It is asking people to believe when it changes a basic law of mathematics.  So if it can change that, it can change anything.

So 2+2=5 is, to me, a symbol of how the Party has almost total control over what people think.

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