Then if you're discussing the topic in the context of "whether our current mathematics is useless in the context of Godel's theorem" - then we can easily define

Then if you're discussing the topic in the context of "whether our current mathematics is useless in the context of Godel's theorem" - then we can easily define progress in mathematics as "how many contradictions we had found today" and thus continue living with an objective till the heat death of the universe.