"We should figure something about a statement about our research."
Frankly, I don't like this about after "something". Would as for work instead? Or maybe there is something else, better in this situation?
There is an AmE usage of figure without the 'out': 'Go figure' (inviting someone to draw an obvious conclusion); in this case it means 'Go [and] figure [it out]'. This is rarely used in BE; I've heard it a few times, but only in situations where there was a multi-national culture with a strong US presence.
I have heard these, in informal speech:
I just can't figure him.
I've never been able to figure people like that.
This usage becomes more common when there is an object complement:
I didn't figure him for a sucker.
And of course, 'figure sth' is quite acceptable if the 'sth' is a clause:
I didn't figure you'd come. [Informal, but quite common - maybe not so much in BE though - to express uncertainty.]
And what about this thread -- https://www.usingenglish.com/forum/a...vs-figure.html ?