To hopefully expand on what m'Lord Emsworth wrote, "I doubt they will accept this proposal" actually means you almost have enough for the trade. If the advisor had said "they will be insulted by this deal.", then you would need A LOT more to make such a trade. As pointed out by m'Lord Emsworth Lizzie could have a turn or two left on researching Monarchy, which if you do the calculations on it compared to the Mathematics tech, costs less than Mathematics *for those last turns*.
I KNOW that I have often researched a tech, got beaten to it, with several AIs learning the tech, and then bought it on the last turn of research for 10 gold... I think even in the late middle ages or industrial ages. Next time I do it, I'll post a picture. Or if anyone else has one, can you please do so?