Re: popsofctown
To me, when to accept a share of Math really depends on what is my aim/perspective at that point of the game...
Let's say if I have already got a good scoring/achievement taking mechanism on the board and I know I am going to follow that track in the following 1-2 rounds, I usually aim at slowing down the pace of the game(e.g. denying my opponent from getting more options/skipping actions/etc.) which means that more likely i am not going to do the Math.
Well when I have no solid mechanism to go for an achievement run, it still depends on what age we are talking about. Say cards in some of the ages would be more brutal, generally the even numbered ages (4,6,8,10). It really depends on whether you want such kind of card for yourself immediately instead of denying your opponent from going on the next age, for example, if my opponent shares the Math to me which both of us can jump to age 6 I would usually take the chance, since I may get cards like Industrialization which I can play around with or Atomic Theory which I can quickly catch up my opponent. To go further in this you will have to know all the cards so well that you know what would both you and your opponent can actually gain from this use of Math, which I do analyze that but most of the time life is easier than I thought
For a more general framework on countering tech-up-maniac(believe me they exists, there are actually players who would search though the whole age 2 by using writing for 6-7 times in order to take away Mathematics), a few tricks can be used, by applying short game pressure(doing scoring and achievements early on), by sharing dogmas which alters your board to your opponent(e.g. 'draw and meld' effects), by robbing hands from your opponent(effects like Archery and Machinery) and by robbing cards directly from your opponent's board(usually crown related cards like enterprise or banking). Too much details to explain from here so I am not going to list them here. There is a trick though, you intentionally give the free draw to your opponent and use hand robbing cards like archery to take that away so you immediately catch back
And concern about scoring power...it really depends on can you activate the 'sweet point' of that particular scorer or not, let's say 'currency' in age 2 is actually quite underrated in other discussions like the one in BGG but if you can achieve certain conditions, that card can sweep some 10-30 points in a single action(eg. your opponent is ramming the age deck by using a very powerful drawing mechanism which both age2,3,4,5 cards are empty but you have more crowns than him since you have those capitalist cards:translation, optics and enterprise on your board. Now with currency, you return 1,2,3,4,5,6 from your hand and you actually scores 2,3,4,5,6,6 which is a total of 26 points). In another POV most scoring cards would not give you anything more than 10 points(if they only let you score 1 card from anywhere) so it really depends on which kind of scoring mechanism you want to go for, is that a burst one like currency or canning which use up a large part of resources from you but scoring a lot, or a sustainable one like machine tools which only score 1 card at a time but don't cost you much.
Well it is really more about did you know about the cards enough, but my general advise is, if you want something brutal which gives you a lot of score burst, DON'T GO AGE 3. there is no burst scorers in age 3 and actually most scoring effects in age 3 is connected to some other effects, e.g. Optics and Alchemy.