As im nowhere near these mega-research cities, I'd thought I would ask when or where is the turning point in the tech tree/race that your civ just really speeds up and leaves the AI in the dust?
Well, this is more of an exercise than a practical application. If you try this at a reasonable difficulty level (bending your entire game around one mega science city) you will probably lose.
Boy did I underestimate beakers from specialists...indeed, we could basically say that infinite beakers is possible, since given infinite time you could get infinite GS.?
I think the last one took 36000 GPPs, somewhere in that neighborhood (remember this was Marathon speed)

. You are right though, if you disable time victory and are very, very patient you could get infinite beakers. Even with time victory enabled if you are willing to manage more GP farms (I only had five or so) you could probably get to 5000 beakers (that would take about 100 Great Scientists). Let's see, how many GPPs does your 100th great person take?
GPP(N) = N*300, ------------------------- N <= 10
GPP(N) = 3000 + N*600, ------------------ 11 <= N <= 20
GPP(N) = 3000 + 6000 + N*900, ----------- 21 <= N <= 30
GPP(N) = 3000 + 6000 + 9000 + N*1200, --- 41 <= N <= 40
Hmm...so the decade changing term seems to go 3K, 3K + 6K, 3K + 6K + 9K, ... If we define n as floor(N/10) and use the magic of z-transforms we find this can be expressed as 1500*n + 1500*n^2. The "current decade" term is simply ceil(N/10)*300*(N%10), so the formula for GPP(N) is:
GPP(N) = 1500*floor(N/10) + 1500*floor(N/10)^2 + ceil(N/10)*300*(N%10)
My 40th Great Scientist (remember I popped a Prophet) would then have taken 31,500 GPPs. That feels about right. The 100th would take 165000. The total for 1 to 100 would take 5,875,000 which assuming Pascifism and Philosophical but ignoring the National Epic and Wonder sourced GPs would take about 65000 GS turns. This also discounts the wasted GPPs for non-popped GSs at the end of the game. I guess 100 is a stretch.
Darrell