There are ~80 techs in the Civ3 tree, subdivided into 4 'Age'-groups (Ancient, Medieval, Industrial, Modern), with ~20 techs per Age, and ~80-90% of each group 'required' for progression to the next Age (non-required techs usually unlock new governments, powerful units, or Wonders). The ability to trade (or extort!) techs and/or skip non-required techs means that a (human-controlled) Civ does not need to research all techs directly. Civ3 also has 'fixed' (moddable) limits on research speed: in the epic-game, regardless of how many beakers per turn are invested (or how few, provided that the total is ≥1) , no tech will take <4 turns (all 3 versions), or >40 turns (Vanilla, PtW) or >50 turns (Conquests) to be discovered.
Unlike in CivDOS, each tech in Civ3 has a (moddable) base-cost, which is then multiplied by a (moddable) factor associated with the (moddable) map-size, so that on larger maps turns-to-research is not decreased simply as a result of having (more space for) more non-corrupt cities per Civ, and thus faster research. Average base-costs roughly double per Age, i.e. Modern techs are ~8 times more expensive than Ancient techs, and there are 5 default map-sizes for epic games:
Size|Dimensions|Max.Civs|Tech-factor
Tiny|60 x 30 tiles|4|160
Small|80 x 40 tiles|6|200
Standard|100x 50 tiles|8|240
Large|130 x 65 tiles|12|300
Huge|160 x 80 tiles|16|400
...with modded maps allowable up to ~256 x 128 tiles and 31 Civs (the 32nd slot is reserved for the Barbarians).
There's also a rubber-band mechanism whereby the first Civ to complete research on a tech pays full price, but as soon as a tech is know to one Civ, its cost is reduced proportionally for each Civ who subsequently learns it, according to how many Civs
they know who already know that tech. This also affects the price of an unknown tech during trade-negotiations, with further reductions possible according to how many beakers the less-advanced Civ has already put into it.
Overall tech-pace therefore tends to be (much) faster, the earlier that Civs can make contact with one another, i.e. it is released (or constrained) by map parameters. Single-landmass ('pangaea') maps tend to see much faster tech-pace than 2-3 landmass ('continental') maps, which are in turn faster than multi-island ('archipelago') maps, and as map-size and/or water percentage (60, 70 or 80%) is increased, some Civs will tend to end up smaller and/or more isolated than others, and thus fall further behind (or off!) the curve.