I think of Star Trek to be the forerunner of today's inventions/culture. Most of what is available/happens in the Enterprise becomes reality soon thereafter (Touch displays, holographic projections, diversity of people collaborating etc.,) However there are things Star Trek that has gone wrong such as Captain Picard saying in one of the TNG episodes that Fermat's last theorem is yet to be solved in the 24th Century (which was later solved in the year 1995 by the Mathematician Andrew Wiles). What other things Star trek famously predicted wrong?
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Quite a few things
This could turn out to be an extremely long list, but I'll focus on the main ones which were mentioned in this article as well as a few others I can think of:
- The Eugenics Wars in the 1990s (Space Seed); that didn't happen (thank goodness)
- Trans-generational 'sleeper' space ships (Space Seed (TOS) and The Neutral Zone (TNG)); don't have them yet
- The Voyager Probes being launched in the 20th century; in The Motion Picture we have Voyager VI; we're in the 21st century and have only launched 2
- A manned mission to Saturn in 2009 (Tomorrow is Yesterday); we haven't even put men on Mars yet!
- The launch of the Nomad probe in 2002 (The Changeling)
To be fair though, have a look at this article which points out a number of technologies which have since been actually developed.