1) As Leigh Palmer pointed out, you can do it by means of a raft with a
windmill and a propeller.
A few years ago my friend Chris Burges asked me to stop by his office so he
could show me his solution to the riddle. I wondered he didn't just tell
me. He said it would be more fun if I came by his office. Sure enough, he
had a proof by construction. Literally.
2a) An interesting corollary is that you can run directly downwind at a
speed greater than the true windspeed.
2b) Another corollary as pointed out by John Mallickrodt is that a
riverboat can sail downriver in calm air faster than it could with a
following breeze that matched the water speed.
BTW I don't 100% agree with JM's assertion that reformulations (2a) and/or
(2b) always make the solution more obvious. I've seen some people get the
right answer to the original "sailing upwind" problem but then be baffled
by the other versions.
3) According to my limited statistical evidence, physicists who are
experienced sailors have more trouble with this problem than ones who aren't.
4) The following may help people understand the solution. It is important
that there be a mechanical advantage between the turbine (windmill) and the
propeller. Quantitatively,
Let c be the velocity of the sea relative to the boat, which is rearward.
Let a be the apparent wind, i.e. the velocity of the wind relative to
the boat,
which is rearward and larger in magnitude than c.
Let w be the true wind, so that a-c = w.
Suppose the linkage is such that c = ka where 1/k is the mechanical
advantage.
Conclude c = kw/(1-k)
which diverges as k goes to 1.
In practice k must be much less than 1, to allow for losses such as
propeller slippage. (Or to say it the other way, if you had no slippage
[for instance if rather than fluids you had two cog-tracks with unequal
velocities] you could go upwind *really* fast.)
5) The foregoing embodies the assumption of large Reynolds number. If the
boat is too small, or if the wind speed is too small, or if the fluid
velocities are too large, then it is *not* possible to sail upwind --
directly or otherwise.