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There's a lovely parable about this in I, Robot [the book].

This poorly designed AI you speak of is the premise of I, Robot by Asimov. In fact, this is one of the fears surrounding AGI - the AGI would be correctly configured to act only for the benefit of humanity, however, in typical AI fashion, this leads to unexpected (and often undesirable) effects.

Straight up impossible for me to search for Isaac Asimov's "I, Robot". Some kinda of input cleaning strips out the I from "I robot", and just searches "Robot". "iRobot" does not get the results. And the search does not accept commas. Just some of the fun that comes with searching I suppose.

His book I, Robot is a series of short stories in which the laws have been tampered with in various ways. https://en.wikipedia.org/wiki/I,_Robot#Contents

It's essential that you complete Isaac Asimov's I, Robot for a thorough understanding of how badly things can get out of control.

D'Aulaires' Book of Greek Myths

Star Trek, the original series

I, Robot by Isaac Asimov. The first science fiction story I read, which lead to all the others.

The Annotated Alice by Lewis Carroll and Martin Gardner. That's Alice's Adventures in Wonderland and Through the Looking Glass, by Lewis Carroll, with wonderful annotations by Martin Gardner.

Depends on what you mean by "rational". My understanding is that many flat-earthers of course don't seriously believe the earth is flat, and the argument is made as a form of artistic expression, which is to say that it is meant to demonstrate that rationality can be abused and does not inherently lead to truth.

One of Asimov's I, Robot stories did a similar thing, with a robot on a space station making rational arguments against the existence of earth.

Of course, there are also nutters...

Closer to Eando Inder's I, Robot than Asimov's.

https://en.wikipedia.org/wiki/I,_Robot_(short_story)

Depends what you mean by 'hard'.

Anything by Greg Egan is probably going to be the hardest sci-fi you've ever read. Dude wrote a book where he considered the ramifications of a universe built on a positive-definite Riemannian metric, and another one where the universe has 2 time dimensions.

Robert L. Forward's Dragon's Egg explores what life might look like if it evolved on a neutron star.

Adrian Tchaikovsky's Children of Time and Children of Ruin explore the evolution of other earth species if they were given a kick towards sapience.

Vernor Vinge's A Fire Upon the Deep is half space adventure (not very hard) and half an exploration of a lifeform which only achieves sapience in small groups. A Deepness in the Sky is generally harder and explores a lot of things, including the power of focused human attention, the difficulty of galactic scale civilization, and alien life evolved in a star system where the star periodically dims.

Steven Baxter and Clarke collaborated on The Light of Other Days, which explores the technical and sociological consequences of a device which allows you to see the past.

With a broad interpretation of 'hard' I can highly recommend Ursula Le Guin's The Left Hand of Darkness and The Dispossessed, which have soft science but hard humanity.

Similarly The Long Earth series, a collaboration between Pratchett and Baxter, where it seems Baxter handles the sociological and technological consequences of the science while Pratchett handles the characters and philosophy.

Asimov's I, Robot is an exploration of what happens when you try to constrain intelligence with rules.

Asimov's Foundation Trilogy gets a lot of hype, but it isn't very hard and I also found it utterly mediocre. Instead I recommend The God's Themselves, which is so good it's like Asimov was channeling a much better writer to get his ideas down. It explores the limited interaction of our universe with one that has slightly different physical properties.

Also perhaps stretching the definition of 'hard', but I want to recommend it because it's relatively unknown, is Leonard Richardson's Constellation Games, in which an incredibly advanced multi-species anarchic alien civilization makes first contact with humanity, and the protagonist really just wants to play their video games. It's actually harder sci-fi than it sounds.