Send humans to Mars
NASA has inspired generations of Americans to study mathematics and science, all while providing us with real, practical results (solar energy, improved ceramics, GPS, better telecommunications, personal computers...). Unfortunately, NASA became derailed after the Apollo program ended and its funding has dwindled. Restore NASA to its former glory and give it a goal they can really sink their teeth into: Send humans to Mars!
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austinlorenz commented
Absolutely. The book "The Case for Mars" demonstrates that a Mars mission would be cheap, easy, and extremely beneficial for technological development and national prestige.