Kennedy had it right: "We choose to go to the Moon. We choose to go to the Moon, not because it is easy, BUT BECAUSE IT IS HARD."
Sometimes you have to push the envelope. And sometimes, that means good people have put their life on the line. Humans in general don't get really serious about things unless they have skin in the game. You have to get them interested. Call it STEM motivation. But one Apollo launch is worth a million laptops in some third-grade classroom.
Forget STEM. Let's think about JUST ONE question on Mars... one we cannot possibly answer inside Earth's atmosphere; only long-term exploration of the Martian surface will suffice: Is there life on Mars? The possible answers are "No", "Yes, a long time ago.", and "OH MY GOD IT'S EIGHT FEET TALL WITH SIX EYES AND IT WANTS TO SPEAK TO YOU SIR!"
Say it's "no" - there's no life on Mars, and never was. That tells us something important - Life is precious, life is delicate. Very important
Or there _was_ life on Mars: what kind of DNA did it have, if any?
Again, very important message: either DNA can fly thru space ("panspermia"- and we are _NOT_ alone) or it evolved separately-
and we are still NOT alone - but there's another way for life to happen!). ... or... if the physics are such that it couldn't have happened naturally, then (1) we are not alone, and (2) Mom is out there somewhere...
Or there _is_ life on Mars: Same messages above, plus a whole new and mostly untarnished ecosystem to understand. We have only 1.1 ecosystems here (I count the undersea "black smokers" as 0.1 ecosystem). Add another, and maybe we can make some understanding headway.
What will we need to invent? I don't know! Neither do you. Neither did Kennedy. And it wasn't velcro, Tang, and funny ballpoint pens that were important. It was things like radar, and heat-resistant materials (look up Carnot efficiency to understand why that's important), and lightweight sensors, and lightweight, fast electronics, and computational fluid dynamics, and finite element methods, and precision navigation, and ...
We went into 1960 as a species that, if you couldn't solve it with fifty guys with pencils, papers, and slide rules, we couldn't solve it. (that shot of a roomful of guys in white shirts with slide rules calculating like crazy in "Apollo 13" was real, dudes.)
We came out of Apollo as a species that, if the problem was important enough, we had the means, the methods, and (most importantly, the confidence) to throw as much computation as had ever been done in the whole history of the world, every second, at the problem.
Oh- and that computer you're reading this on? Doesn't matter what brand, what OS... Wouldn't have happened if it wasn't for deciding that we needed to solve those FEMs and CFDs needed for space flight.
Those solar panels? Every gram you put into space costs you about $500. You're damn right we're gonna go full-bore on making good solar panels, simply because it's cheaper to spend a hundred million bucks on the research than to loft one more overweight comsat.
That pretty weather report with satellite images? Never would have happened if the First Seven hadn't all been shutterbugs, taking photos of weather systems like they were all out for the Pulitzer Prize. Same with the GPS in your phone, or your satellite TV.
It's not what we know we will find. It's what we don't know that is the value.