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US makes strongest-ever armor material with 100 trillion bonds/cm²
(interestingengineering.com)
This is a most excellent place for technology news and articles.
Not to mention, really hard tires would have very poor grip. The rubber needs to be a bit softer to squish around all of the little imperfections in the road, technically increasing the contact area and providing a little lateral bracing (probably not the right term so I hope I'm making sense). This is why a lot of performance tires have shorter lifespans then other tire types, because in addition to a different tread pattern, they also often use a softer, "stickier" rubber, which wears out faster.