This is a general question going out to the materials scientists, chemicals, and metallurgists, none of which, sadly, I am.
We’re all familiar with arenak, the wonder-metal E. E. “Doc” Smith came up with in The Skylark of Space, and its amazing properties of being 500 times stronger and harder than the strongest and hardest steel, and not softening even if heated to the surface temperature of the sun.
(If you’re not, and maybe even if you are, consult this article here for more details, and entertaining speculation which should adequately reveal why engineers in SF universes would dearly love to get their hands on the stuff.)
To you, I throw the question open –
How close could we get? In theory, that is, not just in what we can make in 2025. What are the limits, and how can they be entertainingly and plausibly violated?
From my first year intro to quantum chemistry background, it sounds like the thermal and physical properties suggest we’re beyond conventional ionic, covalent, or metallic bonding here, and arenak involves something exotic - perhaps something like a polymer formed from stable or metastable (at normal pressures) covalent inner-shell bonds, if such a thing could exist (the article does talk about ionic inner shell bonds only - I’m not certain covalent inner-shell bonds are possible from a quantum-physics perspective).
If such material did exist, though, I think its reactivity would be an interesting question to do the math for - maybe the inner-shell bonds cause interesting things to happen to valence electrons so they’re even more reactive than usual, or maybe the complete opposite happens.
As others have said, it will probably have to be exotic matter. But as far as strength goes, it’s interestingly not insanely high.
General, isotropic, reasonably ductile/rigid materials like ductile metals top out at around 300 kN*m/kg. (Yes, this is specific strength, not volumetric strength.)
Various brittle, anisotropic, and/or fibrous bulk materials like carbon fiber and Dyneema that are commercially available get you close to 4000.
Anisotropic nanostructures like graphene and carbon nanotubes get you to 45,000 to 60,000+, which is enough orders of magnitude but not quite there, and also these are not bulk materials, with actually usable materials made from them struggling to realize even a small fraction of their strength. (And Arenak is supposed to yield very ductilely and gracefully, I think it’s suggested that its fracture toughness might be even more insanely high.)
Research on this brought me to talk about dredging the hawking radiation zone of black holes.