Optimal material for a hammer head I was watching a TV show in which a gold hammer was mentioned.  It was not serious but caused me to wonder whether gold would be a good material and, if not, what else might be.  An attraction of gold is that it has a high density but that advantage is probably negated by being more malleable than steel.  So, I started to wonder what properties I need to consider.  Some materials may be hard but liable to shatter on impact. 
Let's suppose that the dimensions of the hammer are fixed: a fixed handle and a fixed size and shape for the head.  The objective is to drive steel nails into a variety of hard substances.  
Cost is not a factor, nor ease of construction, nor safety.  It will need to last long enough to be used so francium and various heavy elements are not suitable.  If depleted uranium is a good material then this would be acceptable.  It is used for armour piercing shells presumably because of its density but there are denser materials.  Is it that it is cheaper than gold or osmium?
What properties should I be researching?
Additional: to make the question more manageable, I will require a homogenous pure material for the head not an alloy.  I hope that this makes me more a question of physics rather than engineering.  This is a thought experiment rather than a real project.  
 A: What the optimal hammer head material is depends on what we are optimizing for. 
A standard hammer has a hard head that has high density, held by a strong but usually light handle. If it has length $l$ and is accelerated at some acceleration $a$ set by user muscle strength it will reach a velocity $v$ after having traversed a distance $\sim l$; that is, $l=at^2/2$ gives $t=\sqrt{2l/a}$ and $v=\sqrt{2la}$. The kinetic energy  will be $K_e\approx mla$. So a long and heavy hammer will be able to drive a nail more deeply (to a depth $K_e/F$ where $F$ is the resisting force). So more mass and length seems good... but obviously not too much either. 
Important design constraints are: (1) the head should not be damaged by normal use, (2) the mass of the head needs to be big enough that it helps drive the nail into the target, yet not so large that it is hard to handle, (3) the handle needs to hold the head well, not break, and ideally dampen vibrations. 
Consideration (1) requires the head to be harder than the nails (while mallets have softer heads since they are being used to reshape other, even softer, materials without breaking them). Consideration (2) seems to suggest we should find a high density material, but if it is too high density the head will be small and hard to hit with.  Currently high carbon, heat-treated steel for strength and durability is used. (3) has traditionally meant wood, but composites may be better.
Since cost is not an issue, we can do material selection rather freely. We want a high yield stress or impact strength so the force from hit nails don't harm the hammer. Compressive strength better be good. Density should be as high as possible, but if it is very high we may have to design weird head shapes. So we should invent a performance index that describes the trade-offs here. Unlike most material selection we actually like density, so we might want a performance index like strength times density. Putting this on an Ashby chart we get this:

The red line is constant performance; the further above it a material is, the better in this respect. In this case we get some cool suggestions: obviously steel, but tungsten and diamond also look good!
The problem is that this is just one factor. Diamond is fairly brittle, and not suitable for hammers! Now, I don't have a proper Ashby chart for brittleness, and I will no doubt make a fool of myself in regards to the different kinds of material strengths (better leave that to the professionals). For fracture toughness we can also see that tungsten is not as good as steels, despite being stronger:

That diagram also suggests that metallic glasses may be a good option for a head. However, they do have a lower fatigue strength: one needs to check that this force is not reached in using the hammer, or it will eventually shatter!
Depleted uranium is dense, but it is not stronger than steel (I assume one can make some interesting alloys, though). Worse, uranium is pyrophoric: when hitting nails, it will spark which is likely really bad for woodworking.
So in the end, my answer is a non-answer: it depends. Plus, engineers will be able to combine things cleverly. A hard steel is hard enough to handle the nails, but one could add some tungsten or osmium weights behind the steel strike surface to boost it... but not too much, since then the hammer becomes hard to use. Probably designing a really good grip might be where things could improve a lot, but now we are way outside physics. 
