Superheated magma is not really much of a problem.

If you don't go too deep (a few thousand KM), the temperature is under 1000 degrees. We have plenty of materials than can handle that. For insulation use vacuum, or aerogel (which melts at 1,473 K) and is a phenomenal insulator. Add a large cold reservoir (liquid nitrogen) and you don't need a conventional A/C - it only has to last 42 minutes, and weight is not a problem.

The pressure is a much bigger problem. You can't bore a tunnel in the conventional sense since the rock is a liquid. You'd need some sort of wall, but I don't know if we have anything strong (and stable) enough. Most metals will oxidize and destroy themself at those temperatures.

Maybe a ceramic, or alumina coated metal. Perhaps a tungsten compound of some sort that is stable in oxygen at high temperature.

Another problem is the speed (reaching 1000 MPH), you'd need magnetic bearings (mag-lev), but magnets don't like being hot. The curie point of iron is 768 C, which is too low. Cobalt might work - but barely.

The coolant would only need to last 42 minutes if you thought it could never get stuck.

If you got stuck while moving at around 1000 MPH you have bigger problems.

And if you survived the crash - how would you get out? The capsule is unpowered, and they don't make cables long and strong enough to pull you out.

But assuming rescue was possible, I suppose they could drop small emergency coolant refill bags down to you.

Then you just poor a ton of liquid nitrogen down afterwards and cryonics will take care of the rest (give or take 50 years).

IANA chemist, but couldn't you solve the oxidation problems by getting rid of the oxygen? In the article, he talks of a vacuum to avoid friction.

Don't forget about the other side of the wall....

Also, I wouldn't want to build something where a single seal failure would mean the entire thing is destroyed. Plus, how would you construct it.

If you read the article carefully, he also talks about shorter tunnels which would only go a few miles below the surface. Not necessarily through the core, although I believe the journalist got a little confused himself with the Moscow-Washington bit (716 miles depth != Earth core).

Anyway, it's nice to see he solved the pathfinding, but it's probably not the most challenging part of the problem!

Have a look at a globe. (or google earth or whatever) The direct line between DC and Moscow is surprisingly shallow. The exact number does seem too low by a factor of 1.5-2 though.

The exact number is right. The depth is R(1-cos(theta/2)), where theta is the angular distance between the two cities and R is the radius of the earth. (Draw a cross-section of the earth.) Let d = R*theta be the distance on land; then the depth is R(1 - cos(d/(2R)). (For short distances this is about d^2/(8R), so the depth varies quadratically with distance, which makes sense. But Moscow to DC isn't that short.) The radius of the earth is 3963 miles, and DC and Moscow are 4850 miles apart; the formula gives 719 miles for the depth of the tunnel, which is close enough to the claimed 716 that I blame rounding errors.