mangu: "if there's an effect here, it should probably be related to neutrinos-through-matter vs neutrinos-through-vacuum"

Cerenkov radiation shows ordinary matter can travel faster than light in a non-vacuum. This would be different but not that different.

http://lbne.fnal.gov/neutrino-beam.shtml indicates another experiment is possibly coming soon

This also would imply that the gravitational radius of a black hole is smaller for a neutrino than for light, so it might imply that black holes could evaporate a bit quicker than previous estimates.

These folks crack a 150-bit elliptic curve in one month (NOT one of the NIST curves...yet) with relatively inexpensive hardware.
Down form hundreds of years. This is non-quantum.

Cover and Decomposition Attacks on Elliptic Curves
Vanessa VITSE
Joint work with Antoine JOUX
Universite de Versailles Saint-Quentin, Laboratoire PRiSM
Elliptic Curve Cryptography – ECC 2011
Cover and Decomposition Attacks on Elliptic Curves
ecc2011.loria.fr/slides/vitse.pdf

Let's forget about the dead heroes in the epic quest to get men to Mars and back (See the race for the South Pole for how it goes.) Lets forget about the quadrillions of dollars. Let's forget about the speed of advances in robotics that have made it possible to explore the Titanic and the deepest points in the ocean with no risk and at low cost.
We do not know what kind of life may still exist on Mars. It may be anywhere in the top couple hundred kilometers of the surface.
I went to Antarctica and saw first-hand what even a bunch of careful scientists can do to trash a place, and it is entirely possible we could destroy all life on Mars before we even knew it was there, if we go in person.
We might also bring back something that we did not consider alive. Andromeda Strain, Alien, etc.
We are being more careful to avoid corrupting Lake Vostok (google it) than we are planning to be with a far more exotic place. There could be entirely new approaches to DNA-based and non-DNA-based life on Mars. The last thing we want to do is go charging in there with guns blazing.
If you want to spend some money, build a huge solar array and send a humongous laser beam to an unmanned vehicle to get it going really fast and lets get something in orbit around a nearby star in the next hundred years or so. Make up some really long-baseline interferometry telescopy application for it when it gets there.
Or play around on the moon. slightly less deadly, get to work on solar powered self-replicating robots to build massive underground habitats for us where we'll be a little safer from impacts and radiation. Start growing a stockpile of food. And then send people up there if you really have to.
DO NOT POOP ON MARS.

"Proofs and Confirmations" by Bressoud doesn't seem to have gotten on the list yet, nor has "A=B" by Petkovsek and Zeilberger. These books introduce a student to the growing impact of computers in advancing theoretical mathematics, and don't require much background for most of the subject matter. If the school has a Maple or other math package, this would allow experimentation.

Assume the shuttle is inspected and after reentry has just started, a tile breaks off. Is there any way of altering the trajectory so that the shuttle bounces back up to a higher altitude, cools off, and then falls back again, repeat as necessary, until the reentry temperatures remain nonlethal to the shuttle airframe? The idea is to limit the worst-case outcome to be a splashdown in an ocean or a crash landing, by actively controlling the trajectory before the temperatures cause the airframe to break up. There's also the possibility of using plasma fields surrounding the vehicle rather than ceramic tiles, to thermally protect future vehicles.

Just call me old fashioned. I don't care who owns the other end of my lifeline, I'd like to be untethered. If I lived on the moon I wouldn't want to be dependent on Earth for my daily needs. Wars and other stuff happen on earth. I'd want to have the capability of feeding myself, generating oxygen, and generating power without technology that I couldn't maintain for myself. Building a solar collector from lunar materials isn't easy but it should be the highest priority. I don't see the need for a nuke on the moon, and I don't think NASA would own my solar panels any more than I think I am a subject of Ferdinand and Isabella just because Columbus 'discovered' America. One key point of going to the moon is to perpetuate the human race if/when a dictator with nukes starts WWIII.