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Get him is a computer and install PARI.

PARI is a command-line calculator for exploring mathematics. It's got *lots* of high-level math functions and commands and uses high precision arithmetic (you can set it to use 5 million digit numbers, for example).

For example: type factor(20345) and it will print out the factors of that number.

PARI will let him explore mathematics concepts, and if he's at all interested in mathematics he'll see the commands, research what they are for and how they are relevant, and perhaps discover interesting corners of mathematics that interest him.

It also allows scripting, so it will introduce him to programming concepts such as flow control and loops, without having to worry a lot about data types and I/O formatting.

Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

You must be new here. (ok, you are not. I am)

Many shlahdotters are actively working on not having kids
in order to reduce the population :)

That reminds me many thoughts I had while reading Asimov's
stories comparing Earth (overcrowded) with space colonies (with
reduced population and very wealthy). I was trying to find
something about that and ...
http://www.emi.u-bordeaux.fr/public/asimov/saveearth.html

"But is anyone listening? Does anyone care?"

GP/PARI and SAGE FTNTW!
(for the number-theoretic win)

6. Most TeX distros [like tetex] are FREE and open source.

And there lot of OSS tools that support TeX. My favorite is using PARI/GP to do some math, and then using the TeX output to copy-and-paste into a document (like a journal submission). I did this for my last paper, and it worked well. The paper had to be submitted in Word format, though, so I made my editor re-enter all of the equations. :)

No-one's mentioned the superb pari-gp yet. It'll draw graphs using gnuplot and unlike much other software of it's type it has excellent documentation.

Lisp is also prominently absent but I agree with what Chaitin says about it being the natural computer language for mathematically minded computer users. Actually I'm surprised it isn't more popular with other software developers - it seems to me to make any kind of programming easier and more pleasurable.

People who've mentioned Maxima also haven't said anything much about graphical (non-plotting) interfaces to it. I like imaxima in emacs and also TeXmacs - which will act as a graphical front end to many other mathematical programs.

Yes it does.

Use Pari/GP. It's even GLP.

It sounds like you want to start with Top-Down Programming or Analysis or Design. The other things you describe are used in a programming language class. A programming class would indeed start with the abstract methods and move to more detailed methods. A programming language might be learned for the examples and homework, but the language is taught as being just one of many tools to implement the design.

>Not to mention the fact that one side of the
>moon faces the sun at all times! Any solar
>collectors on Earth are subject to day/night
>cycles. The moon would rarely be impacted, when
>the lunar eclipses happen.

Doh! One side of the moon always faces the EARTH! (synchronous rotation). We had never seen the far side of the moon until we sent something "back there" to take pictures.

So: that being the case, is it really possible that one side of the moon is always bathed in the light of the sun? If so, then how did we ever get visible pictures of the OTHER SIDE of the moon? Did we use a gigantic flashbulb, or something? ;)

Map of the entire surface including the far side

The Far Side of the Moon Consider how this picture would look if it had been taken during a "full moon:" since during a full moon the entire side of the moon that is facing the Earth is lit up, only the portion of the moon in this photograph that is said to be visible from Earth (see the pic's caption) would have any sunlight on it.

Far Side of the Moon, with animation showing the same side of the moon always toward the Earth. This doesn't show where the sun is in relation to the animation; but figure that the sun is way off the screen from the animation...the darkened part of the moon in the animation is representing the side of the moon we never see from Earth, NOT how the light hits the moon (the Earth does not illuminate the moon, although it does sometimes reflect a little of the sun's light onto the dark portion of the quarter moon...)

So, taking this into account, will it be useful to build these lasers on the moon, especially the power plant?

Apollo 11 Laser Ranging Retroreflector Experiment. "Laser beams are used because they remain tightly focused for large distances. Nevertheless, there is enough dispersion of the beam that it is about 7 kilometers in diameter when it reaches the Moon and 20 kilometers in diameter when it returns to Earth. Because of this very weak signal, observations are made for several hours at a time. By averaging the signal for this period, the distance to the Moon can be measured to an accuracy of about 3 centimeters (the average distance from the Earth to the Moon is about 385,000 kilometers)."

Add to this, the fact that the moon wobbles...

Ah yes, here's a thought... ;)

these look promising.

This program was initially mostly made for number theorists, and I haven't really extensively used it myself, but many people told me good things about it. I'm pretty sure it's free, but it might not be OSS. You can check it out.

Future versions hope to employ new techniques to improve the resolution and base from 8-bit to 16-bit. This may come through using 3d-graphics cards, faster
computers or different modelling techniques. Ideally the engine would be able to run at a number of different processing levels. So even pre-PPC and low-end PC
users could use the engine whilst high end users would experience substantial resolution advantages.