Title pretty much says it all. I have an idea.
Uh, scientific discoveries, sorted by nation, just to be clear.
That would require a very, very large book, about a foot thick, in tiny, tiny print.
Could you narrow down the request a little to something we might manage?
Is this homework or something?
Mine is inventions, by the way.
Candyman: Sure! Major breakthroughs, life-saving discoveries or inventions, things that have greatly improved our collective quality of life, things which a nation can by all accounts be unilaterally proud of.
See, I think it would make a real cool video to collect clips of people from every nation saying their nation’s name, and something cool their scientists have done. Better yet, they could hold up a sign with the data, so that we could have some excellent song playing in the foreground. * (“Luxembourg! Testify! Tell it, Maldives!”)*
hee hee hee! Furthering the notion that science rocks, and scientists are everywhere!
Well, how significant does some finding have to be to count as a “discovery”? Set the standard too low and your list will be unmanageably large. set it to high (assuming you can quantify significance usefully anyway) and lots of countries will not be on your list (even if some others have lots and lots of entries).
Also, do theoretical advances count as discoveries? Often they are important than specific empirical findings.
You might do better to go from the other end. Go country by country and ask what science has been done there. In some cases it might not be anything very impressive.
There’s also a question of which country expats belong to: do Marie Curie’s discoveries count for Poland or for France?
As well as definitions. Who invented the computer? That depends on how you define a “computer”, with Germany, the US and the UK all having valid claims depending on how you cut it.
Yeah, if you go country-by-country and find, say, the top 5 discoveries ever made in Luxembourg, those discoveries will probably be on a par with, say, the thousandth most significant discovery ever made in someplace like America or China.
Back in more naive days a long time ago on this board, I wanted to ask why the U.S. invented such a disproportionate amount of the significant things in the world (like more than the rest of the world combined). I did some research on my own and found that the U.S. is probably the undisputed leader in new inventions but that most of came after the Civil War and through the 20th century. Like others said, there are a lot of disputed claims to work out as well.
You really have to define this question very well for it to be any way answerable. The most important inventions of all like fire, agriculture, animal domestication, and the wheel were made some place(s) long ago but I doubt you care much about that now for this question.
For something like the computer, do you care most about the earliest incarnations of the logic or something that brought it to the masses like the first PC or the first graphical interfaces navigated by a mouse popularized by Apple but invented by Xerox. The Wright Brothers did invent the first real airplanes despite claims to the contrary but the French were among the first to improve on the technology and put it to real use. Where do you draw the lines?
This isn’t a bad start, if you ignore the Peace/Lit/Econ stuff.
:dubious: Or the fifty-thousandth made in Britain, Germany or France.
Well, maybe not quite in terms of those sorts of numbers. But in terms of real, paradigm changing science, Britain, France and Germany, probably Italy too, leave China and even America way, way behind in the dust.
And Luxembourg is still probably well ahead of the Maldives, or say, the Central African Republic, or Suriname (at random).
Can you support this statement? Certainly in the past century or so at least, America has been doing quite well, scientifically.
Well, the US was nonexistent for the Enlightenment and relatively insignificant for most of the Industrial Revolution. But, yeah, in the last century or so that’s changed dramatically, and the US is absolutely on top since some time around the '60s (plus or minus a decade). Dr. Strangelove even linked to a list of Nobel Laureates, which is as good a proxy for “paradigm-changing research” as any. The US has 333 laureates, vs 119 for the UK, 102 for German, and 60 for France (including peace and literature prizes).
How are you going to treat joint discoveries? Esp. with inventions in the 20th century, a lot of work was not done by one lone scientist in his basement, but by dozen or more scientists working at an university or govt. project/ grant.
So does this count towards the country who did the project - US for Manhattan project - or towards each country the respective scientists came from - since they educated them and they have their brains from there? Is there a cut-off age?
And how do you deal with precursors - the A-bomb built on the discoveries of Hahn and Meitner etc. who shared with the scientific community.
The whole idea of dividing accomplishments into countries is contrary to real scientific thought. I also see little value besides nationalistic chest-thumping, which is in itself a thing of past and before-Enlightment.
If you want to get people interested in science beyond chest-thumping, tell the stories of the discoveries themselves, of people cooperating and building on previous efforts, of how important creativity is, that mistakes and errors can also advance understanding, what unintended applications inventions sometimes take (not with the big stuff, but the daily life discoveries) and so on.
Nowhere near a complete answer to the OP but the link below is the periodic table of elements with the flag of the discovering nation on top of it.
http://wp.patheos.com.s3.amazonaws.com/blogs/friendlyatheist/files/2011/07/DSC01522.jpg
Look where the red white and blue is. Kind of makes you think what drives American science.
Anyone to match (off the top of my head) Newton, Darwin, Rutherford, Dalton, Cavendish, Priestly, Herschel, Lyell, Maxwell, Boyle, Davy, Eddington, Dirac, Kelvin, Faraday? (I could go on.) The only Americans who come close in importance, that I can think of, are Benjamin Franklin, Count Rumford and J.D. Watson, and Rumford got kicked out of America well before he made his discoveries, and Watson had to come to to Britain and get lots of help from a bunch of Brits. (Ben Franklin, though, was much more important to electrical theory than most people realize.) (OK, maybe Willard Gibbs might match a Kelvin or a Dirac, but we’re grasping at straws here. And don’t give me any of your string theory or inflation shit, or I will play my Higgs and Hawking, or even my Hoyle.)
Furthermore, most of the best American scientists of the mid-twentieth century were really Germans.
I know America is churning out a lot of papers these days these days, but you Yanks got into the game much too late to make the real running.
All the real elements were taken. 
Quantum Electrodynamics and Chromodynamics were largely developed by Americans–Feynman, Schwinger, Coleman, Weinburg, Dyson (born in Britain), Bethe (born in Germany), and so on. These aren’t handwavey theories like string theory; they are among (perhaps the) most accurately tested theories in all of science.
I suppose I should also bring up the work of Shockley, Brattain, and Bardeen. On one hand, in terms of the revered history of science, they don’t belong alongside greats like Newton (neither do some of your other examples). But on the other hand, they* invented the device at the foundation of the modern world*.
Continuing the “but you forgot about the important Americans in my field!”, many of the big names of genetics and molecular biology are also American. TH Morgan was largely responsible for the development of early genetics. In the development of molecular biology, the big American names include Beadle, Tatum, Meselsohn, Stahl, Watson… and really most of the names you see in any account of the “history of genetics”. And those are just the pre-1960 names that show up in textbooks.
(Of course, the Brits and a few other Europeans had major contributions – Hardy, Weinberg, Fisher, and Crick are also giants. And of course there’s Mendel way back at the beginning…)