Please list up to 3 inventions of particular interest or importance to you that :-
- were invented before you were born,
- were invented during your lifetime, and
- will hopefully still be invented during your lifetime.
Rigil
Mine:
-
Lenses (Italy, c.1280), Wood fired oven (Mediterranean, Roman era), Archery (Several locations, ancient … reportedly invented by the satyr Crotus, altough our own Bushmen might disagree)
-
Citalopram (1989), liquid-crystal display (Furgason, 1971), DVD (1995)
I was surprised to learn that the magnetron (the active ingredient in microwave ovens) hails
from the 1940’s!) -
An anti gravity suit (mostly for trimming the dead leaves off my palm trees),
A pill that makes sleep unnecessary
Efficient steam engines for private vehicles
Rigil
Fire, writing, gunpowder, antibiotics.
2. were invented during your lifetime, and
The interwebs. Hubble Space Telescope. LEDs (I think).
3. will hopefully still be invented during your lifetime.
A cure for the #@%$$@#$ common cold.
- Vaccines, Transistor
- Smart phones, HD tv, internet, Photonic-crystal fiber.
- Teleportation, hyperdrive, immortality.
- The wheel, the printing press, calculus, complex numbers, the scientific method, NMRI, digital computing, ice cream, and rule-breaking. (I know that’s more than three, but they’re all equally important
). - RSA cryptography, quantum computing, and word processors.
- Controlled nuclear fusion, instant & error-free knowledge transfer, and workable moneyless societies.
'Luthon64
Three big guns for sure! Although, with all the time we’ll have at our disposal should immortality be realised first, it could be argued that the other two will become a bit unnecessary… 
It will also wipe out the need for my anti-sleeping pill!
By the way, I’ve noticed that some texts refer to novel mathematics as “discoveries” while others call it “inventions”. Maybe it depends on one’s view on whether mathematical truths exist independently of their contemplation. Or perhaps there is no real difference between discovery and invention at all!
Rigil
Calculus is a mathematical method (or a collection of them), not an object. It was put together from pre-existent mathematics, and has enormous beauty and power. As such, it’s very much an invention. Admittedly, the situation with complex numbers is not so clear. Initially, they were “invented” purely for the purpose of solving certain types of polynomials but their use exploded fruitfully into many other domains with astonishing pervasiveness.
'Luthon64
That would make sense, yes. So when the Arabs discovered “zero”, they actually invented nothing. 
Rigil
Damn. Hyperdrive’s out of order again. You’ll have to beam us all the way there, Scotty. Lucky thing we’re immortal, or it would have been dangerous…
I would think that once you have basic concepts like numbers and shapes, they have certain allowable logical consequences, and in a sense those are discovered rather than invented? But perhaps the boundary between discovery and invention is a bit fuzzy anyway. 
It’s true that the properties of numbers and other mathematical objects in conjunction with the rules and procedures by which they can be validly manipulated form the (idealised) mathematical universe of allowable possibilities. To be sure, it’s a vast one, perhaps even an inexhaustible one. But by the same token, matter, energy, space and time together with the laws of nature form the real universe. Note that the nature of those real entities and those laws also exhausts the allowable possibilities of arranging real things, again in a vast array of possibilities. Yet, we would not hesitate to call a novel and useful arrangement of those things an “invention.” Why should the mere abstractness of mathematics set it apart in this peculiar and ultimately forced way?
(This reminds me of the story told about the sculptor who maintains that he “discovers” the statue in the block of marble he’s working on.)
'Luthon64
I would like to see an automatic junk/spam remover. It must know it as junk without me telling it and remove it unseen by me and then spam the sender. A domestic worker robot would also be nice. Just done a load of dishes…
An invention is the discovery of a way to do or make something.
As I said, the two terms probably overlap. I just rather like this notion of mathematical space existing “out there” somewhere, where it can be endlessly explored. It’s like having a tourist attraction in your head, always available.
Not that I often visit it - I suck at navigating my way through it and get lost in it all the time…
Tell me about it. Apparently there is a non-Euclidean branch of mathematics called taxicab geometry. I’m hoping that it offers an alternative to navigating by oneself!
Rigil
And then there is my own personal favourite, bistromathics:
http://en.wikipedia.org/wiki/Bistromathic_Drive#Bistromathic_drive
Which is identically true in the realm of mathematics, the only differences being the latter’s formal rigour and that its subject matter exists as pure idealisations. As said, all possible unrealised inventions in the real world already exist “out there” in a sense as potentialities, albeit that endless variations on a given theme are conceivable (e.g. there are many different toaster designs all having much the same purpose), whereas mathematical constructs typically don’t leave much, if any, of the same kind of wriggle room. We discover mathematical objects and the rules for manipulating them, just as we discover the constituents of our universe and the natural laws that determine their nature and behaviour. In both worlds, we discover truths; however, when we rearrange things in the former into something new and useful, we call it “invention” while in the case of the latter we still want to call it “discovery” even though the novelty in both cases only existed before as unrealised potentials. On that basis, the only vaguely valid reason I can think of for objecting to the use of the term “inventing” in mathematics is a semantic one: “Inventing” may carry with it a negative subtext of “artificiality” or “fabrication.” To underscore the point, there are mathematical methods that have been patented. Can you patent a discovery?
'Luthon64