The Indians are credited with inventing the number zero. Therefore i assume that all other numbers from 1-9 existed before 0 was invented.
Are there any other numbers that could be invented.
Indians invented the notation for 0 (maybe), not the number, All numbers have existed forever. New numerals and notations could be invented.
Yeah, I just discovered a new number. Here it is:
35717167867687134117687845479624434235624374628456569833
I guarantee you that no one has ever seen this number before.
–Mark
This is a matter of some dispute in the mathematical community, linked to the question of whether mathematics is discovered or invented. Consequently, I don’t think that such a categorical response is appropriate for GQ.
You’re right, I just googled it - no hits!
Not for long, though.
So, what’s the smallest integer with no Google hits?
Ok, consider my response outside of the mathematical community. Even if he was the first no one would consider Columbus to have invented America.
ETA: I have been posting hastily today though. I’ll reel myself in.
Before that, everybody always had at least one of everything. 
The OP’s is an ill-defined question, and there are a number (heh) of ways of thinking about it.
There are “special numbers,” like pi and e and phi, that were at some point “discovered” in the sense that someone was the first to realize that there was something special about them—that they had some remarkable property. There are presumably other such numbers that have yet to be “discovered” in this way.
There are unresolved questions in mathematics and science whose answer would be a number. In some cases it might even be a number that has never been “used” or referred to before by human beings.
There are number systems (e.g. Cantor’s (transfinite) cardinal numbers, quaternions, surreal numbers) that have been invented or discovered (depending on your point of view), and there’s no reason to think that others might be invented/discovered in the future.
Hand engraved, one tenth of a millimeter.
I’m sure he would be willing to do numbers.
Would that be the smallest uninteresting number?
In the base 10 system, there are ten digits. All ten are there.
In the base 1000000 system there are 1000000 digits. Do all of them exist? Yes. There may not be an agreed way to express them, but they certainly exist because their equivalents can be expressed in base 10 or base 2 or any other system.
There are no new numbers waiting for us in the sense of digits or whole numbers.
I think in the sense of the history of mathematics it is fair to say that a number is discovered when at least some of its significant properties are discovered, like the irrational √2 or the ratio ∏ – numbers that had existed forever but were only identified as mathematics developed.
In a similar vein φ (the Golden Ratio) and e were discovered some time later. Later still came the Feigenbaum constants from chaos theory.
I suppose this evolution will carry on endlessly.
I’m pretty sure I saw that once in the decimal expansion of ∏.
It depends on how you define “number.” John H. Conway invented the surreal numbers 40+ years ago … and used them to outplay professional Go players in endgames!
Hugh Woodin investigated Woodin cardinal numbers and used them to posit a system in which both the Axiom of Choice and the Axiom of Determinacy are true! … I hope one of the Board’s mathematicians can explain this is small words.
You probably saw 35717167867687134117687845479624434235624374628456569834. People get those confused a lot.
–Mark
I think BIGFOOT was the last one. They’re all discovered, named and catalogued now.
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Do you have a cite for that? I know surreal numbers are related to game theory, but my understanding is that no software player played even at strong amateur level until AlphaGo was introduced less than a year ago. By “used them to outplay…” I assume you mean he picked his moves algorithmically.
BTW, Conway’s book Surreal Numbers was perhaps the first and only time a significant mathematical development was first published in the form of a novel.
–Mark
I know what it is, but if I tell you, I won’t know it anymore.
Basically this. There are theorems that demonstrate that you can’t invent something like “really complex, complex numbers”, but the example of Conway’s surreal numbers is clearly a case of a rich system of numbers being invented by someone who’s still alive. Again, there are the theorems that there are no “really surreal, surreal numbers”, but one hesitates to assume that there are no similar innovations possible.
Actually written by Knuth. Though I’d hope that nobody’s ever tried reading it as, well, literature.
Douglas Adams ‘discovered’ that the Answer to the Ultimate Question of Life, The Universe, and Everything is 42. This is also the only known value that is the number of sets of four distinct positive integers a, b, c, d, each less than the value itself, such that ab − cd, ac − bd, and ad − bc are each multiples of the value, among other things.