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I'll start this off by saying that I am no computer programmer and only a junior undergrad studying math.

But,I have an idea for a math-based gamethat I think would be really awesometo train students in the art of proving/problem solving. It is the following:

The goal of each game is to prove a given theorem. You are given the results and the implications in two inventory boxes which you can drag into the main workflow to connect statements together.For example, say that you were proving that √2 is irrational.

In the implications box (made up of previously proved theorems,definitions, and axioms) you might have the following [in a random order]:

* For any rational number q, q = a/b where a and b are both integers

* When both sides of an equation are multiplied by the same quantity, the resulting equation is true

* When both sides of an equation are squared, the resulting equation is true

* We may reduce any rational number so that its numerator and denominator share no common factors.

* n is even if and only if n = 2k for some integer k.

* When a quantity equal to a given quantity is substituted into the equation, the resulting equation is true

* Cancellation law for the rational numbers

* If an assumption is made and the negation of that assumption is shown to be true, the assumption was false.

Then in the results box, you would have [again, in a random order]:

* √2 is rational

* √2 = a/b for a, b integers

* √2 = p/q for p, q integers with no common factors

* q√2 = p

* 2q^2 = p^2

* p^2 is even

* p is even

* p = 2k for some integer k

* 2q^2 = 4k^2

* q^2 = 2k^2

* q^2 is even

* q is even

* p and q share a common factor

* √2 is irrational

Whenever you correctly connect two results with an implication, it would light up and you would get points.Also, if someone came up with better names than 'results' and 'implication', that would be cool too.

An easier version would be to put the results in the correct order and ask the player to simply connect them with the appropriate logical steps.

I think this game would be great for teaching college students, and even younger kids, about the principles of logic and proof techniques.I simply don't have the computer know-how to make anything like this happen.

Furthermore, one could hope in the future to combine all the results and implications in the game into a conjecture-proving crowd-sourced version, which would let people try and make the connections from one known statement to the proof of a conjecture. Obviously, each step in the proof to the conjecture would have to be in the game, but it doesn't seem so far-fetched to me that there could be some genuine progress from this game. Much like that game that allows people to manipulate proteins to solve chemical problems.

Anyone want to make this happen? I'm thinking you could call it "Prove It", if that's not already copyrighted.

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# An Idea for an Online Proof Game

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