After reading this thread, I’ve seen the light. Our current system of mathematics, though tried and tested over the course of centuries, just isn’t intuitive enough. The whole concept of things precisely equalling other things, no matter what and under any circumstances, is just too rigid. Where’s the heart? What about people that plain don’t like the current system?
So, let’s just make up our own system, right here. We can take votes to see what equals what. If enough of us are of the opinion that 0.999… != 1, then it doesn’t! Is the definition of an integral too complicated? How about “that thingy that undoes derivatives?” We ought to take into consideration the consequences of our system though… I mean, if 2+2=5, then how will that make you feel?
We should immediately get rid of this archaic system of demanding ‘proof’. It is cumbersome and inegalitarian. Instead I propose (which came up in a group of friends years ago): Democratic Acceptance For Theorems.
If and only if enough X % of the world’s mathematicians believe a specific theorem is true, it is mathematically true.
I say let’s set X at 90, but I’m willing to negotiate. To make it even more democratic, we may have a second clause whereby the general population gets a vote as well.
With DAFT we would have proven Fermat’s last theorem years ago, thereby saving the world zillions of research time that could have been spent better.
I say we should stop all examinations in mathematics until the new system is established. I say we should stop them tonight, because some people* have exams in the subject tomorrow.
I agree with Loneraven. Just make that happen before next Friday, and I will be happy. Also, let’s go ahead and stop all math classes, while we’re at it.
Let a = b
a * b = b * b – multiply by b
a * b - a * a = b * b - a * a – subtract a * a
a(b - a) = (b + a)(b - a) – factor
a = b + a – divide by common factor (b - a)
a = a + a – substitution
a = 2a – combine
1 = 2 – divide by common factor a
Based on the linked thread, all we have to do is eliminate the concept of limits. Sure, that will kill calculus and the rest of higher mathematics, but that’s a small price to pay for making people feel good about themselves.
We don’t need to ditch simple things like algebra or non-decimal bases, because those things are easy.
Maybe if we just renamed the difficult-sounding “asymptote.” Let’s update it and make it more kid-friendly and pop-cultured, instead of stuffy and Greek.
It goes without saying that under the NEW regime, there won’t be “proofs.” I hate that word, “proof.” It suggests that we know something for sure, which is how the current system got cocked up in the first place. Direct democracy, that’s the path to a mathematical system that we can all live with. Everyone gets a vote, mathematician or not, since we don’t want anyone to feel left out. “Counting” the votes won’t be necessary, I’m thinking more in terms of just asserting the number of votes, which is more in keeping with the philosophy of our movement anyway.
It also stands to reason that not only will any currently scheduled math exams be cancelled, but future math tests will be an entirely different beast… lots of essay questions like “how would you prefer to solve this differential equation?”
Of course, I’m not too keen on definitions, or theorems, or postulates, or corrolaries… I figure we lump 'em all into “suggestions.”
BUT, first order of business, we need a name. I’m thinking “The People’s Front of Mathematica.”
I am a contrarian. I love Mathematical proof. It is the search for perfection and order in a mixed up universe. It is the only achievable degree of perfection we have.
If everything is equal if it really really wants to be, then it can be less than anything else, or greater than anything else. You could write a check for $100, and the bank could determine that $100 is equal to $1,000,000 and bounce your check. This could have its consequences.
I love Mathematics that raises to the level of absurdity. I enjoy Dr. Matrix’s proof. Imagine everything that we can prove if we slip in a faulty assumption. Dividing by zero does not preserve equality.
And if we didn’t have limits, then we could never understand what happens when we divide by zero.
As far as 90% of mathematicians agreeing something is true, that does happen. Those aren’t theorems, but axioms. Axioms cannot be proved or disproved, and are agreed upon.
I don’t offer any suggestions on making integrals easier. Integration beats segragation though.
