Math problems too big for our brains

Ottawa Citizen via The Windsor Star ^ | November 8 2005

[jwalsh07]

If a computer can "prove" that only four colors are needed, then the computer is clearly in error.

Computer is OK as long as all countires are contiguous. Since they aren't you are right, the computer is in error when talking about maps of the world.

[CardCarryingMember.VastRightWC]

Here's a slightly less complex version of it:

Given a=b, prove that 1=2.

PROOF:

      a   =   b          Given
    a*b   =   b^2        Multiply both sides by b
a*b - a^2 = b^2 - a^2    Subtract a^2 from both sides
   a(b-a) = (b+a)(b-a)   Factor
      a   =   b+a        Divide both sides by (b-a)
      a   =   2*a        Since a=b as originally given
      1   =   2          Divide both sides by a

[boojumsnark]

I believe Whitehead and Russell already addressed that question. I only got thru the first half of Volume 2, so I don't know how it turned out.

My favorite, though, is to define "regular" to mean words that describe themselves, "irregular" to mean words that do not describe themselves.

BTW, the barber was a Cretin.

[phantomworker]

Of course you know your assumption is faulty. a cannot equal b in an ordered set of numbers.

[phantomworker]

Hey, what are you doing on this mathematician thread?

It must be Dark's fault!

[phantomworker]

That's a good one. LOL

[phantomworker]

Isn't '42' the answer to the Ultimate Question of Life, the Universe, and Everything?

[MarkL]

Isn't '42' the answer to the Ultimate Question of Life, the Universe, and Everything?

Yup, but the problem is that nobody can remember exactly what the question was...

Mark

[Flightdeck]

I can trisect an angle with nothing but a compass and a straight-edge, but apparently it is impossible.

[bobdsmith]

When someone says prove "2 + 2 = 4", unless explicitly stated otherwise they mean base 10.

[JCEccles]

Godel proved this over 70 years ago. In the pages of one slim paper he destroyed the arrogant contentions and made a mockery of the conceit of one of the most celebrated atheists of the age, Bertrand Russell, who, with Alfred North Whitehead, had set out to establish the secure and exact foundations of mathematics.

Incidently, Godel believed in the existence of God.

[kevkrom]

Several people have pointed out why four is sufficient for Russia. My only comment on the "four colors" solution is that is limited to the practical example of existing maps. If by being "adjacent" requires only a single point of intersection on the border, than I can create abstract examples of any size N to show that N colors are insufficient:

Starting with N = 4... Picture a "four corners" scenario like the states in the US Southwest. No problem... even though they all intersect at a single point, you have four colors. However, if you add one region/state/whatever that surrounds all four (or also intersects at the same point), the you would need a fifth color. Repeat as necessary for every N + 1.

The problem is only solvable for N = 4 if "adjacent" requires more than one point of border intersection.

[Bear_Slayer]

Nope. Base 2. Answer = 3

[Cronos]

Greeks, Mayans and Aztecs

err... Aztecs??? I don't think they were so hot on maths, were they? (I may be wrong)

[Cronos]

Your point

(a+b)=(a-b)/(a-b)=1

Then means (by resubstituting a=b=1)

1+1=(1-1)/(1-1)=1
2 = 0/0 = 1

You can't divide by 0.

[Mr. K]

yes- a map of one state needs only one color, two if you include bordering states (that do not also touch each other)