Comments on Skeptic's Play: An intuitive thinker

I've found that what mathematicians find intuitive...

2008-08-26T10:38:00.000-07:00

I've found that what mathematicians find intuitively obvious and what their students do, are not one and the same. It leads me to think that intuition is learned - or rather you learn a pattern of thinking that supports intuitive understanding of subject

During my all-too-brief stint in college, I overhe...

2008-08-25T19:01:00.000-07:00

During my all-too-brief stint in college, I overheard one professor remarking to the other that he simply could not relate to a student who didn't find it intuitively obvious that the square numbers were the the sum of consecutive odd numbers starting from 1.

Since I found the statement profoundly counter-intuitive and the proof refractory, I was dissuaded from a career in mathematics.

Of course, once I saw the geometric proof, the whole thing gelled in a heartbeat.

OK. I haven't done math for a very long time, but ...

2008-08-25T18:50:00.001-07:00

OK. I haven't done math for a very long time, but the truth of the statement seems intuitive, and the proof seems obvious.

That's a relief. I was secretly wondering if some...

2008-08-25T10:18:00.000-07:00

That's a relief. I was secretly wondering if something was wrong with my intuition. ;)

Oh, my mistake! I switched from x and y to a and ...

2008-08-25T10:16:00.000-07:00

Oh, my mistake! I switched from x and y to a and b midsentence. It's fixed now.

Prove that any common divisor of x and y is a divi...

2008-08-25T10:11:00.000-07:00

Prove that any common divisor of x and y is a divisor of the greatest common divisor of a and b.

Am I missing some jargon? What relationship do x and y have to a and b?

Hear hear! I consider intuition to be something w...

2008-08-25T09:48:00.000-07:00

Hear hear! I consider intuition to be something we get out of the internal programming of our brains (being programmed either innately or by repetition), so it's a great shortcut, but I often want to augment it by rigorous justifications so I can consciously see why the result is justified (not to mention intuition being wrong all too often).