Mathematics and Mathematicians
John Challifour told this story in April 2005 to his complex analysis class: Knowing of his absent-mindedness quite well, Norbert Wiener's wife knew it would be necessary to remind him that they were moving house the morning of the last day in their old place. She told him, "Norbert, remember that when you come home from work today, you must go to the new house, because this house won't be ours anymore." "Yes, dear," Professor Wiener condescended to her, in the way academics often do to their better halves. Nevertheless, just as his wife predicted, at the end of the day Norbert did go back to his old house, and he was confused to see that his supper was not ready, and indeed that there were no recognizable objects in the house. After a glance inside, he looked out again and saw a young girl swinging on the door of the fence that enclosed the house. "Little girl," Professor Wiener asked, "who lives in this house?" The girl responded, "It's OK, Daddy. Mommy told me you'd forget to come to the new house." (Here is the reference.)
There are no limits, apparently, to what a mathematician can forget. Another Wiener anecdote:
A student happened upon Wiener pacing up and down in the post office, apparently deep in thought. Struck with the opportunity of meeting the great mathematician, the student was yet hesitant to approach the man. The student thought that interrupting the man might cause him to lose some great result. But the student finally mustered the courage to go and talk with him. "Good morning, Professor Wiener." He stopped his pacing, struck his forehead and exclaimed, "That's it! Wiener!"
Morris Kline, an eminent mathematician and educator, wrote a book entitled Why the Professor Can't Teach. In that book, he makes the comment that mathematicians are, after all, only human, and as regards ego, a rather disagreeable cross-section of humanity.
And there are, of course, plenty of jokes on mathematicians. Mathematicians are known for coming up with elegant, if useless, solutions to problems. An example: a farmer asked an engineer, a physicist, and a mathematician to fence off a maximum area with a fixed length of fence. The engineer makes the fence into a circle, and claims he has found the maximum area. The physicist puts the fence in a straight line, and then says, "We can assume the fence goes off into infinity. Thus, I have fenced off half the earth." The mathematician just laughes at them. He builds a tiny fence around himself and says, "I declare myself to be on the outside."
Here's a mathematical curiosity. Where does this series of equations fail?
1 = 1 * 1 = sqrt(1) * sqrt(1) = sqrt(1 * 1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = i * i = -1.
The answer is not exactly obvious, I warn you.
Here's another curiosity. Pick out the pattern here. (For those of you to whom I have shown this already, you're not allowed to let the cat out of the bag!)
8, 5, 4, 9, 1, 7, 6, 3, 2, 0.
It's a finite sequence, so your task is simply to explain why the numbers are in this order, and not in some other order. This answer is quite different from the previous mathematical curiosity.
Calculus is responsible for the modern technological age. Here's what historian Arnold Toynbee wrote about it:
... at about the age of sixteen, I was offered a choice which, in retrospect, I can see that I was not mature enough, at the time, to make wisely. This choice was between starting on the calculus and, alternatively, giving up mathematics altogether and spending the time saved from it on reading Latin and Greek literature more widely. I chose to give up mathematics, and I have lived to regret this keenly after it has become too late to repair my mistake. The calculus, even a taste of it, would have given me an important and illuminating additional outlook on the Universe, whereas, by the time at which the choice was presented to me, I had already got far enough in Latin and Greek to have been able to go farther with them unaided. So the choice that I made was the wrong one, yet it was natural that I should choose as I did. I was not good at mathematics; I did not like the stuff; ...
... Looking back, I feel sure that I ought not to have been offered the choice; the rudiments, at least, of the calculus ought to have been compulsory for me. One ought, after all, to be initiated into the life of the world in which one is going to have to live. I was going to have to live in the Western World ...; and the calculus, like the full-rigged sailing ship, is one of the characteristic expressions of the modern Western genius.
I would hasten to add that Latin and Greek are of exceptionally high value. I think Toynbee would not disagree. He's only saying that calculus was of much more value than he originally thought. I agree with these sentiments, to the point of concluding that no one ought to be allowed to hold a bachelor's degree unless he has seen and at least partially understood the Fundamental Theorem of the Calculus in all its glory. This theorem is easily the most important theorem in all of mathematics. Without it, technology as we know it could not possibly exist.
I would make one more very important comment. God gives us mathematics. It is not somehow independent of Him. If Christ is not Lord of all, then 2 + 2 = 5, or whatever you want it to be. There would be complete chaos. God gave us mathematics to help us in the Dominion mandate, which was to multiply (interesting choice of words there!), fill the earth, and subdue it.