When I give talks on factoring, I often repeat an incident that happened to me long ago in high school. I was involved in a math contest, and one of the problems was to factor the number 8051. A time limit of five minutes was given. It is not that we were not allowed to use pocket calculators; they did not exist in 1960, around when this event occurred! Well, I was fairly good at arithmetic, and I was sure I could trial divide up to the square root of 8051 (about 90) in the time allowed. But on any test, especially a contest, many students try to get into the mind of the person who made it up. Surely they would not give a problem where the only reasonable approach was to try possible divisors frantically until one was found. There must be a clever alternate route to the answer. So I spent a couple of minutes looking for the clever way, but grew worried that I was wasting too much time. I then belatedly started trial division, but I had wasted too much time, and I missed the problem. …
The trick is to write 8051 as 8100 – 49, which is 902 – 72, so we may use algebra, namely, factoring a difference of squares, to factor 8051. It is 83 × 97.
November 10, 1958
We had your letter this morning. I will answer it from my point of view and of course Elaine will from hers.
First — if you are in love — that’s a good thing — that’s about the best thing that can happen to anyone. Don’t let anyone make it small or light to you.
Second — There are several kinds of love. One is a selfish, mean, grasping, egotistical thing which uses love for self-importance. This is the ugly and crippling kind. The other is an outpouring of everything good in you — of kindness and consideration and respect — not only the social respect of manners but the greater respect which is recognition of another person as unique and valuable. The first kind can make you sick and small and weak but the second can release in you strength, and courage and goodness and even wisdom you didn’t know you had.
You say this is not puppy love. If you feel so deeply — of course it isn’t puppy love.
But I don’t think you were asking me what you feel. You know better than anyone. What you wanted me to help you with is what to do about it — and that I can tell you.
Glory in it for one thing and be very glad and grateful for it.
The object of love is the best and most beautiful. Try to live up to it.
If you love someone — there is no possible harm in saying so — only you must remember that some people are very shy and sometimes the saying must take that shyness into consideration.
Girls have a way of knowing or feeling what you feel, but they usually like to hear it also.
It sometimes happens that what you feel is not returned for one reason or another — but that does not make your feeling less valuable and good.
Lastly, I know your feeling because I have it and I’m glad you have it.
We will be glad to meet Susan. She will be very welcome. But Elaine will make all such arrangements because that is her province and she will be very glad to. She knows about love too and maybe she can give you more help than I can.
And don’t worry about losing. If it is right, it happens — The main thing is not to hurry. Nothing good gets away.