As was written in The New York Times when his biography, The Man Who Loved Only Numbers, was reviewed (1998), Paul “Erdős (pronounced “air-dish”) structured his life to maximize the amount of time he had for mathematics. He had no wife or children, no job, no hobbies, not even a home, to tie him down.”
This was during most of the Cold War between, at the forefront of each side, swaggering mightily like something straight out of a comic book, the USA and the USSR. Except … this wasn’t a comic book. You really could die. Younger people don’t really know what this is like, for the simple reason that the threat of imminent. sudden extinction hasn’t been present since the Cold War ended. The world faces disasters, of course, but a sudden one, greater than the large-city scale, is unlikely in the extreme — now.
Erdős had little regard for Uncle Sam (that’s the United States), nor Uncle Joe (the Soviet Union, with “Joe” being a caricature of Josef Stalin), but he did enjoy clever ridicule, so he heaped contempt, publicly, on both sides, during the Cold War. He wasn’t a big fan of the S.F., either (that’s Supreme Fascist — of the Universe. Guess who. Yep. That’s the guy. Why is God always a guy?)
Erdős just wanted to do math, and this native of Hungary simply dismissed all else. Mathematicians need other mathematicians to talk to, for they are already crazy, in very specific and sometimes unintentionally useful ways, and need other people also so afflicted to talk to, lest they torment the uninterested with mathbabble. That is only one way of looking at it, of course, as people have explained to me about my own mathbabble, which is insufficiently advanced to allow me to comprehend that of Erdős himself.
Life was viewed differently by Erdős, and I do not mean in any way that would seem “normal” to any mathematics professor you might have met (feel free to ask them). If you worked on proving theorems, solving problems, proving certain problems can’t be done — all of which are varied ways of describing the same activity — then you were, to Erdős, “alive.” If you stopped doing mathematics, you “died.” I don’t know what he thought of those who never did mathematics, because he avoided interacting with them. With no home, he could simply get on a plane when all the local mathematicians were exhausted, their brains tired, and he would then go to another continent — there were several available, and he did this for decades — and the local mathematicians would welcome him with open arms, for it was an honor to have Erdős as a guest in one’s home.
Sources, and further reading:
The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth, biography by Paul Hoffman, 1998.
More Erdős vocabulary:
“Women” were “bosses,” with “men” translating as “slaves,” in Erdős’s unique language of his own invention. Children were “epsilons,” and if you laughed at that, I do hope you are happy with the fact that you, too, are a math nerd. (For the benefit of those who aren’t, “epsilon” is a symbol often used, in mathematics, for variables with very small values.) There’s a lot more — and links to use to help you find it, right up there.
Calculators are important tools.
Well, so are guns.
Everyone acknowledges that, if guns are going to be used at all, certain safety precautions are essential. While it generally is not a matter of life and death, the same thing is true of calculators.
I have seen — multiple times — students multiply or divide some number by one, using a calculator, and then be genuinely surprised when they got the same number with which they started. I have also seen a bright student calculate the mass of an atom, and get an answer larger than the mass of the earth. When I informed him of this, his reaction was predictable: “But that’s what the calculator says!”
These are examples of calculator abuse. Aside from avoiding errors, such as the “planetary atom,” it’s also important not to abuse calculators because such an act is insulting to one’s own brain.
Some people treat calculators as if they are omniscient and infallible. They aren’t. They’re small, simple, narrowly-focused computers. The human brain is also a computer, but a far more advanced one. The calculators are our tools, not the other way around.
Here are some tips to prevent calculator abuse:
1. Know how to do arithmetic without a calculator. If you don’t know, learn.
2. Use calculator-free mathematics when appropriate. If you need to know what six times eight is, for example, it insults your own brain to consult a calculator. Don’t do it!
3. Calculator-free mathematics is not to be called “mental math,” for the simple reason that ALL math is mental. Also, if you ever meet anyone claiming to have invented that insipid phrase, kick that person immediately.
4. If you have contact with children, promote the use of calculator-free math to them. This is most important, of course, for parents and teachers. It is no service to a child to raise them to be dependent on a calculator.
5. Finally, when you do use a calculator, don’t be too trusting of the little thing. Check your answers, constantly, by using estimation. Say, for example, you’re multiplying 109 by 36. That’s “a bit over a hundred” times “a bit under forty.” Since forty hundreds is four thousand, the answer has to be in the ballpark of 4,000 — and if a calculator disagrees, the calculator is wrong, probably because a human pressed at least one incorrect button. You will press incorrect buttons on occasion — we all do — and it’s important to have a method in place to detect such errors. This estimation-method is both simple and effective.
All these principles boil down to this: be smarter than your calculator. They aren’t actually very intelligent, so this is neither difficult, nor unreasonable.