Vincenzo Bonifaci

Everything that can be invented has been invented—Charles Duell, Commissioner, U.S. Office of Patents, 1899

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George Cantor has been featured here and here and here before on GLL. Of course, he invented modern set theory and changed math forever. His birthday is soon, so we thought we would talk about him now—he was born on March 3rd in 1845.

Today we thought it might be fun to have a quiz on math quotes.

Wait. Cantor did not invent quotation marks, nor is he known for many quotes. He does of course have many famous results, and they will live forever. But his results were subject to immediate horrible criticism and therefore memorable quotes.

Leopold Kronecker was a particular source of barbs. For example: “What good is your beautiful proof on the transcendence of ? Why investigate such problems, given that irrational numbers do not even exist?”

As a complexity theorist I must say that Kronecker has a point when he also said:

“Definitions must contain the means of reaching a decision in a finite number of steps, and existence proofs must be conducted so that the quantity in question can be calculated with any degree of accuracy.”

David Hilbert defended Cantor and said: “No one shall expel us from the paradise that Cantor has created.”

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Quotes Quiz

On to the quiz. Each quote is followed by two possible authors in alphabetical order. You should pick the one you think is correct. The players are:

1. Douglas Adams 2. Bernard Baruch 3. Eric Temple Bell 4. Raoul Bott
5. Paul Erdős 6. Richard Hamming 7. Godfrey Hardy 8. David Hilbert
9. Admiral Grace Hooper 10. Alan Kay 11. Donald Knuth 12. John von Neumann
13. Alan Perlis 14. Henri Poincaré 15. Srinivasa Ramanujan 16. Marcus du Sautoy
17. Raymond Smullyan 18. Alan Turing 19. Moshe Vardi 20. Andrew Wiles

1. Those who can imagine anything, can create the impossible.
   —Kay Turing

2. I really didn’t foresee the Internet. But then, neither did the computer industry. Not that that tells us very much of course–the computer industry didn’t even foresee that the century was going to end.
   — Adams Knuth

3. One man’s constant is another man’s variable.
   —Perlis du Sautoy

4. The most damaging phrase in the language is: “It’s always been done that way.”
   —-Hopper Perlis

5. The best way to predict the future is to invent it.
   —Kay Turing

6. The purpose of computing is insight, not numbers.
   Adams Hamming

7. Beware of bugs in the above code; I have only proved it correct, not tried it.
   —Knuth Vardi

8. No, it is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways.
   —Bell Ramanujan

9. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
   —Erdős Hardy

10. Mathematics is the art of giving the same name to different things.
    —Hooper Poincaré

11. There’s no sense in being precise when you don’t even know what you’re talking about.
    —Bott von Neumann

12. I hope we’ll be able to solve these problems before we leave.
    —Erdős Perlis

13. Some people are always critical of vague statements. I tend rather to be critical of precise statements; they are the only ones which can correctly be labeled ‘wrong’.
    —Knuth Smullyan

14. Everything that humans can do a machine can do.
    —Perlis Vardi

15. “Obvious” is the most dangerous word in mathematics.
    — Bell Hooper

16. Just because we can’t find a solution, it doesn’t mean there isn’t one.
    — Adams Wiles

17. Mathematics is a place where you can do things which you can’t do in the real world.
    — du Sautoy Turing

18. Millions saw the apple fall, but Newton asked why.
    — Baruch Hopper

19. The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
    — Hilbert Wiles

20. There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else – but persistent.
    — Bott Knuth

Open Problems

“I always have a quotation for everything—it saves original thinking.”
—Dorothy Sayers

Here are the answers:

Mathematical ideas and tools are often used to describe aspects of large macroscopic systems. Examples abound in areas as varied as finance to psychology. In a paper published last month in the SIAM Journal on Applied Mathematics, author Fabio Bagarello proposes mathematical models to analyze political decision-making. Using a dynamical approach which accounts for interactions between political parties and their constituents, the model tries to deduce whether parties should form coalitions under various circumstances.