A Quote by John B. Conway
To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples.
Related Quotes
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.
I started collecting baseball cards and basketball cards when I was younger. I have a CD collection that turned into a DVD collection, and I have a Jordan shoe collection. And I don't drink, but I have a wine collection. I just started a sweatshirt collection. Every city that I'm in, I buy a sweatshirt. It's just something that I do.
We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
What exactly is mathematics? Many have tried but nobody has
really succeeded in defining mathematics; it is always something
else. Roughly speaking, people know that it deals with numbers,
figures, with relations, operations, and that its formal procedures
involving axioms, proofs, lemmas, theorems have not changed
since the time of Archimedes.
The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.
Everything useful in mathematics has been devised for a purpose. Even if you don't know it, the guy who did it first, he knew what he was doing. Banach didn't just develop Banach spaces for the sake of it. He wanted to put many spaces under one heading. Without knowing the examples, the whole thing is pointless.
Once I found out that I was playing 'Deathlok,' I unearthed my old comic book collection. I was going home for Christmas, and I have a collection of thousands of comics. I was surprised to see that 90% of them were Marvel. So, I wanted to go through my collection and start there.
Mathematics is a collection of cheap tricks and dirty jokes.
Mathematics is as much an aspect of culture as it is a collection of algorithms.
Most of all I like "bad" lines, that is those considered bad, in my opinion unjustly, by theory. The reason for the last quotation marks is that most so-called theory is only a collection of examples from master practice.
Theorems are not to mathematics what successful courses are to a meal.
People copy examples and then they wonder what is the trouble. They look at examples and without theory they learn nothing.
It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
I sampled a bit of stuff from my dad's collection. He has probably a bigger record collection than I do. I try to buy as much as possible, because I've never been able to keep an MP3 collection organized. I like to keep my computers as clean as possible.
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