A Quote by David Mumford
I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.
Related Quotes
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.
We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
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.
...One of the most important lessons, perhaps, is the fact that SOFTWARE IS HARD. From now on I shall have significantly greater respect for every successful software tool that I encounter. During the past decade I was surprised to learn that the writing of programs for TeX and Metafont proved to be much more difficult than all the other things I had done (like proving theorems or writing books). The creation of good software demand a significiantly higher standard of accuracy than those other things do, and it requires a longer attention span than other intellectual tasks.
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.
Without computers we will be stuck only proving theorems that have short proofs.
Theorems are not to mathematics what successful courses are to a meal.
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.
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.
So when I can, I try my best to meditate a little bit every day, and that helps a lot. I think that just taking a minute, or however long you can, and really acknowledging everything that you have. Acknowledging what you have, and at the same time, acknowledging what other folks don't have. And you know, you don't have to feel guilty about it, but definitely to feel grateful is the first step in giving it back.
You have to look for a unique quality in that person and it's not just always physical. I don't think models are great models because of their face or their body. Obviously, I think their physical characteristics are important, but I think it's very much about your personality and inner beauty and really understanding how to be a great model instinctively. And that's where it all comes from.
I did gymnastics, I wanted to be like Dominique Dawes. But the good think about role models is that you don't just have them when you are kid. My role models from WWE came when I was older. When I was 27, my role models from WWE became Jacqueline and Beth Phoenix.
Math does come easily to me, but I was always much more interested in what theorems imply about the world than in proving them.
I tell you that studying humanities in high school is more important than mathematics - mathematics is too sharp an instrument, no good for kids.
Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.
Let's face it: Most of us don't realize it, but we are failing our kids as reading role models. The best role models are in the home: brothers, fathers, grandfathers; mothers, sisters, grandmothers. Moms and dads, it's important that your kids see you reading. Not just books - reading the newspaper is good, too.
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