A Quote by Andrew Wiles
We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention.
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Were it possible for us to see further than our knowledge reaches, and yet a little way beyond the outworks of our divinings, perhaps we would endure our sadnesses with greater confidence than our joys. For they are the moments when something new has entered into us, something unknown; our feelings grow mute in shy perplexity, everything in us withdraws, a stillness comes, and the new, which no one knows, stands in the midst of it and is silent.
Valuations are always much-debated. I try to center on what is the value to us. Is it solving a problems for us? If it is, we find a way to proceed. If the valuation has been overhyped on something and it doesn't make sense, we won't. It's very simple for me. I tend not to worry too much about the valuation. It's really what the value is to us.
Give us something else; give us something new; for Heaven's sake give us something bad, so long as we feel we are alive and active and not just passive admirers of tradition!
If each one of us can give full attention to what is actually ‘blocking’ communication while he is also attending properly to the content of what is communicated, then we may be able to create something new between us, something of very great significance for bringing to an end the at present insoluble problems of the individual and of society.
On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.
Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.
Perhaps all the dragons in our lives are princesses who are only waiting to see us act, just once, with beauty and courage. Perhaps everything that frightens us is, in its deepest essence, something helpless that wants our love.
Cameras are simple tools designed to capture images. Images that tell us more about ourselves than we realize. They remind us of the long journey we’ve taken. The loved ones who traveled alongside of us. Those we lost along the way. And those waiting for us on the road ahead.
I have also long held the belief that one's tears are a guide, that when something makes you cry, it means something. If we pay attention to our tears, they'll show us something about ourselves
Arizonans want us to come together, put aside politics, and solve problems. You want us to do our jobs in way that reflects the best of our state. You want us to stop and listen - something that doesn't always come naturally to people in politics.
I once heard somebody say that God had closed a door on an opportunity they had hoped for. But I've always wondered if when we want to do something that we know is right and good, God places that desire deep in our hearts because He wants it for us and it honors Him. Maybe there are times when we think a door has been closed and, instead of misinterpreting the circumstances, God wants us to kick it down. Or perhaps just sit outside of it long enough until somebody tells us we can come in.
I got like a list of things at the beginning. There were ten things that Bryan made for each one of us, and he drew us our own personal picture of our character that was in color. And uh, I just have a copy of it, I think that they're going to do something special with the originals at the end, like presenting them to us.
Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us.
There are few times when we know with absolute certainty we are going to do something for the last time. Life has a way of moving in circles, bringing us back to places we didn’t expect and taking us away from those we do. There are too many times we don’t pay close enough attention, and moments are lost in our assumption we’ll have another chance.
We have no reason to mistrust our world, for it is not against us. Has it terrors, they are our terrors; has it abysses, those abysses belong to us; are dangers at hand, we must try to love them.... Perhaps all the dragons of our lives are princesses who are only waiting to see us once beautiful and brave. Perhaps everything terrible is in its deepest being something helpless that wants help from us.
Perhaps . . . our lot on the earth is to seek and to search. Now and again we find just enough to enable us to carry on. I now doubt that any of us will completely find and be found in this life.
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