A Quote by Simon Singh
Most of all, a good maths education encourages students to embrace difficult problems, not shy away from them. In my opinion, the problem is that most UK secondary schools don't stretch good mathematicians and therefore fail to turn them into excellent mathematicians.
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As for mathematicians themselves: don't expect too much help. Most of them are too far removed in their ivory towers to take up such challenges. And anyway, they are not competent. After all, they are just mathematicians-what we need is paramathematicians, like you... It is you who can be the welding force, between mathematicians and stories, in order to achieve the synthesis.
Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.
The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken, they have not as yet succeeded. I therefore dare hope that the mathematicians will receive this memoir with good will, for its purpose is to fill this gap in the theory of algebraic equations.
Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.
Students shy away from Maths, but in reality Maths is the best friend of man.
Relations between pure and applied mathematicians are based on trust and understanding.
Namely, pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians.
I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.
I think expectations are a good thing. As a player, you should embrace them and not shy away from them.
Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.
For the most part, people use "empathy" to mean everything good. For instance, many medical schools have courses in empathy. But if you look at what they mean, they just want medical students to be nicer to their patients, to listen to them, to respect them, to understand them. What's not to like? If they were really teaching empathy, then I'd say there is a world of problems there.
Most students who take math classes aren't going to be mathematicians. They're going to be engineers, statisticians - in many ways, that's the more important mission of math education.
I see the root of the education crisis in the primary and secondary schools. Academia is doing a fairly good job. The root of the problem is the teachers. Some are great. But too many of them are not capable of being good role models. They can't control the classes. They lose too much time trying to create a learning environment.
The only time we can fail is if we quit. Most perceived failures are only stepping stones being small problems encountered along the path to a goal. Obstacles are opportunities for growth, therefore, encourage and embrace them.
Outside observers often assume that the more complicted a piece of mathematics is, the more mathematicians admire it. Nothing could be further from the truth. Mathematicians admire elegance and simplicity above all else, and the ultimate goal in solving a problem is to find the method that does the job in the most efficient manner. Though the major accolades are given to the individual who solves a particular problem first, credit (and gratitude) always goes to those who subsequently find a simpler solution.
Sure, some [teachers] could give the standard limit definitions, but they [the students] clearly did not understand the definitions - and it would be a remarkable student who did, since it took mathematicians a couple of thousand years to sort out the notion of a limit, and I think most of us who call ourselves professional mathematicians really only understand it when we start to teach the stuff, either in graduate school or beyond.
When I was in Wuhan, I went to the art school, which was one of the most important art schools in China, an enormous art school. One of the things that I saw is that the schools are very big and there are so many students. It is very difficult to me to teach creative activity to great numbers of people, because I think you need personal contact with students, you need to speak individually, you need individual contact between teachers and students, you need continuity. To me this is a problem in mass education in every society now.
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