A Quote by Leon Henkin
One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.
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One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed.
I wanted to answer big questions about humanity, about how it is that we understand about the world, how we can know as much as we do, why human nature is the way that it is. And it always seemed to me that you find answers to those questions by looking at children.
You see, the problem in life isn't in receiving answers. The problem is in identifying your current questions. Once you get the questions right, the answers always come.
We have this yearning to know the answers to the big questions about space and why we're here; we can't evolve fast enough to figure these answers out on our own, but we can do it through artificial intelligence. But there's also some very scary downsides that could come if we don't put the right safety precautions in there.
The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.
You don't actually need to know anything, you can find out at the point when you need to know it. It's the teachers job to point young minds towards the right kind of question, a teacher doesn't need to give any answers because answers are everywhere.
When I don't know the answer to something, I write a book about it because it gives me a chance to explore it and go to some people who do have the answers.
All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.
religion is about having the right answers, and some of their answers are right... but i am about the process that takes you to the living answer... it will change you from the inside. there are a lot of smart people who are able to say a lot of right things from their brain because they have been told what the right answers are, but they don't know me at all.
Everyone reads a different book. That's what's interesting. Everyone sees a different film, as well. We bring our past lives to whatever work of art we're experiencing at that moment, and that's what makes it interesting. It's not mathematics. There are different answers for different people.
Insatiable curiosity is infectious to everyone around you. We live in an era today where we can get the answers for everything. In my generation, going to school meant learning the answers. Today, education should be more about knowing what the right questions are. The answers come for free.
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 don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.
As human beings, don't we need questions without answers as well as questions with answers, questions that we might someday answer and questions that we can never answer?
Biblical social scientists have an advantage because they know truths about human nature. Those who dismiss the Bible and create surveys that don't measure crucial factors are the ones who have closed minds. Sometimes the Bible gives us clear answers and sometimes it doesn't, but it always helps us to ask the right questions.
Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive.
