I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.
Terence TaoRead
I remember having this vague idea that what mathematicians did was that some authority, someone, gave them problems to solve, and they just sort of solved them.
Interpretation
The quote reflects a common misconception about the nature of mathematical work, emphasizing the autonomy and creativity involved in mathematics.
Terence Tao's quote highlights a prevalent misunderstanding about the role of mathematicians. It suggests that many people believe mathematicians merely receive problems to solve from external authorities, whereas in reality, the practice of mathematics requires a significant amount of creativity, curiosity, and self-driven exploration in order to formulate and tackle new problems.
In practice
In a lecture about the learning process in math, this quote can illustrate the importance of self-driven problem-solving.
I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.
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.
For me, I guess the main motivation is the satisfaction of finally understanding some tricky mathematical concept or phenomenon and then explaining it to others.
One can think of any given axiom system as being like a computer with a certain limited amount of memory or processing power. One could switch to a computer with even more storage, but no matter how large an amount of storage space the computer has, there will still exist some tasks that are beyond its ability.
I recall being fascinated by numbers even at age three and viewed their manipulation as a kind of game.
Talent is important, but how one develops and nurtures it is even more so.
That's the public-school system all over. They may kick you out, but they never let you down.
Weird behavior is natural in smart children, just as curiosity is to a kitten.
I think we should stop asking people in their 20s what they 'want to do' and start asking them what they don't want to do. Instead of asking students to 'declare their major' we should ask students to 'list what they will do anything to avoid.' It just makes a lot more sense.
Your understanding of what you read and hear is, to a very large degree, determined by your vocabulary, so improve your vocabulary daily.
Results show that just one year of chess tuition will improve a student's learning abilities, concentration, application, sense of logic, self-discipline, respect, behavior and the ability to take responsibility for his/her own actions.
Except when he has regressive tendencies, the child's nature is to aim directly and energetically at functional independence.
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