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
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.
Interpretation
This quote illustrates the limitations of any system, no matter how advanced it may be.
Terence Tao's quote highlights the inherent limitations of computational systems, emphasizing that even the most powerful computers or axiom systems have boundaries to what they can achieve. No matter how much memory or processing power is available, there will always be tasks or problems that elude even the most sophisticated systems, underscoring the philosophical idea that some truths or complexities may be beyond human understanding or technological capability.
In practice
In a discussion about the future of artificial intelligence at a tech conference.
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.
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.
When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed.
The way I see it, commercial interests should manage a lunar base while NASA gets on with the really important task of flying to Mars.
Faced with the evidence, many deniers have started to admit that global warming is real, but argue that humans have little or nothing to do with it.
Yes, I am the last man to have walked on the moon, and that's a very dubious and disappointing honor. It's been far too long.
The first mission to Mars did not expect to find craters and river valleys, and yet they did. The first mission to Jupiter didn't expect to find ocean worlds and volcano worlds, but they did.
If the history-deniers who doubt the fact of evolution are ignorant of biology, those who think the world began less than ten thousand years ago are worst than ignorant, they are the deluded to the point of perversity.
It may be said "In research, if you know what you are doing, then you shouldn't be doing it." In a sense, if the answer turns out to be exactly what you expected, then you have learned nothing new, although you may have had your confidence increased somewhat.
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