Problem-solving improvement

[Jakelaker]

Looking at research and research degrees in mathematics, it is clear that 90% is based on existing results. Most PhD students generalise and specialize existing research, yes? (unless you are John Von Neumann).

Yeh, what are you trying to say?

 

[Daniel Duffy]

Yeh, what are you trying to say?

Is it not clear?(?) WYSIWYG
We all stand on the shoulders of giants?

 

[Jakelaker]

Is it not clear?(?) WYSIWYG
We all stand on the shoulders of giants?

It's not clear to me what you're trying to say

 

[Jakelaker]

Are you just stating a fact? I do agree with it

I feel that you are sharing knowledge first then planning to say something after about it.

 

[bigbadwolf]

Looking at research and research degrees in mathematics, it is clear that 90% is based on existing results. Most PhD students generalise and specialize existing research, yes? (unless you are John Von Neumann).

Unless you're Serre or Deligne. One of the things that used to irritate von Neumann about himself was that the truly seminal ideas didn't originate with him. But he was capable of taking those ideas and developing them very rapidly. This seems to have been the case with quantum mechanics, game theory, and weather forecasting.

 

[Daniel Duffy]

Unless you're Serre or Deligne. One of the things that used to irritate von Neumann about himself was that the truly seminal ideas didn't originate with him. But he was capable of taking those ideas and developing them very rapidly. This seems to have been the case with quantum mechanics, game theory, and weather forecasting.

Doesn't make him a bad person LOL

He was a terrible driver.

He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.

Apart from that, he didn't do all that much really.

 

[Daniel Duffy]

Are you just stating a fact? I do agree with it

I feel that you are sharing knowledge first then planning to say something after about it.

Here is a nice one
1. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes

But I am interested in your steps in arriving at an answer

 

[bigbadwolf]

Here is a nice one
1. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes

But I am interested in your steps in arriving at an answer

100 minutes obviously. Or maybe 5 minutes.

 

[Daniel Duffy]

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100 minutes obviously. Or maybe 5 minutes.

100 minutes sounds plausible. Long live linear extrapolation.

 

[Jakelaker]

Here is a nice one
1. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes

But I am interested in your steps in arriving at an answer

I had a go at this question as I was writing my comment that had the 9 marbles puzzle in it. So here is what I was thinking during that time:

Of course, obviously 100 minutes but I don't trust my mind. Then I noticed the simplification of 5-5-5 to 1-1-1 did not make sense since 1 machine, 1min makes 1 wedge means 5 machines, 1min makes 5 wedges. So the correct simplification of 5-5-5 is 1-5-1 as each machine starts and ends at the same time and no machine is off while others are working.

So ans is 5min.

___________________________

By the way, can you explain the purpose of your comment earlier?

This one:
"Looking at research and research degrees in mathematics, it is clear that 90% is based on existing results. Most PhD students generalise and specialize existing research, yes? (unless you are John Von Neumann)."

 

[Daniel Duffy]

I had a go at this question as I was writing my comment that had the 9 marbles puzzle in it. So here is what I was thinking during that time:

Of course, obviously 100 minutes but I don't trust my mind. Then I noticed the simplification of 5-5-5 to 1-1-1 did not make sense since 1 machine, 1min makes 1 wedge means 5 machines, 1min makes 5 wedges. So the correct simplification of 5-5-5 is 1-5-1 as each machine starts and ends at the same time and no machine is off while others are working.

So ans is 5min.

___________________________

By the way, can you explain the purpose of your comment earlier?

This one:
"Looking at research and research degrees in mathematics, it is clear that 90% is based on existing results. Most PhD students generalise and specialize existing research, yes? (unless you are John Von Neumann)."

Most PhDs extend existing results, like e.g. Banach Fixed Point Theorem in a Hilbert space that generalizes algorithms for the reals.

And in many cases you work on a topic that is dear to your supervisor's heart

 

[Jakelaker]

Most PhDs extend existing results, like e.g. Banach Fixed Point Theorem in a Hilbert space that generalizes algorithms for the reals.

So you were just sharing a fact, right?

I was confused because that comment came out of nowhere. I couldn't see a link between that comment and the previous comment.

Thanks for the advice.

 

[Daniel Duffy]

A. 1 machine to make 5 widgets (==> 25 m)
B. 1 machine to make 100 = 5*20 widgets (==> 25*20 m)
C. 100 machines to make 5*20 widgets ==> 100 times faster that B (==> 25*20/100 == 5 m)

I take it step by step, one at a time and I can trace the step backwards and forwards. That's the way boring mathematicians like yours truly do it LOL

//
Now apply Polya's questions! QED

e.g.
what is input and output
getting from output back to input
Check every step

Write a small C program to test it.

//
I was confused because that comment came out of nowhere
It came from the archives