You can extend it beyond craftspeople to anyone at all. We all use tools, and we all have tools that we love, and tools we wish we had.symbolipoint said:What tools, does not or do not matter. He made an analogy between ANY crafts-person who uses tools/devices/equipment/materials/the skill in choosing and handling the tools; and most scientists/engineers/accountants_&_such who rely on or explore Mathematics in their work.
I think to consider mathematics merely as a tool box, is a bit like high school students think of mathematics as a mean for calculations.Archie Medes said:You can extend it beyond craftspeople to anyone at all. We all use tools, and we all have tools that we love, and tools we wish we had.
I thought the question is the general public asking what the practical use is?fresh_42 said:I think to consider mathematics merely as a tool box, is a bit like high school students think of mathematics as a mean for calculations.
As if it had anything to do with calculations.
Yes, and the fact, that it is very different from toolboxes and calculations is exactly the point, at which it becomes difficult to explain.Archie Medes said:I thought the question is general public asking what the practical is?
Yes, the engineer's problem is the exercise. The theorems are why it can solve the engineer's problem, not how. And it has absolutely nothing to do with philosophical pursuits. Your point of view is as if you said physics is good to keep your car on the road.Archie Medes said:But it isn't different at all.
Engineer has a problem, uses the relevant mathematics to solve it.
I mean, no wonder laypeople are having difficulty understanding it if people are over complicating it with their philosophical pursuits!
Archie Medes said:But it isn't different at all.
Engineer has a problem, uses the relevant mathematics to solve it.
I mean, no wonder laypeople are having difficulty understanding it, if people are over complicating it with their philosophical pursuits!
A hammer doesn't tell a carpenter what to nailfresh_42 said:The theorems are why it can solve the engineer's problem, not how.
Done plenty of logic, and love proofs.Bipolar Demon said:Mathematics is not a toolbox in itself.
if you haven't spent hours on logic, proofs, set theory, and other foundations of mathematics, I doubt you can do much real mathematics.
I told you the metaphor is wrong. Thank you.Archie Medes said:A hammer doesn't tell a carpenter what to nail
Simple? No. Tool? Only a very small part of it is actually in daily use.And logic is simple, and a tool
I don't know. Why should they? The small part that is actually used can merely be called set theory.No, I haven't done set theory, but let me guess, people apply it to solve problems, right?
You told me it is wrong, yes, but I'm not agreeing with you. With logic, sorry, I was thinking of programming logic, which is very simple.fresh_42 said:I told you the metaphor is wrong. Thank you.
Simple? No. Tool? Only a very small part of it is actually in daily use.
fresh_42 said:I think to consider mathematics merely as a tool box, is a bit like high school students think of mathematics as a mean for calculations.
As if it had anything to do with calculations.
The way Mathematics works, is that people also like to explore; and this is what is the study and development of new Mathematics - the insights which Mathematicians and others did not have before.Archie Medes said:I thought the question is the general public asking what the practical use is?
But I also honestly don't see it as anything other than a toolbox. Why do people use mathematics if not to solve problems?
The pursuit of it, well, that is another matter.
dkotschessaa said:This answer is too vague for most people, unfortunately. What tools? What do you mean?
-Dave K
Yes, but is the question "why do you pursue knowledge?" or "what does that knowledge end up used for?"symbolipoint said:The way Mathematics works, is that people also like to explore; and this is what is the study and development of new Mathematics - the insights which Mathematicians and others did not have before.
The way to select the right example is by first asking the questioner about themselves and their lives. If people want a one-size-fits-all answer, well whoever comes up with one will make an absolute fortune in education.Mark Harder said:The kinds of tools we mean are manifold. Perhaps the concept is best communicated to lay persons with a few examples. Read my earlier post about abstract algebra and equations for what I envision as one instructive example.
Archie Medes said:The way to select the right example is by first asking the questioner about themselves and their lives. If people want a one-size-fits-all answer, well whoever comes up with one will make an absolute fortune in education.
Like create credit default swaps or some other financial scam for big bucks.lavinia said:When the proof of Fermat's Last Theorem was announced on the front page of the New York Times a mortgage securities strategist at an investment bank said to me, " How much money did he make spending his whole life on this?" I said "None. He didn't do it for money." He shook his head and said,"What a waste." and walking away - no doubt to go do something practical.