Has the invention of the calculator made mathematicians lazy?

Poll

Calculator

I was in maths and we were doing these intergration stuff..and the teacher worked it all out by hand and I used my calculator. Then the teacher said that the calculator was one of the worst things to hit maths!

What do you guys think?

Reply 1

Bismarck

13

papz_007

I was in maths and we were doing these intergration stuff..and the teacher worked it all out by hand and I used my calculator. Then the teacher said that the calculator was one of the worst things to hit maths!

What do you guys think?

Most advances in modern mathematics would be impossible without advanced computers (calculaters are so last century). That's like asking if the invention of an X-Ray machine made doctors lazy...

Reply 2

Ferrus

19

Most advanced maths is algebra in which a calculator is pretty useless...

Reply 3

Fernand

Most advances in modern mathematics would be impossible without advanced computers (calculaters are so last century). That's like asking if the invention of an X-Ray machine made doctors lazy...

That is not the best of examples, as doctors couldn't look at the skeletons of people before with their own eyes.

Reply 4

Akhoza

papz_007

I was in maths and we were doing these intergration stuff..and the teacher worked it all out by hand and I used my calculator. Then the teacher said that the calculator was one of the worst things to hit maths!

What do you guys think?

My teacher keeps on calling calculators 'thick,' especially in trig when they dont give you all the answers. He was telling us about when he was in school there were no calculators and he used some frighting looking tables used for logs. :eek:

He also uses his figures to work out trig questions. Its frightening!!!!!!!!!!!

Reply 5

warranty-ideal

12

Fernand

That is not the best of examples, as doctors couldn't look at the skeletons of people before with their own eyes.

Actually.... It is.
The MOST advanced mathematics of out time is calculated using supercomputers as previously stated. The tool is nessessary to advance the science. In both cases. :smile:

Reply 6

Spunky

14

Mathematics at any appreciable level is far more than simple (or for that matter complex) arithmetic.

Reply 7

Bismarck

13

Fernand

That is not the best of examples, as doctors couldn't look at the skeletons of people before with their own eyes.

Human beings are physically incapable from doing the type of calculations that modern computers do.

Reply 8

John82

They've certainly made people worse at mental arithmetic but overall they have been benificial. I remember some really old textbooks at school that had tables in the back for trigonometry, they must have been 20 years old!

I can understand why hardcore mathematicians dislike the calculator. Also, as others have said, much advanced maths is algebra based anyway.

Reply 9

Don Bosco

Yep, the calculator has made us lazy. An example: most students can't find the square root of e.g 26 without a calculator.

Akhoza

My teacher keeps on calling calculators 'thick,' especially in trig when they dont give you all the answers. He was telling us about when he was in school there were no calculators and he used some frighting looking tables used for logs. :eek:

He also uses his figures to work out trig questions. Its frightening!!!!!!!!!!!

I used those 'frightening' tables for my GCSEs in Nigeria and they're not that bad when you get used to them. :wink:

I still love the calculator though, and I don't agree that it's a bad thing for mathematics. It just saves time.

Reply 10

Kernel

1

That doesn't make us lazy- why should we waste time finding the square root of 26 manually, when we can use a calculator? Does using a table of logarithms make people lazy too? Also, Bismark is right- the proof of the four-colour theorem, for example, was done by using a computer, and would have taken longer than a lifetime to do by hand.

Reply 11

Dekota

Calculators discourage students/people from mental arithmetic. Reliance on it will scare people away from the mental maths when faced with it without a calculator.

That's why people sometimes run away from the thought of numbers when unarmed. (without a calculator) :rolleyes:

Reply 12

Dekota

Kernel

That doesn't make us lazy- why should we waste time finding the square root of 26 manually, when we can use a calculator? Does using a table of logarithms make people lazy too? Also, Bismark is right- the proof of the four-colour theorem, for example, was done by using a computer, and would have taken longer than a lifetime to do by hand.

The four-colour theorem is something completely different. Obviously a calculator can't solve/prove theorems. A computer might be able to, baring in mind that a programme has to be made and the programmer should know what he's trying to do.

Even finding the square root of 26 isn't difficult with practise.
- Just for examples sake, root of 26 will be approx 5, and will be bounded by 5 and 6. With further arithmetic you can go for 1 dp and as some brilliant people demonstrate how such feats can be done as to calculate square roots with high precision. It all comes with practise.

Reply 13

AlphaNumeric

10

Bismarck

Most advances in modern mathematics would be impossible without advanced computers

Most?! When was the last time you looked at recently published maths? It's a long way from 'most'.

Calculators (or rather, computers) certainly have gained in usage in APPLIED maths, because there you are trying to model something. Even then, that's only once a group of mathematicians have spent a lot of time doing algebra to come up with the equations they want to put into the computer. If someone said to you 'I want to model electrodynamics within a chruning molten metal', you'd still need to be very well versed in the mathematics of fluid flow and electrodynamics before you could hope to use a computer to model it!

In the area of pure maths, calculators have next to no usage, it's all done on blackboards or paper. Could you use a computer to prove Fermat's Last Theorem? Of course not, it's got infinitely many cases to check.

Calculators make people who have only studied a bit of maths lazy in the mental arithmetic department. Actual mathematicians by degree or profession do not rely on them to do actual maths. I'm in my 4th year doing maths at Cambridge and I don't even own a calculator! Never had a need for one.

A huge question for AI people is whether one day computers will be able to think abstractly, like humans do, about maths. Sometimes a simple argument if powerful enough to prove a theorem, instead of needing to check dozens, hundreds, even millions of cases. Computers go for the brute force approach at the moment, it'd be a big indication of possible intelligence if they could reason a mathematical solution.

fragreaper

The MOST advanced mathematics of out time is calculated using supercomputers as previously stated. The tool is nessessary to advance the science. In both cases. :smile:

Those are almost always results, not the actual mathematical development.

I'm doing a course in spectral scattering. It's incredibly abstract but comes down to inverse spectra scattering. It allows a computer to take a set of detections and work out the image of what created that pattern. It's how PET scans on the brain work! It's not the computer developing the maths, it's just blindly applying maths developed by hand to something.

Reply 14

milady

9

calculators are fantastic, they cut down the time you need to do something by so much, plus there's less chance of errors.

though i suppose when you're actually learning it's better to do things the long way so that you gain understanding rather than just pressing buttons and getting the answer - seemingly - by magic.
eg. i have not yet learnt the whole deal with inverse trig functions and where they come from, etc, yet i've used them to solve problems for ages.

Reply 15

Teehar

10

the calculator has allowed for the quicker calculation of certain mathematical problems, however in doing so, it has resulted in the less able becomeing better at maths but the more able becoming lazier and not keeping themselves as sharp as they shud be.

damn the heathen calculator!:vmad:

Reply 16

Kolya

17

It has not made mathematicians lazy, but it has made the average teenage maths student worse at simple calculations.

A good analogy is, "Why drive a car to the shops around the corner when you can walk?"

Reply 17

Evil-Tuna

2

Its not the calculators which make a true mathmatician lazy it is the invention of tweed. Tweed is an evil fabric draining away the life force of an individual.

Reply 18

Nysh

1

My mental arithmatic has degraded significantly sinc ethe introduction of the calculator. My younger sister, though, is much worse- she wasn't even taught long division because a calculator could do it.

Reply 19

master-chafe

Maths is not adding things up. Generally calculators save a lot of time doing mindless things that just take a long time (looking up trig/log tables, finding the inverse of matrices, dividing horrible irrational numbers to a high degree of accuracy).

I am doing an engineering course and having a calculator means you can do *far* more work than you could without one in a given time; you can use programs like matlab to do enough number crunching to keep ten maths professors employed (or bored) for a decade in a matter of seconds. The maths in pure maths itself and to a lesser extent things like theoretical physics are far less based on number-crunching since they are almost always general scenarios and do not involve figures (although in physics when they do, the figures will probably be horrible).

I agree that the calculator has made mental arithmatic poorer, but far more so for the non-mathematition/engineer/scientist/accountant than for people who use maths on a regular basis and for whom using mental arithmatic is a prequisite and is faster than banging 23+7 into the calculator. Watching shop assistants try and tot up prices without the use of a calculator or till can be embarassing. I was on a train where the woman-selling-drinks (probably a refreshment coordinating consultant) had to add up something like £1.20 and £1.30 and took out her calculator and got the wrong answer anyway. The guys she was serving were no better; they noticed something was wrong but couldn't work out the proper cost. You could see all the professional-types on the train cringing...

Has the invention of the calculator made mathematicians lazy?

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