h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Is traditional maths becoming an irrelevance nowadays?

Mathematics was originally conceived, and is still thought in schools today, as a means of explaining processes in the real world, and determining how things will happen in the future. It is the equivalnent of a crystal ball, if you like.

However the basis upon which the real world uses of mathematics must now be seriously eroding away. Compared to the computational power of computers, traditional mathematical approaches must seem hopelessly inadequate. Examples of "traditional approaches" include the rigorous solving of differential equations, the use of abstractions so that only the simplest cases can be solved, etc.

Even in primary schools children are learning mathematical techniques (such as long division) which they will never use once they leave school. Calculators and computers are far superior replacements than the tortuous (not to mention excruciatingly boring) processes of mental arithmetic required.

Maybe maths in primary school and secondary schools need to be replaced with a new computational mathematics curriculum, where children learn how to develop computer algorithms to solve problems? Its a bit more relevant and it will make maths far more interesting for children.

The abstract and esoteric type of pure mathematics is for purists only, a bit like Latin and Ancient Greek.

As an engineer I can say that I really appreciate having been taught how to do things the "traditional" way. There have been many times when it has taken me at least twice as long to get a computer to do a problem that I could have solved myself on paper. I can see your point though.

But one thing one of my lecturers said to me was you need to know the "traditional" ways in order to tell if the computer gives you a "sensible" answer. Computers are not the infallible machines they are made out to be.

However, I do agree that schools should spend some time on computational mathematics and algorithm development as this was definately a problem area for many engineering undergraduates.

I'm an engineering graduate too, and this entry was a bit tongue in cheek, but with a serious point attached - how do you keep a kid's interest in maths going when all they get for the first few years is a continuous dose of 7-times tables, long division problems, theorems and a dose of problems about trains meeting each other in opposite directions? It's hard for a kid to see the relevance of all that stuff, and hard to blame them for being turned off.

The real applied mathematics is all about modeling and prediction, and of course understanding the techiques and basic mathematical tools are really important. They could be taught better though!

(Maybe it's all changed since I was in school, so I could just be ranting here about something that no longer exists!)

In the final year of High School in Victoria, Australia, students are given these massive amounts of data (about 100 pieceis of info) which we are then to manipulate to produce required outcomes. We are strongly encouraged to do this using Microsoft Excel and othe rsuch programs. This means we must learn how to take complex eqns and break it up so that the computer completes it in the correct order. While the exercise itself is completely irrelvant to anything our futeure lives will hold, it teaches us to adapt teh old to the new.

It is also strongly suggested that each student invest in a Graphics (or Graphing) Calculator. These wonderful thing will draw graphs for you if you enter the formula or find the formula if you enter a series of numbers. Once again the formula must be adapted to fit in with the way teh computer process the data.

Also, long devision when simply dealing with numbers has ben declared irrelvant and stricken from teh primary school education. However, when students reach yr. 11 (form 5) they need to know how to long divide so that they can find teh values of 'x' in cubic equations or anything larger (quartic etc.)

It's a wonderful time to be a student..... 8^(

Good stuff. At least it appears to be quite relevant!

When I was a kid I thought that maths was devised by evil people to torture us for annoying our parents!

OK I accept I was weird but I liked maths at school (until I got to A-level anyway).

And number crunching is boring whether you use your head or a computer.

I was on my way back home to Hampshire from Nottingham. I stopped in a service station and a colleague ordered a BK meal for her and myself. The hapless person (16ish) behind the counter added 3.99 and 3.69 and came to something in the order of £11. Having alerted my colleague to this a £20 was removed from hapless person and replaced with a tenner. We then explained how much the bill -should- be (£7.68). Obviously confused, and daunted by the prospect of having to deduct 7.68 from 10.00, the hapless person then asked us how much change we should be getting back. When we answered £2.32, the poor employee then gave back £3.50, obviously confused as to how to nake up 2.32 from British coinage.

The bare basics of maths are dull. However, I think this illustrates how important they are to us all. We can't always rely on computers and calculators ...

There are two points to be said about this:

1) Trust me, those people writing the programs for the computers need QUITE a lot of maths. Writing a complex mathematical algorithm for lets say solving a differential equation numerically (i.e.not classically) is not done by saying "well, I guess it works most of the time, and it works maybe fast and efficient". You need an awful lot of "classical" mathematics to PROVE that it ALWAYS works and to make it run EFFICIENTLY. Users don't like waiting for a possibly wrong result for days... Once again, this is something an ordinary programmer can't do... It is not a question of programming skills, but of "pure" mathematics.

2) Even those who only use the computer, pocket calculator... should have at least some idea of what they are doing. Wrong results (due to wrong inputs) or wrong interpretations of right results would be quite probable otherwise.

It is also important to be aware what maths actually is, and this is a lot more than just "calculating" (which truly can be done by a calculator more efficiently, still you should know how to do it by hand, for those cases you dont have a calculator with you). The essence ot mathematics is logic. Analysis of problems (in the most general and not only mathematical meaning), finding structures and using them to find solutions. What do I have, what do I want and how do I get it. Yes, I know this is not what everybody associates with maths at first, but I think this is the basic concept behind all those complicated formulas. And this concept will never get irrelevant.

I hated maths at primary school - "little or no interest" the teacher said. Didn't enjoy it much at secondary school, although my teacher said I was quite good. And when I got to Uni, intent on studying Physics I found maths fascinating, I loved it so much I did a degree in Maths and then a PhD. And then I got a job becuase I was bored of pure maths and wanted to studying more practical problems. I now work in the City and study risk. I find it a fascinating slippery concept. What does it mean to say there is a risk associated with this project? Hmmm....
Whats the point of what I'm saying? I think that the mathematics most people are exposed to, while it would be a bit extreme to say it wasn't maths, is certainly nothing like the kind of maths professional mathematicians do.
Also I think that a study of pure maths is without a doubt the best education a mind can have. Why? Maths teaches you to think. Most people can't think at all. I don't mean they are stupid, lots of people aren't its just that they can't think through a problem. Thinking is a technical skill that can be taught, and nothing teaches it better than maths.

Welcome to h2g2! I'm not sure if these are of any use, but here's a couple of links: http://www.h2g2.com/F617?thread=55960 (the newcomers welcome), http://www.h2g2.com/A344756 (a quick reference guide). Share and enjoy! :-)

Maths is surprisingly relevant. You know calculus? That is generally considered one of the most complex, esoteric branches of all, but it was invented by Sir Isaac Newton in order to determine the orbits of planets, as well as other things.

There is also a rather complicated operation which combines calculus and mathematical series called the MacLaurin series. When this is applied to arctanX (ie the angle whose tangent is X), it can be used to work our pi.

pi is a very important number in several engineering applications.


Arithmetic, however, is incredibly boring. Perhaps teachers should dress it up a bit, show it is relevant. (Example: suppose you have twelve sweets. Bully #1 demand half, bully #2 demands one third. Who should you give to and why?)