# Maths and Further Maths

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#41

*Originally posted by cayley-hamilton*

Your first sentence perfectly explains why mathematics are sooo pedantic. Its obvious that 2+2=4. In fact it reminds me of the Matrix: “you only believe what you want to believe”.

Your first sentence perfectly explains why mathematics are sooo pedantic. Its obvious that 2+2=4. In fact it reminds me of the Matrix: “you only believe what you want to believe”.

On the contrary in mathematics once the basic axioms (rules) have been established we can then PROVE things that are FACT. they always work, not just in the tested range but always.

Finally you statement that it is obvious that 2 + 2 = 4. If this hadn't been proved ie the basic laws of addition being established from axioms, would you KNOW this is always the case. the answer is definitely no and without the mathematical rigour of a proof it wouldnt be obvious and we could do little more than assume it is true

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#42

*Originally posted by bloodhound*

**first of all i am realy passionate about maths. maths is one of greatest not only in terms of contents but also in terms of carrer opportunities and wages. if u wanna do economics you ned maths even if u dont have economics a level.**

Explain how would a physists approximate the value of pi using a needle and a grid of lines???

Explain how would a physists approximate the value of pi using a needle and a grid of lines???

You've just trashed your argument. Economics? Mathematical with all the "rigour" and "beatuty" you so love it by? Sitting there trying to put equations to or model economics (which is even more abstract the some parts of physics) is not mathematical as YOU know it because there is no certainty to such things!

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#44

*Originally posted by bloodhound*

**i got no idea what ur talking about. i am just saying that maths is useful.**

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#45

What began with someone suggesting more people should do more further maths, turned into an all-out maths vs physics contest . All in the fun of forum discussion though, but still amazes me how weird things come from straight forward posts.

From my pov, maths is an empirical science that is used by other sciences, notably chemistry and physics, but only marginally by biology. I wouldn't consider it true though that mathematicians waste their time with proofs and are so involved in a pointless endless pursuit, they miss the big picture and don't make the ground-breaking discoveries physicists do. As someone already said, without proofs, we are left with assumptions that are almost as likely wrong as they are right. Without proofs we have no real science, just guesses. From that I would say maths is at least just as important as physics, if not more.

I see a lot of argument about how pointless something is, whilst something else is more useful. Surely, maths having a broader basis and facilitating physics as well as other sciences will always be the greater source of innovation/useful things. It may however be physics that applies these innovations to things we better appreciate, but this in it self only reinforces the idea that the mathematical proofs were useful.

As someone said, without the maths (e.g. calculus) developed by Newton and others, Einstein's theories just wouldn't be possible. But simultaneously without the maths Newton developed/used, his laws of motion, etc wouldn't have been derived. Newton needed to be a mathematician before being an experimental physicist as all true physicists have a sound mathematical foundation.

I don't agree though that maths is about predictability/certainty or the mere pursuit of proofs. It's more to do with logic that is true and non-contradicting. Perhaps the real problem is that whenever maths is applied to the real world and becomes practical/experimental, we suddenly no longer call it maths but call it physics/statistics/mechanics (etc) creating a difference where none needed to exist.

From my pov, maths is an empirical science that is used by other sciences, notably chemistry and physics, but only marginally by biology. I wouldn't consider it true though that mathematicians waste their time with proofs and are so involved in a pointless endless pursuit, they miss the big picture and don't make the ground-breaking discoveries physicists do. As someone already said, without proofs, we are left with assumptions that are almost as likely wrong as they are right. Without proofs we have no real science, just guesses. From that I would say maths is at least just as important as physics, if not more.

I see a lot of argument about how pointless something is, whilst something else is more useful. Surely, maths having a broader basis and facilitating physics as well as other sciences will always be the greater source of innovation/useful things. It may however be physics that applies these innovations to things we better appreciate, but this in it self only reinforces the idea that the mathematical proofs were useful.

As someone said, without the maths (e.g. calculus) developed by Newton and others, Einstein's theories just wouldn't be possible. But simultaneously without the maths Newton developed/used, his laws of motion, etc wouldn't have been derived. Newton needed to be a mathematician before being an experimental physicist as all true physicists have a sound mathematical foundation.

I don't agree though that maths is about predictability/certainty or the mere pursuit of proofs. It's more to do with logic that is true and non-contradicting. Perhaps the real problem is that whenever maths is applied to the real world and becomes practical/experimental, we suddenly no longer call it maths but call it physics/statistics/mechanics (etc) creating a difference where none needed to exist.

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In maths, (3 x 10^8) + (3 x 10^8) = 6 x 10^8, but in physics (3 x 10^8 m/s) + (3 x 10^8 m/s) doesn't equal 6 x 10^8 m/s because you cannot travel faster than the speed of light in a vacuum. You can never travel this faster so its not true, but in maths it is true because there only two numbers.

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*Originally posted by rIcHrD*

**As someone said, without the maths (e.g. calculus) developed by Newton and others, Einstein's theories just wouldn't be possible. .**

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#49

*Originally posted by Sir I. Newton*

**In maths, (3 x 10^8) + (3 x 10^8) = 6 x 10^8, but in physics (3 x 10^8 m/s) + (3 x 10^8 m/s) doesn't equal 6 x 10^8 m/s because you cannot travel faster than the speed of light in a vacuum. You can never travel this faster so its not true, but in maths it is true because there only two numbers.**

whatz your point exactly?

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#50

The expression "3x10^8+3x10^8=6x10^8" is always true. The equation for calculating the relative velocity used only applies to small velocites and so is inappropriate to use, giving a meaningless result.

I never knew the equations of motion took so much work to derive :-s. Interesting though .

I never knew the equations of motion took so much work to derive :-s. Interesting though .

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*Originally posted by rIcHrD*

**I never knew the equations of motion took so much work to derive :-s. Interesting though .**

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#52

Sorry if it wasn't clear. I meant I never knew F=d(mv)/dt, sometimes F=ma, took so long to derive. I know how the constant accel formulae are derived and they don't take long at all. Wasn't supposed to be a sarcastic statement though it seems you saw it that way.

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*Originally posted by cayley-hamilton*

**whatz your point exactly?**

Maths > Physics.

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*Originally posted by rIcHrD*

**Sorry if it wasn't clear. I meant I never knew F=d(mv)/dt, sometimes F=ma, took so long to derive. I know how the constant accel formulae are derived and they don't take long at all. Wasn't supposed to be a sarcastic statement though it seems you saw it that way.**

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#56

I agree that with the way Sir I Newton put it. IMO as I said before whenever maths is applied to real situations, we call it phsyics/mechanics/statistics/anything but maths when all it is is maths.

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#57

*Originally posted by Sir I. Newton*

**Sorry about that mate, took it the wrong way, I appologize. I bought the translation of Newtons Principia, his math paper in which F=ma is derived, its over a 1000 pages long, with drawings and calculus on every page. Whereas Einsteins Special Relativity paper where the lorentz factor and transformations are derived only takes up a small section, its all trigonometry.**

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My approach to maths is to understand exactely what is happening in a function or section of maths such as calculus or trigonometry, my belief is that once you understand the basics fully, you have a solid foundation on which you can build. Most people can use the product and quotient rules but how many people can prove them from first principles? I believe thats understanding exactely whats happening, instead of doing the calculation and not thinking about how its done, but sadly you don't get credit in an exam for your background knowledge, just the write whats on the mark scheme and you've got the marks.

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#59

Yeh, I know what you mean. I try to understand as much as I can b4 I do the questions, because when I don't, I can make mistakes that I don't understand and so get stuck. When I understand the topics, it makes things easier because I can always be assured that I can do the same problem several ways and to check answers all I do is make sure I get same answer inconsiderate of technique. Sadly though, I have little idea how the quotient/product differentiation rules are derived from first principles. I concentrated my efforts on the things I find more difficult to do, such as some of the mechanics I did in which understanding was crucial.

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What Actually is STEP Mathematics? I've looked at step 1 and 2, they don't look that bad

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