I cringe when hearing "Math teaches you to think".

It's a well-meaning but ineffective appeal that only satisfies existing fans (see: "Reading takes you anywhere!"). What activity, from crossword puzzles to memorizing song lyrics, doesn't help you think?

@mark: Heh, awesome :). Yeah, I was really surprised by that “something from nothing” relation [0 = 1 + (-1)]. I think there may be a difference between true “nothingness” and “no net difference” (i.e., two forces which are there, yet cancel).

@gunsa
Mathematics is first and life is next. It rules not only our lives but even that of animals. Its right there before we opened our eyes, not in the analytical sense but in the basic sense. A child calculates how much to cry for food, and then how much to cry when in pain. Even an illiterate person has to know price of goods if he wants to survive (even if he barters). Now think about animals. Even they have to know how to count! A bird has to figure out how many days will it take to build its nest, if it doesn’t then it will not survive. A predator must have a sense of how many steps it should be behind its prey and how much force it needs to apply on the ground so that it can catch its prey.

Instinct? yes, but its just another name of built in analytical engine inside living things.

Even non living things are ruled by mathematics. If you look around and see nature itself shows how important mathematical equations are. We throw a stone and its governed by the equation of parabola! And who does not know the amazing occurrence of Fibonacci series in nature!

Maths is the most fundamental science in the actual meaning of the word ‘science’ - the knowledge. It is this fundamental nature of mathematics that makes us ‘math aware’ and you have described this in a nice way.
The energy-mass relation found by Einstein or the anti-particle discovery by Dirac’s solutions are examples of how maths is far ahead of our ideas and if we truly respect the fundamental nature of maths we can explore the vast information however non-intuitive it may seem to be.

Whilst I’d never say “maths teaches you to think”, I think it is entirely true (and apposite) to say “maths teaches you to reason”: after your first undergraduate analysis course you never again make unwarranted generalisations or assume properties that can’t be proved; you learn to make clear, structured arguments that are logically sound; you learn how to proceed where intuition fails.

In fact, I suspect that once the “think” to “reason” refinement is made, the rest of your article becomes redundant!

Thanks Harish. Yeah, I love thinking about these types of things – and math gives us the tools to do it. Would anyone ever consider that something could come from nothing without the 0 = 1 + (-1) example as a starting point?

How could the universe come from nothing? Well, how can 0 be split into 1 and -1?
As usual … so insightful. This one line will probably occupy my week.
My mind flashes back to a conversation where a 6th grade teacher was bemoaning her students apparent inability to get the concept of “number” place. And yet the “gamers” in class I presume had already moved on to interpreting the various effects of changing entries within a matrix the started to delve into the Xbox infused space time continuum (infinite lives).

your explanation is still complecated and hard to understand. Can you give a simple concept of matematics that could inspired and give motivation for childern and adults. Why people should learn matematics, what is the direct benefit for living, for small business and for house wife to save the money. Make it simple and factual.

I’m trying to understand part 3.7 - 3.8 on measuring distance in Maths Better Explained, the one about Rambo, Bambi and Seinfeld. I just can’t figure how you arrived at 6.7 and 13.34 respectively out of those other figures you gave. Could you please help me out

Sometimes, Math makes you feel small, either that, or mathematical knowledge feels so insignifigant or unimportant that you’d wonder, “have I been wasting my time doing it”

That is probably why I think it’s a lonely subject.

Good one Kalid. I would go for the latter one - reality might be an approximation of math!

As for Mark’s comment on nothing, let us think about the Big Bang. The theory goes that there was nothing - no space, no matter and no energy before the event. If it was ‘something’ then it has to be ‘nothing’! And everything that is today is out of that ‘nothing’. Even the word ‘before’ can’t be defined in the context, its like zero time (as is zero Kelvin). So, the universe came out of ‘nothing’ as 1 and -1 come out of zero! Wow! satisfying example of ‘reality being an approximation of math’

Your insights and intuitions that underscore mathematics are a joy to read!

However, I can’t say I concur with the analogy that the universe coming into being from nothing might be likened to splitting 1 and -1. This may work for abstract objects but we should be rightfully suspicious when transposing such a notion across to physical reality. True nothingness has no properties, not even abstract ones, and as such cannot undergird a formula let alone anything tangible. It would seem then that the Lucretian principle of “ex nihilo nihil fit” still holds true… Out of nothing, nothing comes.

I like this article’s presentation about the function of mathematics. I think it’s an interesting way of using an analogy of how we thinks with words and more words. But I also think that mathematical ideas were shape by our intuitive sense of direction and space as well. Zero is a math idea; but “emptiness” probably had existed before zero were discovered.

Words have layers of meaning. Some meanings are lay terms but the same word may also be assigned to specialized meanings as well - this means that some words or meanings are more on the side of abstraction. And this is probably also true for math idea. Lawyers are the worst students of mathematics (I’m a lawyer), but even they use fancy terms like “denominator” when they want to borrow the idea of division (just want to sound smarter). But most mathematical terms goes to the side of more abstraction - at least I thinks mathematicians want to keep them that way. In the end, very little math will become intuitive enough to be internalized. What I think is the problem with math is that math is always taught in school - not as a concept of thinking - but as a problem solving science/art. Most people are not problem solving geniuses so they fall apart and hate math. These same people don’t actually hate abstract thinking; they can be very intelligent individuals. But for them, learn to think in abstract with words is easier and more accessible. Whenever one turns to maths, one faces problem-solving challenges.

I think this is what turn people away from math - and lose its benefit as a tool for abstract thought.