Maths is not one of the *natural sciences* but could still be considered "a science" in a broader sense, I think.

Those who have a problem with maths as a science would probably argue that it is not falsifiable.

It depends on what you mean by science or the definition of science. So it's an epistemological question.

The physicists that I know consider math to be the language of science. The mathematicians that I know consider math to be the ultimate form of logic and philosophy, which science is a subgroup.

Though I am not sure if any of these distinctions is meaningful. It's more important about the paradigm and logic that undergirth the particular discipline, not its categorization.

Engineering, is probably less likely to be considered a science, seeing as its primary purpose is to manipulate the natural world, which often, but not always, requires understanding. As Engineers build increasingly complex devices, though, I believe a better understanding of science is increasingly necessary.

@Jamiet

How is math not falsifiable?

@ Jamiet oh how I agree with you here: ''Those who have a problem with maths as a science would probably argue that it is not falsifiable.''

Science cannot prove or disprove the precepts of mathematics and yet it almost totally relies on them. I would further argue, perhaps even more so, that this also applies to logic (or ‘’philosophy’’ if you should wish to be more inclusive).

Note I do not regard this as a problem for the scientific method, but it is nevertheless a limitation of which we should do well to be aware. The danger, as we are discussing in another thread, is the reductionist zealot.

Math is a tool for scientists, science is a tool for engineers.

Engineers use a lot of math, as well.

I'd say that math is a science, in that there are theorems that can be proven or disproven. Every few years there is another long-standing theorem that is finally laid to rest one way or the other.

From http://en.wikibooks.org/wiki/Famous_Theorems_of_Mathematics
"Mathematics deals with proofs. Whatever statement, remark, result etc. one uses in mathematics it is considered meaningless until is accompanied by a rigorous mathematical proof."

That sounds like science to me. You propose a theory. And then you try to prove it. The only difference between that and other sciences is that you will use more math to prove it and not look to the outside world for physical evidence. There are exceptions like the four color theorem.


The main goal of Engineering, though, isn't to find out how the universe works. It's to take what we know of how the universe works and do something useful with it. Make plastic. Build buildings and bridges. Make a better pair of running shoes. For an engineer, everything else is a tool used to get to the destination, math and science included.

Math, the mother of all sciences is the means of understanding the "sciences of nature" which are the acquired and probed accumulated knowledge of how one may understandably work with this knowledge, and that is named: engineering...

Math is not a science. Of course, one must be careful in these definitional questions not to just end up with word games; but there is a meaningful distinction between how math works and how science works that is useful to preserve. (As zultar said, one could introduce the term "natural science" if one wanted to call math a science).

Science proceeds by empirical observation, experiment, and falsification. There is nothing empirical about mathematics: it proceeds by pure reasoning from axioms and definitions. (Of course, empirical observations have been *extremely* useful in motivating and inspiring math, but that's a different thing). Epistemologically, in other words, they have completely different methods.

Jamie is also correct that math is not empirically falsifiable in the sense that physics is. Suppose that you had 2 items and another 2 items, and you put them in a box and suddenly found 5 items. Would you decide that 2 + 2 was equal to 5? By no means! Humans couldn't consistently reason about anything if 2 + 2 was five. Rather, you would conclude that the objects had some strange reproductive capability and would formulate a new law of science to account for it. This is the case for essentially any imaginable empirical falsification of mathematics. One might conclude that a *particular* mathematical model did not describe the universe (for example, that space is not Euclidean), but there is no conceivable experiment that could show that, on a Euclidean plane, the pythagorean theorem failed.

So I think it's useful to maintain a distinction: math is its own thing really, or if you like, a subset of philosophy, which uses pure reason to study "mathematical" objects and relationships, such as quantity, shape, symmetry, etc. Science studies the properties of our actual universe using empirical observation as its ultimate foundation.


One of the classical distinctions here is that mathematical facts are necessary (in the philosophical sense), whereas scientific facts are contingent.

I would also disagree that "math can be considered a part of the natural world." One runs into definitions again, of course, but "natural world" typically refers to the physical universe, and math is not a part of that.

As for engineering, I agree with Theo. Engineering is the fundamental activity of technology, which is the application of science to solving human problems. They are concerned with fundamentally different things: science, at its purest, is the search for knowledge for its own sake. Technology (engineering) is the quest to solve problems of human interest using that knowledge.

They bleed together an enormous amount, of course. Much science requires a huge amount of engineering to do, and much of it is only actually studied because of the potential applications. I think there is a useful conceptual difference, though.

A few clarifications and expansions, by the way:

i) I was referring, of course, to pure math. "Applied math" often bleeds into science, although it also often doesn't.

ii) Apart from my early parenthetical, I was assuming that "science" and "natural science" are synonymous. It might, indeed, be more useful to reserve "natural science" for what I was referring to, in which case mathematics would then still be a science, but not a natural science. (This corresponds better to pre-20th century usage).

iii) I do also want to be clear on the point that math *does* contain more content than pure logic does, qua Godel's theorem, so it's also not just logic -- it is a body of knowledge to itself.

And finally, going back to my opening sentence, I think context is really useful to distinguish what definitions of words are appropriate. If we're classifying bodies of knowledge or doing epistemology, then math is not science. But it IS very closely related as a human activity, and a fundamental scientific tool, as abge pointed out; so in the broad classification of human activities, math and science do belong closely together. If I were at a party and there were a side room for the scientists to hang out in, I wouldn't think twice about going in (and neither should the engineers).

So it does depend on context.

I still don't see how math is not falsifiable. Let's sat Pythagoras proposed the following theorem: a^3 + b^3 = c^3.

All one would have to do to empirically disprove this is measure any triangle. I feel I'm missing something here.

Because, abge, theorems aren't "proposed," they're *proved.* Once proven, there isn't any possibility of a measurement that would falsify the theorem.

If Pythagoras had proven that a^3 + b^3 = c^3, and we measured a triangle and found a^2 + b^2 = c^2 instead, we would just have to conclude that one (or more) of the premises or axioms did not apply in our actual universe -- not that the theorem was wrong.

This is actually really close to an easily imaginable idea -- that we should find a triangle where a^2 + b^2 = c^2 DOESN'T hold. This has been considered ever since Gauss, and is now considered a very real or even likely possibility due to GR. But when we find one, it won't mean Pythagoras was wrong; it will just drive home that our universe is not Euclidean.

OK I see what you're saying. So, at what point does math becomes science? I'm thinking of a field such a String Theory, which has a lot more math than empirical evidence.

"f Science is the study of the natural world"

This is not a definition of science I've ever seen put up. Anyways mathematics doesn't fit. Aspects of pure speculative mathematics do not have anything to do with the natural world. What does the infinity of primes have to do with the natural world? Nor do I accede to mathematics being the "language of science" for the above reasons, mathematics doesn't necessarily have anything to do with science.

Science is a method, it is not a subject of study. As such mathematics and engineering do not qualify, because they do not follow the method. Science relies on observation as its proof. Mathematics relies on logic. Mathematics is more appropriately conjoined to philosophy, not to natural science.

Theory is not a concern to engineering and some branches of engineering seem almost gleefully atheoretical. I'm thinking specifically of civil engineering. Urban design is a mess thanks to its reliance on civil engineers. Its atheoretical quality disqualifies it from being a science.

Didn't see Semck's post before I made mine. My thoughts can be subsumed into his.

That's a really interesting question. Of course, whether string theory is science is itself very controversial these days, even among physicists.

But before talking about string theory, I think it would be helpful to think more about general relativity (GR), which I think also presents a really borderline case. GR is a theory which people believe, on the basis of various experiments, to be an accurate description of how the universe works (on scales above the quantum, anyway). However, it's notoriously mathematically difficult, and there are quite a few mathematicians who spend their lives striving to figure out just what the theory actually says, i.e. what its consequences are.

Are these people doing science? I think it's a thorny question. The activity they're involved in is not essentially scientific, in the sense that they're largely not interested much (if at all) in empirical tests of anything they prove; and they proceed as mathematicians, proving theorems. On the other hand, because they happen to be working on a poorly-understood theory that is, nevertheless, believed for empirical reasons to describe our universe, their results can have major direct impact on what we believe to be true about the physical world. (Much like results in Euclidean geometry back when we thought space was Euclidean).

So I think it's something of a gray area. These people are fully engaged in mathematics and mathematical epistemology, and in particular are proving things mathematically. But they also have the potential to make discoveries about the real world, because empirically, the theory has already been tested.

(Of course, it's also possible that they would derive a new consequence which would then actually be falsified, and GR would then be discarded, after all. In that case, their results would still be true math, but we would no longer consider it descriptive of our universe, which highlights the sense in which they are and aren't doing science).

Back to string theory, then: I think it's the same as GR, except that in this case, the theory hasn't even been tested yet. So what you have is a physical theory about the universe, and mathematicians (and physicists) are working hard to figure out just what the heck the thing says so that maybe, some day, it can be evaluated empirically. (Which is looking worse and worse). Perhaps eventually it will be decided that string theory isn't good physics (for example). Then the physicists who worked on it will be sad; and the mathematicians will say, "Huh. Too bad the universe doesn't work that way, but look at the great math we discovered!"

I agree about engineering. Both the goal and methodology is different from science. I'm not exactly sure what your problem with Civil Engineering is though. The Civil Engineers I know have a pretty solid understanding of physics. A lot of people are responsible for building a whole city. Not sure you can lay the blame on 1 subset for a poorly designed city.

Math science social studies and language arts are all used in each others categories language arts could have history and math in it. Science could have math history and language arts. math has science and language arts and history has science language arts and math so basically all subjects are connect in a way through education.

So basically its all the same core and sub classes are all the same because well if you guys remember like a math final it would have a LONG sentence problem and it could be about a famous scientist chemistry set and you would have to find all of the possible outcomes then try to find the right answer out of it. Engineering has math and science in it but also you need to learn some new vocabulary words with the subject so that's where English comes in. then you could research who created or who discovered said item and that's where history comes into play. =)

Math, language arts, science and history started all the others sub core classes in school but the real question should be which one of the four came first? =)

LEGION, I'm really excited to watch your YouTube channel tonight.

This lecture was enlightening on the predominance of civil engineers in urban design. Especially watch beginning around the 26th minute for graphic charts on their predominance.

https://www.youtube.com/watch?v=X69sSSegiDk

Personally I really like the influence civil engineers have had on urban design, though I realize that (among people who care about cities) that may be a minority position.

Well we try to make it entertaining I recommend the mario kart or the star wars battlefront II videos those are my favorite but the groups favorite is the super monkey ball and I will give you a hint on which one of the screaming idiots is me if you watch that one I'm the one who got stuck on a level with giant balls for half an hour.lol that sounded kinda wrong. @abgemacht last Night me and another member of my group made a cod waw nazi zombie video it may not be posted right away. Our tech guy needs to leave few days.

For a few days.* stupid phone.

Dude can you punctuate, curb the run-ons, or capitalize your posts. They tend to make my eyes bleed.

Yeah sorry when I have alot of info I tend to forget doing that. I know you need to have punctuation in sentences. I will slow down and start punctuating just for you putin.

Ew, no. Math isn't a science.