[BengalTiger]

Q: What is the difference between a Ph.D. in mathematics and a large pizza?
A: A large pizza can feed a family of four...


An engineer and a physicist are in a hot-air balloon. After a few hours they lose track of where they are and descend to get directions. They yell to a jogger, "Hey, can you tell us where we're at?" After a few moments the jogger responds, "You're in a hot-air balloon." The engineer says, "You must be a mathematician." The jogger, shocked, responds, "yeah, how did you know I was a mathematician?" "Because, it took you far too long to come up with your answer, it was 100% correct, and it was completely useless."

[Herra Tohtori]

No it isn't.

Math doesn't follow the scientific method. Theory in science has a different meaning than theory in math.

Now you're generalizing natural sciences to mean all science. Which they don't. Mathematics is in my opinion a science just as much as physics; it just researches abstract concepts rather than sticking to describing reality... natural sciences just pick the tools from mathematics that fit best in describing their theories in a formal sense most accurately. Good example would be Einstein using Riemannian geometry in General Relativity.

Of course mathemathics isn't an empiric science, but as for not following scientific method... I have to disagree on that, mathematicians can also have hypotheses and conjectures and they have to confirm them with experimenting (calculations) with the set variables or axioms - the only difference is that experimentation doesn't happen in real world but rather within the abstract set of rules defined in the hypothesis. For example Fermat's last theorem (actually a conjecture until it was proven) is a good example of a hypothesis that wasn't proven to be true until several hundred years after it's postulation (because the original proof didn't fit into the margin of the page).

Proving something with mathematical logic can be just as tricky as setting up reliable experiment to negate unknown variables to prove some physical hypothesis... it's just a bit different kind of science.

[Ghostavo]

Now you're generalizing natural sciences to mean all science. Which they don't. Mathematics is in my opinion a science just as much as physics; it just researches abstract concepts rather than sticking to describing reality... natural sciences just pick the tools from mathematics that fit best in describing their theories in a formal sense most accurately. Good example would be Einstein using Riemannian geometry in General Relativity.

Of course mathemathics isn't an empiric science, but as for not following scientific method... I have to disagree on that, mathematicians can also have hypotheses and conjectures and they have to confirm them with experimenting (calculations) with the set variables or axioms - the only difference is that experimentation doesn't happen in real world but rather within the abstract set of rules defined in the hypothesis. For example Fermat's last theorem (actually a conjecture until it was proven) is a good example of a hypothesis that wasn't proven to be true until several hundred years after it's postulation (because the original proof didn't fit into the margin of the page).

Proving something with mathematical logic can be just as tricky as setting up reliable experiment to negate unknown variables to prove some physical hypothesis... it's just a bit different kind of science.

Science is an attempt to describe reality. Mathematics makes no such attempt therefore incapable of being described as science. Science makes use of mathematics, but as a tool, not as an adjacent field.

Regarding the scientific method, no, mathematics doesn't use it. Theories in mathematics are not falsifiable (Fermat's last theorem as you stated, wasn't a real theorem, it was only dubbed as such because it was such highly regarded) and therefore cannot be regarded as scientific theories (again, to express the point, it isn't science). Yes, they are similar but not the same.

Regarding dificulty, it's not really the point is it? I'm by no means trying to demean either science or math. Just pointing out they are not the same and one isn't a field of the other.

P.S.
And to make matters worse, the words theory, conjecture, hypothesis, axioms and so on have different meanings in mathematics and science.

[Col. Fishguts]

The graph is data from the COBE mission, which looked at the background microwave glow of the universe and found that it fit perfectly with the idea that the universe used to be really hot everywhere. This strongly reinforced the Big Bang theory and was one of the most dramatic examples of an experiment agreeing with a theory in history -- the data points fit perfectly, with error bars too small to draw on the graph. It's one of the most triumphant scientific results in history.

COBE mission

[Herra Tohtori]

Science is an attempt to describe reality. Mathematics makes no such attempt therefore incapable of being described as science. Science makes use of mathematics, but as a tool, not as an adjacent field.

Natural sciences are an attempt to describe reality. Formal science such as mathematics and logic are different, their working methods and sujects of research are different, but it doesn't mean that they aren't science. I'm not trying to say that mathematics is a natural science, but you are apparently trying to say that if something is not natural science, it's not science at all, which is at best ignorant of origins of the term "science" and at worst downright insulting to every science maker not researching natural sciences because apparently their work is not science...

No disrespect but I dislike it when people overgeneralize things. It is unfortunate that the term science has managed to galvanize itself as synonyme to natural science in English language and subsequently in many others as well, but in my opinion it would be a good thing not to synonymize science and natural science, and rather keep science as an umbrella term. I don't make languages, but this practice doesn't make much sense to me since quite obviously there are a lot more branches of science than natural science...

Regarding the scientific method, no, mathematics doesn't use it. Theories in mathematics are not falsifiable (Fermat's last theorem as you stated, wasn't a real theorem, it was only dubbed as such because it was such highly regarded) and therefore cannot be regarded as scientific theories (again, to express the point, it isn't science). Yes, they are similar but not the same.

Yeah, but again that's only because scientific method is defined as a method used by science, specifically natural sciences. I see circular logic or something here - science is science because it uses scientific method; scientific method is the only way to make science because it's scientific; therefore anything that doesn't use scientific method cannot be science?

Formal sciences like mathematics and logic use a priori methodology rather than the scientific method used by natural sciences, but science originally meant knowledge (and technology meant art or skill), and mathematics certainly is knowledge. I don't see a problem in saying that mathemathics is a science, and sociology, and anthropology and whatever, as long as one differentiates between natural sciences and formal sciences and social sciences.

Regarding dificulty, it's not really the point is it? I'm by no means trying to demean either science or math. Just pointing out they are not the same and one isn't a field of the other.

True and I agree that they aren't the same. Which is exactly why I think using an umbrella term like science as synonyme to just natural sciences is a bit narrow view on the matter. I don't think that the term science should be limited to natural sciences just because the linguistic definitions say so.


Summa summarum, we agree on the facts but disagree on terminology, it appears.

[CP5670]

This issue has been debated for hundreds of years and there is no clear answer to it. You might find this article on it interesting. Depending on how you look at it, math can be seen as either a science, an art or both.

As for experimentation, that is actually common in math. A theorem is an irrevocable fact, but the process of actually discovering that theorem is essentially experimental. One way to think of a published proof is a set of instructions for a reproducible experiment that anyone can carry out and get the same result.

[Ghostavo]

Natural sciences are an attempt to describe reality. Formal science such as mathematics and logic are different, their working methods and sujects of research are different, but it doesn't mean that they aren't science. I'm not trying to say that mathematics is a natural science, but you are apparently trying to say that if something is not natural science, it's not science at all, which is at best ignorant of origins of the term "science" and at worst downright insulting to every science maker not researching natural sciences because apparently their work is not science...

No disrespect but I dislike it when people overgeneralize things. It is unfortunate that the term science has managed to galvanize itself as synonyme to natural science in English language and subsequently in many others as well, but in my opinion it would be a good thing not to synonymize science and natural science, and rather keep science as an umbrella term. I don't make languages, but this practice doesn't make much sense to me since quite obviously there are a lot more branches of science than natural science...

http://en.wikipedia.org/wiki/Formal_science

However, many scholars oppose including formal science as a branch of science. They admit that formal science is a very powerful tool to natural and social science, but it does not mean formal science is science. Most importantly, they define science as the discipline using scientific method which bases on observation and empirical study. As knowledge in formal science is a priori and always constructed by rules of deduction from axioms and definition without any empirical study, they refuse to classify formal science as a branch of science.

Basically what I've been saying all along.

Yeah, but again that's only because scientific method is defined as a method used by science, specifically natural sciences. I see circular logic or something here - science is science because it uses scientific method; scientific method is the only way to make science because it's scientific; therefore anything that doesn't use scientific method cannot be science?

Formal sciences like mathematics and logic use a priori methodology rather than the scientific method used by natural sciences, but science originally meant knowledge (and technology meant art or skill), and mathematics certainly is knowledge. I don't see a problem in saying that mathemathics is a science, and sociology, and anthropology and whatever, as long as one differentiates between natural sciences and formal sciences and social sciences.

See above and again, if a scientific theory isn't falsifiable, it isn't scientific in the first place.

Also, every branch of science uses the scientific method. If it doesn't use it, what does it mean to be a science? Sociology uses the scientific method, anthropology uses the scientific method. Therefore they can be regarded as science.

True and I agree that they aren't the same. Which is exactly why I think using an umbrella term like science as synonyme to just natural sciences is a bit narrow view on the matter. I don't think that the term science should be limited to natural sciences just because the linguistic definitions say so.


Summa summarum, we agree on the facts but disagree on terminology, it appears.

I think it goes a bit beyond that but, yes it's basically that.

In the end, it seems we aren't the only ones who disagree with even mathematicians disagreeing about this.

[Scorpius]

Im glad that my misnomer has generated such an interesting debate but let me clarify my point.  I used the example of Calculus because without it physics, chemistry and much of biology wouldn't exist.  I believe mathematics is a form of science because it is a logical approach to explaining the nature of the universe.  Just because much of the modern mathematics doesn't seem to apply to "Real life" doesnt mean the rest of math has no use in explaining the natural world. In other words, I fail to see the difference between modern physics and math.

[Aardwolf]

I like the xkcd panel.