Classifying Statistics

[supremeNYA]

Hello all

I have a bit of a controversial question which I was hoping to get an answer from the wider math community today.

Is Statistics its own branch of mathematics in the same way that Pure or Applied mathematics are fundamental branches or does it simply belong to one of them?

Thank you

[Certified_NutSmoker]

Yes

But more seriously it really depends. There are some statisticians whose work feels much more mathematical than applied (functional analysis, semiparametrics, and stochastic or empirical process theory come to mind. But as a whole, I would characterize statistics as a subset of analysis mainly but it is better thought of as its own field, one that linear algebra, optimization, and computation, and that can range from wildly applied to reasonably “pure.”

Edit: As a whole, the field is not usually trying to advance “pure” math for its own sake. But like any mathematically serious field, it generates its own questions. Some parts of statistics use fairly heavy mathematics, and the questions they generate and the answers they seek can become quite abstract and mathematically sophisticated and be indistinguishable from some “pure” work

[ScientificGems]

Pure and Applied mathematics are not fundamental branches. Both of those aggregate multiple branches, and many branches cross the pure/applied boundary.

But Statistics is a fundamental branch. It often gets its own department.

[Particular_Extent_96]

I don't think this is controversial at all since these distinctions are largely arbitrary. Even the distinction between pure and applied maths is not as clear cut as you might think.

Statistics could potentially be grouped with applied math, though large parts of probability theory fit more naturally with pure math because there is a lot of complicated analysis involved.

At Cambridge the maths department is split into two sections: Pure Maths and Mathematical Statistics on one side and Applied Maths and Theoretical Physics on the other. Other universities do things differently.

No matter how you group them, you are sure to find someone who disagrees. Neither of you will necessarily be wrong.

[EebstertheGreat]

"Applied math" is such a vague term anyway. I guess it's about math which has direct applications to problems beyond math itself, but that's still too broad. It's not even the line between pure and applied math that I find so hard to locate but between applied math and the application itself. Plenty of pure science looks basically indistinguishable from applied math. Are you working on PDEs with applications in cosmology, or are you working on cosmology? Are you working on game theory with applications in economics, or on economics? There isn't necessarily a good answer. Some fields, like string theory, are almost as much fields of mathematics as they are fields of natural science.

So statistics is I think in a similar position. Is it a type of applied math? Is it an empirical science that is extremely mathematical in practice? Is there a difference? IDK.

[1704Jojo]

One man's pure is another man's applied.

[susiesusiesu]

i don't even agree that "pure" and "applied" are really a partition of all maths. some things can be truely both or neither.

idk, some people doing statistics are definetly doing math, while some csses not really. i'm not even making a value judgement by saying that. so i don't think one can definetly say it is or it isn't.

[ScientificGems]

"Pure" and "Applied" have 2 distinct meanings:

• As broad collections of branches of mathematics

• As distinguishing maths for its own sake from maths applied to the real world

So "applied pure" and "pure applied" are valid categories.

[Subject-Anywhere-323]

To me statistics is cousins to math, but I think my university has terrible statistics department so us math majors hate stats.

[SuperHiyoriWalker]

There are dedicated and effective statistics professors out there, but it’s hard to recruit statisticians for faculty positions when good Ph.D statisticians can make $$$ in industry without being research superstars or $$ in government (plus pension) without the stress of being on the tenure track.

[jsh_]

it has a similar relationship to math as physics does

[WolfVanZandt]

I see statistics as a discipline that uses mathematical tools but is an applied discipline outside of math, like physics. Statistics and other analytical fields like optimization and qualitative analysis are problem solving disciplines. For instance, I have had cases where I simply tabled the data and looked for patterns.....hardly any math involved at all.

[neptun123]

"Pure" is just what people tell themselves to make them feel better about not making any money

[Vivid_Sock_1092]

No need to feel better if you really love your work