If statisticians are mathematicians then so are physicists and engineers.
Using math is different from being a mathematician. Mathematicians discover new mathematical principles, not just make use of existing ones.
this post was submitted on 02 Jul 2026
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Yeah I don't think this is the burn on statisticians OP makes it out to be. Lots of technical disciplines use mathematics, like... all of them I think? I don't know of any field that doesn't incorporate math that isn't purely artistic.
Also why are dentists catching strays?
Statisticians are typically lumped in with mathematicians because Statistics is typically treated like a mathematics course. This isn't really the case with other technical disciplines.
Dentists are catching strays because they're likewise kinda considered "doctors" in a medical sense. They're specialists in their own field that get lumped in with the more general field by a quirk of categorization.
I don't know how it is elsewhere, but in the US they aren't "kinda considered" doctors, they are doctors. They have terminal medical degrees and practitioner's licenses same as any other medical practitioner. They're kinda segmented off from the rest of medical practice because of how dentistry evolved alongside other historical healing practices, but they are doctors.
Second, is statistics not a branch of mathematics? The courses I took on probability and statistics were taught by the math department. I don't see how it can't be. Is it "pure" math? Depends on how you define pure but probably not. Is it "easy" math? Arguably some of it is, though I think people who think stats is an easy science probably aren't very good at it. All that I get. But the idea that it is (uniquely among technical disciplines) "not math" is... confounding to me.
I think the chasm really is within the statistics discipline, less so between statistics a d mathematics. If you're doing statistics research you're essentially a mathematician in the statistics subfield. If you're applying statistics in another field, you're a statistician in the professional worker sense.
I think that's so, but that relationship between theory and application exists for every technical discipline. Computer scientists vs software engineers, for example. The line is usually blurry; I tend to operate closer to the applied side of software, for instance, but I still think about and am informed by the theoretical side, just as theory is shaped by the experimental results of application.
"Mathematics" is an odd case because what people call "pure mathematics" is upstream of even the theoretical side of technical specialties. Like, what a theoretical mathematician might call an applied mathematician, I might call a data scientist, because they're closer to pure theory than I am, but still closer to technical application than the theoretical mathematician. It's a super-theory that underpins other theoretical domains.
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Statistics results change based on the lens through which you interpret the data. Pure math doesn't do that. Assigning probabilities is arguably pure math, but assigning error bars is purely subjective. It's more a reflection of the subjective selection and definition processes than of the underlying probabilities.
assigning error bars is purely subjective
I don't know where you got this idea from but it is incorrect. Error bars are used to indicate uncertainty in measurements and they are used to indicate confidence (or lack thereof) in those measurements. Measurement is hard, and precise measurement is harder, so engineers of all stripes use error bars to indicate how precisely their data have been recorded. It's not just a stats thing.
also this:
results change based on the lens through which you interpret the data
happens in every field, including pure mathematics. Look up the axiom of choice if you would like a lot of further reading about the implications of interpreting mathematics through that particular lens. Much as we may long for a "purely objective" language of the universe, free from the limitations of human interpretation, we haven't discovered it yet. The best we can do for now is try to make good assumptions and build from there.
Assigning probabilities is arguably pure math
Not even that is pure math. It depends on your prior knowledge, for example if you think one event is more likely. On the other hand if you don't include prior knowledge/assumptions like one event being more likely you're implying that the prior knowledge behaves in a way that makes your combination of probabilities and data the way it is (for example a flat prior, aka every event has the same likelihood, but in some cases it gets even weirder and would effectively force an absurd prior, so you typically just avoid that by defining some prior knowledge beforehand).
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And by extension, so is a cashier.
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Statisticians are somewhere between Sociologists and Psychologists according Mathematicians and between Chemists and physicists according to Statisticians.
Between chemists and physicists is where I would place them too, as someone with a physics degree.
philosophers way to the right of mathematicians saying "oh! I didn't notice you there"
i'm an economist (basically advanced statistics with weird assumptions).
I'd rank them macro econ > sociology > psych > micro econ > stats > bio > chem > phys > > > math > > > > > > > > > > philosophy
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I don't think I will ever figure out the order to read these things.
Just... Why? Wouldn't you want it to be formatted in a way that's immediately obvious what order to read them?
I used bluesky lately (which i guess uses the same format?) and it looks like so because we are viewing a reply(3) to a post (2) that cite another post (1)
Thanks. I hate it.
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Same
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As someone who has taught both mathematics and statistics in his life the real difference boils down to proof Vs evidence.
The mathematician is uncertain because Gödel showed no system can prove its own consistency. Proof is (generally) rigourous enough that this is the main issue; once it has been proven (assuming your axioms are good), it's considered true.
The statistician is uncertain because they work with samples rather than the population. There is also the issue of inferring causation even if your sample isn't unrepresentative. With statistics you're always building evidence, but you can never have concrete proof via statistical methods alone.
Also fun fact, given that there is more than one type of mathematics (e.g. platonist Vs intuitionistic), some giving different answers to the same question (excluded middle/trichotomy on the reals), and all of which are equiconsistent, we realise that mathematics really is just a branch of philosophy (i.e. what axioms are you willing to believe).
Everything is philosophy, ultimately
"statistics" can mean two things: it's a field of mathematics, and it's also the application of that field to the real world.
There are many theorems in statistics: the central limit theorem, the proof of the t-test, for example. This is maths.
But if what you're doing is assuming a certain real distribution is normal, or testing for normality of real data, that's not maths any more.
Just like calculus is real maths, but once you're solving real integrals for real scenarios, you're doing science.
This is a very very very good analogy
And technical analysis is the astrology of the investing world
Statisticians in reality are programmers, typically using R or Python to run models. You only ever touch math in undergrad.*
There's a long tradition of skipping hard math, though-- ever have a stats class that has you looking at a t-table for a critical value? That's because it gives us a cutoff to use instead of calculating a p-value (which is hard).
*Note: statistics majors in PhD programs still need the hardcore math. Matrix algebra, calculus, etc. Who else is gonna make the packages we use?
I took statistics with Roger Purves. I distinctly remember him saying that stats wasn't "math" in his intro lecture.
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I have a graduate degree in statistics and use it heavily in my job. I always tell people that mathematicians study math, but statisticians just use math the study data.
To badly paraphrase Mark Twain..."There are lies, damned lies, statistics, and polls!".
Even the original quote isn't from Twain. He misattributed it to British PM Disraeli, but the saying originated after Disraeli's death.
A bit ironic given the quote.
https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics
Cool info. Thanks!
I am oscillating between "math is just applied philosophy" and this.
Terrance Tao is an absolute beast. If you debate him on this you'll get a rigorous proof back on how you're wrong.
Irl they become actuaries. It's usually applied mathematics and if by mathematician one means someone exploring mathematics alone then this is accurate. CompSci kinda falls half into this and half outside of it.
It reminds me of the statement by Clifford Stoll, (paraphrased) the first time you do something it's science, the second time you're an engineer, the third time you're a technician. link.
In essence most statistician work ranges in the engineer to technician level of mathematics.
Then who are the chiropractors?
Are they constantly contradicting the advice of the rest of the mathematicians?
Mathematics is a search for absolute truth, as proven from axioms.
Meanwhile, this is said about statistics: There are lies, damned lies, and statistics.
And even when used in good faith, statistics tends to move toward approximate truth. Statistics can tell you the exact chance that you'll pull a red marble out of a bag of other marbles, but until you actually pull the marble, it still can't tell you exactly what color marble you'll pull. Run the experiment again, and it may turn out differently next time. You never get absolute truth, only percentage approximations.
Very different than other types of math, yes, where 2+2 is always 4, and you can know it for absolute certain in every case for all of time.
Stats is technically math but it's the softest math you can imagine. A huge amount of it is data collection and interpretation. It works different parts of your brain, requires different skills than pure math
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Or the surgeons, who started off as glorified barbers, and to this day don’t get the title of doctor, even though “brain surgery” and “open-heart surgery” are metaphors for tasks requiring extreme skill
What? That must be a thing in other countries. Here in the USA all surgeons are doctors.
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I like to think of them as accountants. They sure use numbers, but I'm not sure what they're doing with them is in a'y way shape or form morally acceptable.
In that case probability theorists are the chiropractors of math
Most of them won't do mathematics research. And since realistically it is quite hard to both innovate in mathematics and in an applied field at the same time, the differentiation is valid.
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That's why I was happy that my math course in uni was just 90% statistics
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