People Twitter

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.

Statisticians are somewhere between Sociologists and Psychologists according Mathematicians and between Chemists and physicists according to Statisticians.

https://xkcd.com/435/

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?

7 out of 5 statisticians say yes

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).

"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.

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?

This is a very very very good analogy

I am oscillating between "math is just applied philosophy" and this.

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.

And technical analysis is the astrology of the investing world

Are they constantly contradicting the advice of the rest of the mathematicians?

To badly paraphrase Mark Twain..."There are lies, damned lies, statistics, and polls!".

Terrance Tao is an absolute beast. If you debate him on this you'll get a rigorous proof back on how you're wrong.

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

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.

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.

That's why I was happy that my math course in uni was just 90% statistics

Then who are the chiropractors?

I was a music history major, and we had to take 2 math courses, and one had to be Acoustics, which we were all afraid of, and waited until we were seniors to take it, and then it turned out to be pretty easy. I ended up working for a classical record label, and used my acoustics knowledge pretty often during recording sessions. I became the guy they talked to about acoustic treatments in the recording halls and such. We even switched recording halls, when I figured out that the hall sounded better when there were pillows in the seats to simulate people. I got an A in that class.

The other math class I took was Statistics. I was terrible in Math during high school, and barely survived Algebra 2. I was not looking forward to more of that, and statistics sounded like it had a real-world use that I could understand, and I was right. I could understand the math because it had a reason that I could see, unlike the abstract nature of most math. I got a B in Statistics, which I was really proud of.

I still use my statistics knowledge to this day, whenever one party or another starts crowing about a new poll, and I see that it had a tiny sample size, and a margin of error of 5%+, and it is essentially useless poll.

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.

Most STEM scientists i know end up doing statistics instead because it's easier to have a paycheque

In that case probability theorists are the chiropractors of math