My first degree is in mathematics, and I am currently pursuing a degree in statistics, so my perspective might be of interest. The analogy made by De Veaux and Velleman (that music is to mathematics as statistics is to literature) in the paper to which Jason linked is interesting, but I think it ultimately falls flat. It is not clear to me that the prevalence of prodigies in a field is a good proxy for how much worldly experience one needs to excel in a field. (Mozart's early music is not particularly engaging, either intellectually or emotionally; many mathematical prodigies make no substantial contributions to the field.) Their discussion of the differences between teaching math and teaching statistics compares poorly taught math courses, in which answers are given neatly and creativity is discouraged, to ideally taught statistics courses, in which students are opened to an entirely new way of looking at the world. I do not find this comparison convincing.
Kalyan is, I think, getting to the heart of the matter. To define a field of study, I think it is best to define not only the subject (e.g., physics concerns itself with certain aspects of nature), but also the means by which the field approaches that subject (e.g., physics uses the scientific method). Without this distinction, it is difficult to clarify the difference between physics and mythology, both of which deal with the nature of the universe.
(The terms "field", "subject", etc. are often used synonymously, but I am using them here to refer to distinct things. I hope the meaning is clear.)
My working definition of mathematics is that it concerns itself with measurement per se, and generalizations thereof. The means by which it does so is a combination of logic and intuition. The logic part is fairly easy to see; the intuition part is specifically an implicit appeal to reasonableness of assumptions (e.g., the selection of axioms) and a general agreement that anything left logically vague in the proof could, in theory, be expressed as a formal logical proof.
Mathematics is not a science. Its methods and proofs are fundamentally different from those of science. A statistical analysis bears far more resemblance to a scientific proof than to a mathematical one.
By this definition (the correct one, of course!), statistics is clearly not a sub-field of mathematics. Statistics, like physics, uses measurement extensively, and therefore the use of mathematics is similarly extensive. That does not make statistics a sub-field of mathematics, though. The approach of statistics to its field is different from the approach of mathematics: the former is a science, and the latter is not.
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Jesse Miller, Ph.D.
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Original Message:
Sent: 07-04-2022 13:52
From: Jason Wilson
Subject: Statistics and Mathematics
Hi all,
Interesting discussion!
There was a paper published in Amstat News some years ago by De Veaux and Velleman that speaks to this issue, though I can't find it on
amstat.org, here's a
copy. I've found it to be an insightful paper.
When I teach IntroStats, I tell my students that they are not taking a math class, but rather a statistics class, and they are different. Though we'll use math in this class, the goal is not to learn the math; the goal is to learn how to discover the truth about the world (i.e. the real, physical world, including human beings) through data. We will learn some mathematics towards that end.
Shalom,
Jason Wilson
Chair, Mathematics and Computer Science Department
Associate Professor of Statistics | (562) 944-0351 x5145
Original Message:
Sent: 7/1/2022 6:46:00 PM
From: Nayak Polissar
Subject: RE: Statistics and Mathematics
HI Elizabeth, it is very impressive on how many sources you found that lump us under mathematics. However, even if 15,000 sources lump us under mathematics, I still feel like a statistician and not a mathematician.
Thanks for finding all those interesting sources.
Humans, gorillas, chimpanzees, baboons, etc., all seem to have come from the same place, but they all are recognized by their separate names and qualities.
Best wishes,
Nayak
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Nayak Polissar
Principal Statistician
Original Message:
Sent: 06-30-2022 20:19
From: Elizabeth Newton
Subject: Statistics and Mathematics
Britannica is not alone.
This site identifies 33 branches of mathematics. Here probability, statistics and game theory are part of applied mathematics.
This site, on the other hand, identifies 10 branches of mathematics, with statistics the 10th (and"easiest"):
This site identifies only 4 branches of mathematics,
"Algebra, Geometry, Calculus and Statistics & Probability are considered to be the 4 main branches of Mathematics".
Elizabeth Newton, Ph.D.
Newton Statistical Consulting
Original Message:
Sent: 6/30/2022 7:19:00 PM
From: Nayak Polissar
Subject: RE: Statistics and Mathematics
That is interesting, Elizabeth, but since we escaped from the British in 1776, I am not sure I am ready to have the British (Encyclopædia Britannica) define what I do. Also, their sales plummeted in the internet era, and I am not sure that they are considered to be the authority that they used to be. (Side note: when I was a kid, I loved looking through Encyclopedia Britannica.)
If we want to aggregate even more, we are all just scientists: physics, chemistry, biology, statistics, geology, mathematics, etc.
LIke the Declaration of Independence, I think that we can declare that the differences are enough that we are on our own boat. Definitely mathematics is a parent, but we have grown up and become our own thing. Just as the tension between Britain and America was intense long ago, and now we are friends (pretty much), so the days of us being just a part of Math Departments (which some statisticians found hard) are mostly over, but we all get along.
Finally, this process of defining new entities is not over. There are now Departments of Biostatistics. And Statistics has also calved "Data Science," and Data Scientists are now happily defining themselves as different.
On we go.
Best wishes,
Nayak
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Nayak Polissar
Principal Statistician
Original Message:
Sent: 06-30-2022 17:10
From: Elizabeth Newton
Subject: Statistics and Mathematics
There are so many branches of mathematics. Statistics seems to be widely considered to be one of the branches.
From Britannica:
Among the principal branches of mathematics are algebra, analysis, arithmetic, combinatorics, Euclidean and non-Euclidean geometries, game theory, number theory, numerical analysis, optimization, probability, set theory, statistics, topology, and trigonometry.
Elizabeth Newton
Newton Statistical Consulting.
Original Message:
Sent: 6/30/2022 1:41:00 PM
From: Harry Khamis
Subject: RE: Statistics and Mathematics
I will share a story that relates to this line of discussion only because it is, in my opinion, fascinating.
I worked at the Department of Mathematics and Statistics at Wright State University (WSU) for 35 years. In the mid-1980s the great David Blackwell came to WSU to visit the African-American Student Union ("Bolinga Center"). The Bolinga Center generously allowed our department to borrow Dr. Blackwell for a couple of hours for a brief visit and colloquium. Shortly before his talk, during general banter, he said "I find that statisticians understand mathematics talks better than mathematicians understand statistics talks." I'm afraid the mathematicians in the department were privately upset by this statement.
I suppose one can argue the veracity of such a statement endlessly, but that a person of such stature should make it is, as I mentioned before, fascinating.
Harry Khamis
Professor & Director Emeritus
Department of Mathematics & Statistics
Statistical Consulting Center
Wright State University
Dayton, OH
Original Message:
Sent: 6/29/2022 7:01:00 PM
From: Nayak Polissar
Subject: RE: Statistics and Mathematics
This is a fun and interesting topic. The following may be out of left field, but i have found that when I have hired graduate students for statistical support, it did not work so well when I hired graduate students from the mathematics department. The students from the statistics or biostatistics department usually worked out quite well. I don't think the difference was that the students with a statistics background had learned the things that I needed. No, in learning new material the mathematicians did not "get it" as quickly as the statisticians did. Statistical work involves a different way of thinking than mathematical work. Neither one is better or worse than the other, they are just different. They are quite different fields because of the different kind of imagination and way of thinking involved. There is my 2.04 cents worth on the topic.
Nayak
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Nayak Polissar
Principal Statistician
Original Message:
Sent: 06-29-2022 18:21
From: Alexandra Kapatou
Subject: Statistics and Mathematics
Hi Michael,
In my opinions statistics is not mathematics, because all data and all random variables have distributions. Most (if not all) statistical ideas are based on reality and on randomness. Mathematics is absolute in many ways. Mathematics also uses a lot of imagination (think of the properties of symmetry and all possible structures that can come from this). So, philosophically, statistics and mathematics are very different.
Now, statistics uses many mathematical results in proofs, but so does physics. This does not make physics an area of mathematics. The same is true for statistics.
However, people who love mathematics can also learn statistics, but they may not love it.
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Alexandra Kapatou
Hurst Senior Professorial Lecturer
Original Message:
Sent: 06-29-2022 15:53
From: Michael Anderson
Subject: Statistics and Mathematics
Hello all,
I haven't given this much thought, but with a current collaboration, I can use your knowledge on the topic.
Is the field of statistics a branch of mathematics, science or something else all together. The always reliable WWW is all over the place on this topic saying:
- Statistics = branch of mathematics
- It is a separate discipline and not a branch of mathematics.
- Statistics is a branch of applied mathematics.
- Statistics is a mathematical science.
- Statistics is an applied science.
- Many universities have their Department of Mathematics and Statistics
Some solid wisdom on the topic would be appreciated.
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Michael J. Anderson
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