Mathematicians should stop naming things after each other

Hard disagree.

Once you get to the advanced levels of any field, terminology being "accessible" doesn't really matter, but being precise does.

Areas like philosophy and law actually suffer in my opinion when they overload common words with uncommon meanings, or descend into weird disambiguations that depend on suffixes.

For example, in philosophy there's "contractarianism" and "contractualism", and trying to remember which is the general term and which refers to a specific theory drives me nuts. (If "contractualism" were just known as "Scanlon's theory" it would be a lot easier.)

Naming things after their creator is actually super-helpful because it's really easy to disambiguate, helps situate things historically, and once you're at that level there often isn't a single unique word or phrase that can easily encapsulate the idea anyways and isn't easily confused with something else.

> Imagine how much steeper the learning curve would be in medicine or law if they used the same naming conventions, with the same number of layers to peel back:

I she kidding? Off the top of my head: diseases named after people. Parkinson's disease. McArdle's disease. Bell's Palsy, Hodgkin's Lymphoma, ...

https://en.wikipedia.org/wiki/List_of_human_anatomical_parts...

In Law, precedents are referred to by plaintiff and defendant names: Smith vs. Klein. There are laws named after people, e.g. in the US. Kirsten's Law; Mann Act; Wetterling Act; Sonny Bono Copyright Extension; ...

Meh, that's like saying it's so hard to remember San Francisco from San Jose from Mountain View from Palo Alto, why can't we just name them as Big Sea City, Big South City, Middle Town, and Expensive Town.

I.e., it's a fake problem that only sounds plausible to outsiders - if you live in the Bay Area, then Mountain View being called Mountain View is the least of your problems in driving to Mountain View.

This is one of those articles that might sound convincing to non-mathematicians (because it is annoying to learn names for difficult concepts, and many people can relate to that experience), but will not sound all that convincing to domain experts.

It'd be hard to deny that descriptive terms are easier to memorize. Sometimes a piece of natural and/or physical intuition allows such terminology to arise.

Scientist and mathematicians do tend to think about terminology quite frequently: communicating with other scientist and mathematicians is a major part of doing science, and "the reviewers couldn't follow your argument" is a valid, and not especially rare reason for rejected articles in mathematics. Given the amount of thought put into it, "intuitive" names do tend to come about when possible (as it happened with what we now call the Ham Sandwich theorem, the concept of Fibration, the Squeeze Lemma, and countless others).

Given that mathematicians do put thought into terminology, there's often a good reason for not having more intuitive names: maybe no good common-sense intuition was available (e.g. Chu constructions are too general for this sort of thing), or the thing comes up only in highly specialized contexts where it's not worth bothering with it (e.g. Girard's paradox), or there are too many different metaphors that one would have to invoke to describe the situation appropriately, so that it's more efficient to derive a completely new term from an associated name (e.g. Abelian became such an adjective, which now has its own associations).

It's telling that the author criticizes terms like "Calabi-Yau manifold", but doesn't suggest any alternative: coming up with an insightful name that communicates the key properties of such an object, and is easier to use and remember than "Calabi-Yau" is, let's just say, very very hard.

The same phenomenon is not limited to mathematics. Would Dijkstra's algorithm, the Haber–Bosch process or the Otto cycle be easier to learn and remember if they had snappy, insightful names? Probably. But the same concerns apply. It's hard to come up with genuinely better, more descriptive names for these processes. And even if we were successful in popularizing newer, better names, we would find that the names were not the real bottlenecks that made computer science, chemistry or mechanical engineering difficult to master.

I don't think descriptive names per se would be especially helpful. The challenge of understanding a concept typically dwarfs the challenge of remembering a name.

Some people, though, have so many things named after them that Googling for concepts can become challenging. In my thesis, I needed to use something called the Steiner point, which is sometimes also called the Steiner curvature centroid, although I didn't know about this name at first. For a convex set K, this is the limit, as R goes to infinity, of Bar(K + B(0,R)), where Bar(L) denotes the barycenter of L. This is the unique continuous map S on convex sets with the two properties

(i) S(K) is in K for all K

(ii) S(aK + bL) = a S(K) + b S(L).

It is also the map on convex sets satisfying (i) which has the smallest possible Lipschitz constant when the space of compact convex sets is endowed with the Hausdorff metric.

It took me a while to get a thorough enough grasp on the literature to learn these things, though, because when you Google "Steiner point", you mostly get stuff about a triangle center, also named after Steiner, which is a totally different concept. It's not that I thought this other triangle center was the Steiner curvature centroid, it was that I literally didn't know what to search for in order to get results on the Steiner point I was interested in.

Here we see the classic tension between synthetic names and natural names.

The best discussion I've seen of this topic is in the 1st chapter (which is fortunately freely accessible and concise) of this excellent programming book:

https://leanpub.com/elementsofclojure/read_sample

Relevant excerpt:

> Most natural names have a rich, varied collection of senses.3 To avoid ambiguity we must use synthetic names, which have no intuitive sense in the context of our code.

> Category theory is a rich source of synthetic names. ‘Monad’, to most readers, means nothing. As a result, we can define it to mean anything. Synthetic names turn comprehension into a binary proposition: either you understand it or you don’t. Between experts, synthetic names can be used to communicate without ambiguity. Novices are forced to either learn or walk away.

> Conversely, a natural name is at first understood as one of its many senses. Everyone understands, more or less, what an id is. In a large group, however, these understandings might have small but important differences. These understandings are refined, and gradually converge, through examination of the documentation and code. At the cost of some ambiguity, novices are able to participate right away.

> Natural names allow every reader, novice or expert, to reason by analogy. Reasoning by analogy is a powerful tool, especially when our software models and interacts with the real world. Synthetic names defy analogies,4 and prevent novices from understanding even the basic intent behind your code. Choose accordingly.

This falls a little flat with me. Let's consider an example from the article- a Kähler manifold. I'm not a geometer, so I looked it up on Wikipedia, and it says that a "Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure." https://en.wikipedia.org/wiki/K%C3%A4hler_manifold

Two of those things are not named after a person, and none of them are understandable without special training. Naming something after a person doesn't make it any harder to understand unless there are multiple things named after that person and you can't figure out which they mean from the context.

In case you're wondering about those structures, here is what Wikipedia has to say about them:

- A Riemannian manifold "is a real, smooth manifold, M, equipped with a positive-definite inner product g_p on the tangent space T_p M at each point p."

- "A complex manifold is a manifold with an atlas of charts to the open unit disk in C^n, such that the transition maps are holomorphic."

- "A symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form ω, called the symplectic form."

The only thing in the above descriptions accessible to non-specialists is probably that the Riemannian manifold is probably named after that guy that they heard of in calculus class. Let's not get rid of our ability to honor people in a failed attempt to make the communication more effective. You can call a Riemannian manifold or a Kähler manifold whatever you want, but it's not going to prevent someone from having to spend years before they are able to understand them.

Yep; check out how the programming community does it! We have descriptive names for things like "Apache", "React", "nginx", "Rust", and "Java"!

I have often found eponyms confusing and I try to avoid them when a good alternative exists. Take "Gibbs free energy" as an example. I had trouble remembering what it is compared to "Helmholtz free energy", but then I learned that "Gibbs free energy" is actually "free enthalpy", at which point I could remember it more easily. Perhaps my point isn't that eponyms are bad, per se, but that it is much better to have descriptive names if possible, and better yet to have self-discoverable and structured names.

Stigler's law [1] also exists, and I have found far too many eponyms to be named after people who had nothing to do with the concept (and sometimes they did not want their name attached to it even).

Eponyms have the advantage of being short and simple. Descriptive names can be pretty wordy. Take "Mach number" as an example. Surely I can call it the "ratio of the velocity to the speed of sound", but that's pretty much the definition at that point. "Mach number" saves a lot of space. Terms like "sonic number" or "sonic ratio" could also work, but everyone already knows what the "Mach number" is, so there is no point in introducing a new word needlessly and sowing confusion (in my opinion).

[1] https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy

I fear the alternative would be all the good names becoming heavily overloaded: https://en.wikipedia.org/wiki/Normal.

Not sure how feasible or necessary this is in general, but there are certainly some places for improvement.

Some more modern examples than "isosceles":

- Heaviside function → step function (edit: though maybe this one is, amusingly, already descriptive by accident?)

- Fourier domain → frequency domain

While I'm here, just a couple suggestions from me:

- Markov chain → memoryless chain

- Lebesgue integral → horizontal integral

I think the reason is that the concepts are so abstract, no concrete word makes sense. So in the face of an arbitrary choice people use names.

The situation isn't much better in computer science, where now when you look up half the simple nouns in the dictionary, you get some language, tool, or javascript library claiming it.

The lack of eponymous names used in category theory, for example, do nothing to aid in learning it. The term functor is no more descriptive than Carnap mapping.

Some profiling would show that names increase the difficulty of math by 0.001%. I don’t see an issue here.

I agree that this article is basically preposterous. But there is a grain of truth in it.

The foundations of algebraic geometry were basically rewritten in the 1960s by Alexander Grothendieck, perhaps the greatest mathematician of the 20th century. He found names to be extremely important, and many of the basic objects that he developed have very carefully conceived and suggestive names: schemes, stacks, topoi, etale morphisms, dessins d'enfant,... none of which will I attempt to define here. But all of these have stuck.

On the other hand, things other than the foundations of the subject? Sure, name it after who did it. Suggestive names aren't really possible for most stuff.

This seems to misrepresent why people bother naming things. It's not like mathematicians are spending their time randomly naming every object/property/structure/... they encounter just for the sake of it.

A "Kähler manifold" exists, as a name, because there is no way to fully describe what it is (and bring forward in the reader all the corresponding context) in two or three words. Using a long sentence (full of things that could themselves be artificial labels, recursively) instead would be a waste of everyone's time.

If one can use a short descriptive name for something, then it's not a name, it's just the thing, and everyone refer to it directly. And when you can't, or when you want to indicate its importance, or you want to neatly package all the relevant context about it, all the mathematical baggage that should come with it in something short, then the pretty obvious thing to do it to abstract it away and stick a label on top.

It doesn't really matter whether they use mathematicians, flower names or characters from The Lord of The Rings, as long as it's unique enough, in context, then it's fine. The names become part of the vocabulary of the field, just as much as supposed "descriptive" names. All those "descriptive" names have to be precisely defined too anyway, because they carry natural-language connotations, assumptions, and so on, that just don't apply.

Tangential--I used to work with a lot of caves as a hydrogeologist:

Seven favorite cave names: Abisso "Queen Mama", Big Cave with Bats, Cave of the Swords, Eisriesenwelt (world of the ice giants), Hell Below, Lemon Drop, Mad As A Wet Hen Pit

Nice caves, but seven names that could use some help: Carroll Cave, Ellison's Cave, Fitton Cave, Kartchner Caverns, Lehman Cave, Lilburn Cave, Russell Cave

> "In the last decade, the field of algebraic geometry was set on fire by “perfectoid spaces” rather than “Scholze spaces” because Peter Scholze kept on calling them that in his talks and papers."

Skip to 5:10 to see Peter Scholze apologize for the name: https://youtu.be/J0QdTYZIfIM

An important thing for name sis that you want them to be immutable because it's hard to refactor both all the writing using that name, and everyone's memory to change the concept of a spheroid from one definition to another.

This makes it hard to choose generic names from the get-go since the first person to use name might not attach it to the best concept for it, making it unavailable for the best concept for the name to describe.

-----

I've always imagined people's names in concept names to be a shorthand for the papers that defined them. Eg. "Calabi-yau manifold" is just another way to write "manifolds as described by calabi and Yau in <well known paper>" and importing all the detailed definitions from that paper. To get the same from properties from a generic name, you need to get a canonical definition that everyone agrees with

The fact that mathematics honors the people that built it is one of the things I love the most about it.

But speaking practically, it’s by far the beat option in many cases. There might be a small number of basic concepts (like dodecahedron or inverse) that can be given actually descriptive names, but for anything even slightly complex it’s impossible, so we end up with a mixture of almost nonsensical and often confusing “descriptive” names, and concepts named after people.

Is it harder to remember and distinguish “Hamiltonian”, “Dirac delta” or “Lagranian” than “cohomology”, “homomorphic” and “homeomorphic”?

Having said that, in many cases the names are quite evocative, like “fibre-bundle”.

If you think plain English words help with this, try either explaining what a compact space is or a normal subgroup. Or, if you don’t know, figure it out from the descriptions on the internet.

And these are not hard concepts as far as maths goes.

Complex things cannot be explained easily. As such, from this perspective, it doesn't matter if a complex topic is named by a person or by some abstract, ridiculously compressed word describing an aspect of it.

But on the other hand, names are simply irrelevant. Anything is better than a name of a person, even if that person was brilliant. The person may be remembered as an aspect of some discovery (say, Einstein), but the concept as such should have some distinct name, not tainted by history, or mere human lifetimes. It should transcend existence as experienced by a human.

I disagree. There are only few cases in which you can describe a mathematical concept with few meaningful words. Like this is the list of number types I could think of. If you don't know it, there is no benefit of knowing what it is called in English. Are rational numbers rational, and are imaginary numbers imaginary? Can the author come up with better name than this, I doubt so.

    Rational numbers
    Real numbers
    Imaginary numbers
    Complex numbers(including imaginary numbers)
    Hypercomplex numbers
    Hyper real numbers
    Surreal numbers

David Hilbert was so prolific that one of his eponymous theorems was also numbered: Hilbert's Theorem 90.

I recall Paul Halmos (https://en.wikipedia.org/wiki/Paul_Halmos) once advocated for naming things in mathematics descriptively rather than honorifically. I recall his argument was that it aids in recall and understanding to name descriptively, and that there are better ways to honor discoverers.

I found this statement in "How to Write Mathematics" (https://bookstore.ams.org/hwm):

"... surely I cannot stop without a discourse on the proper naming of concepts (why 'commutator' is good and 'set of the first category' is bad) and the proper way to baptize theorems (why 'the closed graph theorem' is good and 'the Cauchy-Buniakowksy-Schwarz theorem' is bad)."

I thought he'd said more in "I Want to be a Mathematician" (https://www.springer.com/gp/book/9780387960784), but I just looked through the book and couldn't find anything. (Halmos was a particularist, and thought very highly of examples, and "I Want to be a Mathematician" has examples/opinions of how to do nearly everything in the profession, from teaching to writing to being a department chair to giving talks to doing research ... He was very opinionated, but also specific and absolutely clear, so at least if you disagree with him you know what you're disagreeing about.)

Well, unless Hairy Ball Theorem is called after her, I don't think it's up to her to decide, what mathematicians "should" do. Jeez, these journalists researching "computational morality"...

To be fair, I do actually think some math jargon is unnecessarily complex and we could do better, and that it is something that actually matters. And I do think, for instance, that "commutative group" is better than "abelian group", since it is descriptive, unlike the latter. But this rarely is the culprit. Kähler manifold is called after Kähler, because he is the one who introduced such a thing, and we don't really have any better name to describe it. (And it wasn't Kähler who named it after himself too.) Can she propose a better name? I'm curious to hear it, but she conveniently skips that issue in her musings. If not, this whole argument of hers is just silly, as is thinking that "monster group" is a "cool name". It is not cool, it's rather awful, it's called that precisely because we don't have a clue WTF this thing is, and I sincerely hope that some 300 years later we'll have a much better understanding of group theory to rewrite all that stuff and to see that "monster group" is not such a "monster" after all, but quite a natural thing, that can be described conveniently and assigned some proper name.

So if we want to improve the landscape, let's rather start small, by abandoning π in favor of ½τ. Let's see how many centuries that will take.

If it's unique name, it's fine. What I don't like it is math notations. Many math notations requires complex typesetting and layout which cannot be expressed in the plain text. It may be not much of a problem when math notations were written by hand, but not anymore in the age of computer.

The mathematicians should have invented and standardise the notation that can be expressed as the plaintext decades ago.

Sounds reasonable. Let's call this new policy "Ball's Law".

Also, naming things is hard. If the things you are naming are specific concepts, and the conclusions reachable by reasoning about such concepts are highly sensitive; that is highly dependent upon such specificity, then the problem of naming things is even harder. I think this may be because what is hard about mathematics is the degree to which specificity matters. The names are just pointers to ideas, and these ideas are often unique but similar to one another, with differences that matter. It’s as if in naming a mathematical concept we are performing a compression algorithm on an object of great detail. A loss of information is expected. Of course, this process is an art form. Are some names easier to remember than others? Are there good names? Bad names? Of course. But I do think generalizing that “naming ideas based off people is bad” to all cases is a bad idea — rather a mixed approach is fruitful.

This is the nature of mathematics.

Statements and theorems are extremely dense with information, where every word might have a it's own area of study.

Of a problem may begin with something benign like, the following function is blah blah, but even then, the term function is well defined, and you may need to know the intricacies of functions to be able to solve the problem.

I think good naming convention is something like Chesterton's Fence. "Fence" describes the idea well, and "Chesterton's" makes it unique.

Something like "Djikstra's Algorithm" is too vague. Maybe if it were something like "Djikstra's Path", it would be easier to understand.

meanwhile, fields that do feel at liberty to come up with “common word names” usually wind up reinventing 18 names for the same goddamn thing. ML/data science/statistics is notoriously bad at this.

It took me about 3 months to realize that i’d known what “ReLu activation” was for a decade by another established name.

> Imagine how much steeper the learning curve would be in medicine or law if they used the same naming conventions, with the same number of layers to peel back:

I don't think medicine or law are the best examples to use here unless you think Sarbanes-Oxley or the anterior medial malleolar artery are well named.

Please give me only one example how one can come up with a single name for a complex mathematical concept. There are so many details, that the naming can never be precise enough to be useful. But they need to be named. So why not by their inventors?

Name is like a pointer to an information for people to access.

I think when people name things, unless they are very narcistic, should be having that sole purpose in mind.

This comment by xamuel relatably describes what people usually do when naming things https://news.ycombinator.com/item?id=24386695

> Rather, what really happens is that mathematicians are a community, and they refer to things in whatever way is convenient. Davis's colleague refers to such-and-such theorem as "Davis's Theorem" not because of some committee on naming, but rather because they were there at the conference where Davis announced the theorem, and everyone at said conference excitedly talked about "Davis's Theorem" for the whole rest of the conference because it was so exciting.

The arguments that say names should be self descriptive is only a part of the discussion.

There's the name overloading problem, where we only have a limited set of existing descriptor which can cause two object name to conflict.

There's the memorability aspect.

There's the homophonic / homographic problem where multiple names could be perceived differently.

There's the complexity aspect. The more complex an information, the harder it is to write an accurate name.

There's context aspect.

There's the extreme connotation aspect. Some words triggers extreme emotional response to someone.

There's the dependency aspect where people have been using a name for years.

All in all, naming things are hard problem. But the important thing is naming things should be done for the sake of naming things in mind. If naming things is done primarily for other agenda, like someone's glory, the result might be questionable.

Assuming that people are naming things for the right cause, problems that arise from names should not be attributed to naming process. For example the article author's problem might be simply caused by the complexity of the information referred by the name.

Edit: grammar and formatting

Compensation in academia is already bad enough. Take away the boosts to the ego and you are going to make the politics even more toxic, and potentially cripple an entire generation.

I’m not opposed to naming things after people. That said, I often suspect that the naming conventions and rituals of mathematicians (and sometimes physicists) serve as gatekeeping mechanisms that make life extra difficult for newcomers to a field while preserving the authority of current experts in a field by turning their history and duration of involvement into a more powerful resource than it probably deserves.

I have no opinion on naming stuff at advanced levels. But in high school and university I felt a palpable frustration on a very regular basis for randomly named stuff. I couldn’t and still can’t get my brain to remember things with unrelated names.

So when I learn about and need to recall “isostatic rebound” and not “the Chip Dipson Effect” it just eliminates an entire layer of key lookup and parsing I have to do.

The pattern of using eponyms instead of descriptives is also recognized in medicine: https://scopeblog.stanford.edu/2020/01/30/eponym-debate-the-...

I actually agree with the author's premise, I think she makes a good case that some of these concepts would be both more approachable, and more memorable, with simpler names.

However, coming up with simple names is incredibly difficult. It's easy to write a 10,000 word on a complicated topic, but incredibly difficult to squish it into a few letters.

I think the optimal or universal language is more difficult in practice than in idealism. Reading is the art of sorting through the mess in any field, and acquiring context. I think a lot of this underestimates the complexity and nuance of language for any field.

The alternative is common words meaning different things, depending on field or specialty. Case in point:

Entropy

Humans are social beings. An abstract concept that is named after its human creator establishes an immediate link to this person. My guess is that many people like this, because it adds a social dimension to otherwise "dry", technical papers.

Maybe I misinterpreted what the author is trying to say by using Conway as an example, but I don’t think Conway discovered the Monster group. He credits Fischer and Griess.

Conway just referred to it as a monster while corresponding with Fischer and the name stuck.

There's an equally annoying problem in software engineering at large corporations (aka Google), where hundreds of services you need to know about are named with some cute name that gives you no idea what the thing actually is.

The focus on mathematicians naming things (possibly for legacy) seems similar to the politicians venerating each others with statues.

And of course... naming remains one of the hardest things to do in any field.

You know, why don't you discover some new ridiculously hard thing and then you get to decide to not name it after yourself? This level of entitlement is beyond the pale.

This is not a naming problem. In fact the naming is consistent: There's a base-case "manifold". Another one build on top of it; another one build on top of that second one, etc.

This is precisely how knowledge is built, one thing on top of another. Naming would not have solved this "manifold" issue, in fact in would have obscured the root of that bit of knowledge.

In short, the author's real problem isn't names, is that they don't fully appreciate the way knowledge is built with ever more complex layers of abstraction.

Oh thank god. I thought the point was going to be that naming things after people was discriminatory to women and minorities.

Naming this is things is hard.

Also many of the people who are doing their PhD dream of one day having a theorm named after them.

IT equivalent: Obscure shell commands with one-letter flags and a manpage that really wanted to be a novel.

>Polish Mathematicians never getting things named after them because their names were too hard to spell

Yeah let's stop reminding people that it was mostly white men who invented everything

Meh. Shaka, when the walls fell.

This article really betrays a lack of deep understanding of the concepts involved.

I’d suggest that people that prefer “descriptive” names should come up with clever descriptive names the next time they invent a new mathematical concept or prove a new theorem. I’m quite sure nobody will try to stop you.

if you think maths is bad you should take a look at geology. At least mathematicians stick to their names or names of other mathematicians.

See also: https://news.ycombinator.com/item?id=24382438

And more descriptive variable names would be handy too. The whole field seems optimized towards obfuscation.

Do the work and you can name it whatever you want.

Humans are vain, it's just how it is.

This is some mediocre people came up with idea that they could easily understand what Calabi-Yau manifold is, if only mathematicians defined it with simple plain words. They don't like the idea that such a full definition would be 1000 pages long, full of complex concepts.

My biggest gripe with mathematical naming isn't what the author wrote, but by the inconsistency of noun/adjective endings. For example, Hermitian and Brownian are adjectives, much like Ethiopian or Libertarian or anything else ending in -ian. But Hamiltonian, Jacobian, and Lagrangian are nouns. I'd much prefer they be called the Hamilton, the Jacob, and the Lagrange, for consistency in syntax in parsing.

It always trips up my mental English parser when someone says "the Hamiltonian" and I'm always like "the Hamiltonian what? what is or isn't Hamiltonian?"

Why. They spend all that time dedicating their life to their research. They deserve to name shit after themselves?

Strongly Disagree!

You name things after who discovered it. In these case you name it after mathematicians like Newton, Euler, Turing, Gödel. For me its some sort of ignorance if you do not honor the one who discovered it.

Other sciences has it too named after persons Fahrenheit, Celsius, Pascal etc.

We all know what this article is really about. It is disappointing to see these kinds of articles on hn. (posted multiple times as well) ref: http://www.paulgraham.com/say.html