# Blackboard bold

Why do people use blackboard bold here and elsewhere in print? I thought the whole point of the font was as a substitute for bold when one was writing out something by hand. Shouldn't we be using just bold R, Z, N, etc.?

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• I think we just got used to it. $\mathbb R$ is more fancy than $\mathbf R$. Well, it's a personal matter to me, at least. – Patrick Da Silva Jul 6 '11 at 23:01
• If the question is about mathematical practice in general, not just on this site, you might want to ask it on tex.stackexchange.com . I'm not a community member there, though, so I don't have a good sense of their community norms. – David E Speyer Jul 6 '11 at 23:54
• Apparently you can use blackboard bold for field extensions, as in the recent question math.stackexchange.com/questions/49914/…. Yuck-o. – KCd Jul 7 '11 at 0:01
• You might as well argue about Mac vs Windows, or whether 0 is a natural number. It's more like a question of religion than of logic. For what it's worth, I agree with the sentiments Stephen expresses, and never use blackboard bold on this site. – Gerry Myerson Jul 7 '11 at 0:08
• I recently had the occasion to use a blackboard bold greek letter eta in a paper. That was fun! I was forced by internal logic of the paper. I was using blackboard bold to denote chain complexes and sans serif to denote the resulting homologies. At one point I needed to lift a map already denoted $\eta$ in the literature to the chain complex level, with the most natural notation for that lift being blackborad bold $\eta$. – Cheerful Parsnip Jul 7 '11 at 2:29
• Surely making what you write and what you type look the same is the best way to ensure notational consistency and clarity? :) Anyway, $\mathbb{R}$ is now just a standard, accepted symbol. I've seen $\mathbf{R}$ and even just $R$ before, but the reals are such a commonly used thing that they kinda deserve their own notation. I could easily envisage myself wanting to use $\mathbf{R}$ or $R$ for something else! – Billy Aug 3 '11 at 20:31
• For what it's worth, I'm reading a differential geometry textbook that has a habit of using $R$ to refer both to a region of a regular surface and to the set of real numbers, sometimes in the same sentence! "We shall consider bounded regions $R$ which are contained in a coordinate neighborhood $\mathbf x(U)$ of a parametrization $\mathbf x\colon U \subset R^2 \to S$." I find this horribly confusing; though I'm gradually getting used to it, I wouldn't recommend this style to anyone. – Rahul Apr 10 '12 at 17:14

Traditionally, people did use bold in typesetting, but at the same time they would not have had blackboard bold variants in professional typesetting systems (in 1940, say).

Here is my speculation on some reasons why blackboard bold became more popular:

• During the brief period when a lot of mathematics was typeset on typewriters, many people were unable to type bold easily, but they could fake blackboard bold by adding an I to the front of the desired letter, offset just enough for the serifs of the two letters to touch. This then influenced the way people typeset in TeX when it first arrived, because they were used to seeing typewritten mathematics.

• Bold symbols, in some fonts, are too dark and break up the color of the text. Blackboard bold fonts match the text color much better.

• When photocopied, bold symbols sometimes become indistinguishable from their normal counterparts. This depends greatly on the font and on the photocopier. Historically, this issue was particularly problematic for the "boldface/lightface" convention in descriptive set theory.

• Having another face for the basic number systems allows an author to use bold for some other purpose.

• If typeset mathematics looks like handwritten mathematics, it is easier for me to read than if it has a completely different appearance. I think this also one reason for the popularity of varphi; if someone writes $\varphi$ on the blackboard, there is additional mental effort in reading $\phi$ in print.

• Other purposes for bold: generic algebraic or combinatorial structures (rings, graphs, etc.), matrices, topological spaces. The "mathbb" special cases are recognizable because of their limited number. – hardmath Jul 6 '11 at 23:44
• It seems that blackboard bold is often used to denote sets of numbers, e.g. $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, $\mathbb{O}$, or a general field $\mathbb{F}$ or $\mathbb{K}$, and in probability to denote expectation of a random variable $\mathbb{E}(X)$ or probability of an event $\mathbb{P}(E)$. Sometimes you see a sphere denoted $\mathbb{S}$ or a torus denoted $\mathbb{T}$. Other uses seem to be less frequent. – Chris Taylor Jul 7 '11 at 0:28
• The "boldface/lightface" convention seems to be a catastrophe wanting to happen, really :-) – Mariano Suárez-Álvarez Nov 26 '13 at 5:28
• @MarianoSuárez-Alvarez As far as I'm concerned, the catastrophe already happened. I wrote a paper that made extensive use of this convention. When printed on my department's printer, it looked fine. When printed by the publisher, the boldface and lightface symbols looked exactly the same. And the publisher never sent any proofs to correct (probably assuming nothing can go wrong, since it was my TeX file). – Andreas Blass Dec 3 '13 at 19:36

Anyone here seen Fiddler on the Roof?

("You may ask, how did this tradition get started? I'll tell you! ... I don't know.")

[Sorry to re-bump an old question, but I couldn't resist.]

• Did you just see Fiddler on the Roof ?? - oh, I see that Jyrki had resurrected it before you :) – The Chaz 2.0 Apr 10 '12 at 16:56

I think we just got used to it. $\mathbb R$ is more fancy than $\mathbf R$. Well, it's a personal matter to me, at least. The more badass our symbols look like, the better we feel when looking at it, hence all the greek letters and big product/sums symbols and such.. $$\prod \sum \alpha \beta \gamma \delta \varepsilon \forall \exists \mathbb R \mathscr N \varphi$$ =D I love those.

• Hmm. Yeah, the symbols may look cool and may add some street cred, but as a teacher I must disagree. The goal should not be to obfuscate the simple underlying ideas with 'badass' symbols. IOW I use greek alphabets, only when it helps the reader. The common practice in trigonometry to use roman letters for lengths and greek letters for angles is a case in point. This SpikedMath strip hopefully drives the point home :-) – Jyrki Lahtonen Apr 11 '12 at 7:12
• I agree. Those symbols make sure that everybody outside of math thinks we must be geniuses to understand all those symbols haha – Kasper Nov 28 '13 at 0:25

Boldface is often bad typography when used in text. Boldface stands out a lot. If you print out a page with many boldface letters and look at it from some distance, it will look like a light grey background and on it some huge black spots. The spots are where the boldface letters are.

• Sorry, I don't see why it matters what a page looks like from a distance. That's not how I read papers. – Gerry Myerson Jul 23 '12 at 12:32
• @Gerry: Wait a few more years... :) – cardinal Jul 23 '12 at 16:49
• @GerryMyerson: It is a test for how balanced a layout looks, something that people more competent than I consider a fundamental principle of typography and layout. – Michael Greinecker Jul 23 '12 at 20:21

I think blackboard bold is usually reserved for some sets such as reals, naturals or integers, while simple bold is reserved for matrices and vectors. At least that is the convention I use. For instance R to me always means a matrix R, and not the real line.

• In general this is the case, but this convention is not always adhered to. In particular, it's not uncommon to see $\mathbf{R}$ to represent the real numbers or to see $A$, $x$ to represent a matrix and a vector respectively. – Chris Taylor Jul 7 '11 at 0:22
• This is my (flimsy) excuse for using $\mathbb R$, since I tend to use boldface for vectors and matrices... – J. M. is a poor mathematician Apr 14 '12 at 3:01

I am a loyal disciple of the school that teaches: blackboard bold should stay on the blackboard - it has no place in typeset math.

Earlier I practiced what I preach, and used boldface exclusively. I don't think that this ever resulted in any misunderstandings. But I rarely write anything about calculus questions, so my sample is too small to be conclusive ($\mathbf{Z}$ vs. $\mathbb{Z}$ is a more common cause of grief for me). Upon further reflection I decided that I should stick to the preference of the OP. The overriding principle should be to make the answers extra easy for the newbie to follow.

But then comes (one of) my pet peeve(s). One of the more common thing the eager beaver editors touch is to replace a regular 'R' with a symbol of their choice. They probably try to be helpful, but they also force a personal preference upon an unsuspecting newbie. It was irritating (needless to say, I was having an otherwise bad day) to type an answer using the font of my choice only to discover that, while I was typing, an editor had replaced the original non-descript 'R' with a blackboard bold version. It wasn't easy, but I somehow managed not to start a futile editing war.

• What happens if your university only has whiteboards? Can the blackboard bold be used on a whiteboard, or should we invent a whole new font for whiteboards? :-) – Asaf Karagila Apr 10 '12 at 10:27
• @Asaf LOL! Luckily our math department has successfully managed to keep the chalkboards. One of our senior tenured lecturers is a very convincing negotiator. I do have a whiteboard in my office, so I need to concede your point. Our section of the sciences building is scheduled for renovations, so the future is all murky. And, yes, the blackboard bold can be used on a whiteboard quite well. It's just that the whiteboard markers in lecture rooms are not nearly as dependable as chalk. – Jyrki Lahtonen Apr 10 '12 at 10:44
• I have a follow-up question. Suppose I use a computer for a presentation, and the projection is onto a whiteboard. Can I use \mathbb in this case? If that is the case, shouldn't I just assume from the beginning that whatever I write may end up projected onto a whiteboard and therefore use \mathbb everywhere? :-) – Asaf Karagila Apr 13 '12 at 14:52
• @Asaf, there is a positive probability that at some point I will reach the conclusion that there is a lesson to be learned from this exchange. I dare not speculate, whether that has happened already?? :-) – Jyrki Lahtonen Apr 13 '12 at 16:09
• Simply because the outline typeface is often called "blackboard" in English is no reason to avoid using outline letters for their traditional mathematical meanings in other media. – Henning Makholm Jul 23 '12 at 12:57
• @Henning: The OP's (and my) point is exactly that this is not the traditional usage. Traditionally ordinary boldface ($\mathbf{R}$ etc.) was used, but because boldface letters handwritten with a thick piece of chalk are not always distinguishable from non-bold letters on the blackboard, the doubled vertical lines were invented as a substitute (for clarity). Now some people want the weak substitute to become the new norm... – Jyrki Lahtonen Jul 23 '12 at 13:05
• How can a particular typeface symbol possibly be more traditional than a handwritten symbol? Traditionally, mathematicians themselves would not be able to chose any such symbol at all, they would write something by hand which would then be imitated by the typesetter, who likely would have access to bold symbols but not to outline symbols as we have nowadays; so even if all mathematicians always wanted the exact $\mathbb{R}$ symbol we still wouldn't find it in old typeset papers and books. – leftaroundabout Aug 17 '12 at 1:16
• Jyrki, your last sentence in the last comment from last year reminds me how in Yiddish (I think) the vulgar word for penis was "Ze'reg", its cleaner form was abbreviated to the first letter, "Za'in". Nowadays the latter is the vulgar and the former is the softer and milder term. These substitutions happen. :-) – Asaf Karagila Nov 26 '13 at 9:12
• LOL, @Asaf. I have more or less given up this struggle. My own lecture notes still use boldface. But I had the foresight to define a TeX-macro (backslash-R) to produce the symbol. At the time it was mostly to save kludgy typing, but it has the additional benefit that I only need to replace the macro definition, and be done with it. – Jyrki Lahtonen Nov 26 '13 at 10:05