How should one vocalise difficult terms, which have no short names, in a talk? Have you other hints for talking about maths to other people? Do I need all to mention, what I write down on the blackboard?

For example how should I say $\left(D + \frac{b}{2m} - \sqrt{\frac{b^2}{4 m^2} - \omega_0^2} \right) \left(D + \frac{b}{2m} + \sqrt{\frac{b^2}{4 m^2} - \omega_0^2}\right) y = 0$?

It's probably quite painful to read in the exact way as it is written there. Maybe one should simple say 'We get this equation' and point at it on the blackboard. More generally refers to it by saying 'this...' and 'that...'.

• For your example, one possibility is to say "the product of this difference, this sum, and y is zero." – Joel Reyes Noche Oct 29 '14 at 1:53
• If you only have to say it once, go with "this" and "that." If the terms come up multiple times, start coming up with new names (call $\sqrt{\frac{b^2}{4m^2}-\omega_0^2} = C$ for instance). – Gyu Eun Lee Oct 29 '14 at 5:54
• Just talk in latex. You'll get to be "that" prof. Students will love you. – Chantry Cargill Oct 29 '14 at 6:23

With long equations, it is probably best by far to just write it out and say "this equation". Nevertheless, I think it is worth noting that there is a way to say equations like this out loud, and in principle it should work for any equation. For example, many of us were taught to memorize the quadratic formula in middle school: $$x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}$$ "x is equal to the opposite of b, plus or minus the square root of quantity b squared minus four a c, all over two a."

Here's a transcription of the formula you mentioned: $$\left(D + \frac{b}{2m} - \sqrt{\frac{b^2}{4 m^2} - \omega_0^2} \right) \left(D + \frac{b}{2m} + \sqrt{\frac{b^2}{4 m^2} - \omega_0^2}\right) y = 0$$ "The quantity capital d plus b over two m minus the square root of the quantity b squared over four m squared minus omega naught squared, end quantity, end quantity, all times the quantity capital d plus b over two m plus the square root of the quantity b squared over four m squared minus omega naught squared, end quantity, end quantity, times y, is equal to zero."

Obviously, there are some order of operations issues and a lot of potential for ambiguity, but using "quantity...end quantity" in theory can remove all such ambiguity. The order can also often be discerned from the context.

As an alternative to "quantity...end quantity", in casual speech with friends I have noticed a common practice of using longer spaces to indicate order. This often comes up in distinguishing $x_n + 1$ and $x_{n+1}$; the first is usually voiced as "x sub n [pause] plus 1" while the second is voiced as "x sub [pause] n-plus-one".

• I wonder if you could simplify even by saying "The quantity capital d plus b over two m minus the square root of the quantity b squared over four m squared minus omega naught squared, end quantity, end quantity, all times its own conjugate, times y, is equal to zero... That of course could only be applicable to this specific case – Liam McInroy Oct 29 '14 at 0:47
• For the quadratic formula, I was taught: "ex equals minus be plus or minus the square root of be squared minus four ay see over two ay" Just for interest :-) Granted, however, that is pretty much useless unless you've seen it written down first (how much is over "two ay", is one problem), but it was a way of saying it out, and remembering it, once you already have seen it. – Mac Cooper Oct 29 '14 at 16:12

There's no reason you need to say a complicated equation out loud. It's fine to just say "this equation". It took humanity thousands of years to develop a compact notation for describing relationships between numbers - the Babylonians would have to describe it in words, but we don't have to.

• The one exception is when there’s a blind person in the audience. Then perhaps it might be wise to spell it all out. And of course there’s Victor Borge’s method, where each punctuation mark has its own sound. This could be adapted to mathematics, I’m sure. – Lubin Oct 28 '14 at 21:05
• Thanks, J. Taylor. An other question: Do I need all to mention or refer, what I write down on the blackboard? Or can I say nothing about and go on? – bjn Oct 28 '14 at 21:11
• @Lubin: That's true. I haven't encountered that situation myself. I'd think that some kind of accessibility technology would be useful there. – Jair Taylor Oct 28 '14 at 21:31
• @bjn: I'm not sure I understand the question, but usually just referring to it as "the equation" would be fine. The context should be clear based on what is written on the board. – Jair Taylor Oct 28 '14 at 21:33
• @J.Taylor: Maybe I can rephrase my question in a more clear way: Should I comment all, what I write on the blackboard? Can I also say nothing and go on? – bjn Oct 28 '14 at 22:03

I usually LaTeX it. Just say;

\left(D + \frac{b}{2m} - \sqrt{\frac{b^2}{4 m^2} - \omega_0^2} \right) \left(D + \frac{b}{2m} + \sqrt{\frac{b^2}{4 m^2} - \omega_0^2}\right) y = 0

• @bjn: It may be impractical, but it seems a legitimate attempt to answer the Question. Why should I (or someone else) be offended? – hardmath Oct 28 '14 at 22:16
• I gave it +1 for humor. I don't think it's any kind of insult to you. Life is a finite quantity, so I wouldn't spend it being offended at math jokes. – Jair Taylor Oct 28 '14 at 23:12
• I feel that this "answer" would be better off added as a comment as it does not really serve to answer the question. – 1110101001 Oct 29 '14 at 0:44
• There is a serious Comment to be made about the problem of encoding the two-dimensional presentation of formulas, equations, and proofs into a one-dimensional representation, with speech being a sine qua non of one-dimensional representations. LaTeX is also such a 1D encoding, by necessity, and while impractical for realtime talks (except in the company of the truly nerdy), its design offers some insight into what concessions have to be made for disambiguation. – hardmath Oct 29 '14 at 1:27
• There is enough in this world to be offended at. Make your day better by skipping over this one. I gave it a +1 because it made me laugh, but I agree with user2612743- it would be better off as a comment. – daOnlyBG Oct 29 '14 at 2:02

TL;DR Explain properly and don't read out loud.

I must apologize in advance since this is really a subjective opinion from me.

I never really had an ability to just learn equations blindly; rather, I wanted to find the answers on my own. Sure, working through long, tedious equations slows me down, but also gives me complete understanding of everything within the given equations. When I build an equation, I usually do several steps in order to produce the correct result. It's like a tree of throwing and seeing what sticks. When I find the correct way, I spend a little time compiling all the equation chain into ONE equation. Sure, this equation is almost impossible to read- it's like reading obfuscated JavaScript. In programming, it's almost religion to keep code readable. Sadly, that is not the case with mathematics. Some think it's clever to use 1-letter notation as "it's the norm" and bloat all of the stuff into one big pile of symbols. Now have the student decompile this equation. Only few of them will actually do it.

So I'd say., "don't teach what you don't even understand yourself." I have seen many teachers than blindly funnel information down their student throats but don't even know half of what's going on. When a student finally questions an equation as why wasn't it constructed in a different way, the teacher doesn't know because he didn't make this equation.

Show the student how you got to that equation. Show the student the mistakes you've made before reaching this result and why it was wrong. Take it apart and show all the individual parts of the problems this equation solves.

In regards to how to read an equation out load: Don't! Reading it out loud as a machine serves no purpose as human memory is very limited and the student would be better off with it text format so he can copy easily and chew on it.

I currently give one lecture a week in which audio but not video is recorded. For the benefit of students who cannot attend this lecture, I don't have much choice but to read out every symbol as I write it down. About the only shortcuts I can take are to label things if I'm going to use them again later, so I can say, "let's call this equation 7" and then later say "by equation 7...."

• Is the audio recordings accessible for someone not enrolled in your class? I would be very interested in experiencing a math lecture without visual input. – Alecos Papadopoulos Oct 29 '14 at 11:02
• Sorry, I'm pretty sure you have to be enrolled in the class to access the recordings. – Gerry Myerson Oct 29 '14 at 12:09