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Dear readers,

If you have mathematically inclined friends or are mathematically inclined yourself, you may know that mathematicians tend to use a very specialized language when discussing their work. This is not a matter of trying to make the subject of discussion appear inaccessible to outsiders (though sometimes there is an element of that). Instead, it’s a communication necessity: everyday language is even more inadequate for discussing mathematics than it is for discussing topics such as music, philosophy or law.

But the terms used in mathematics are rarely invented from scratch; a great number of them are in fact taken from everyday language, but given different meanings. This is why you might hear words like *filter* (in lattice theory), *flag* (in linear algebra), *ring* (in abstract algebra), *saddle* (in calculus and analysis), *sheaf* (in topology), *soul* (in geometry), at a mathematics lecture. Their meanings, though usually inspired by natural language, frequently drift to the point of becoming unrecognizable.

Fortunately, this exchange between mathematics and natural language is a two-way street, and today I’m going to discuss some of the words that mathematicians often use in day-to-day conversations that are derived from mathematical terms. Using them might make you sound strange, but it might also help you express things concisely. I present to you the top 5 words I’ve heard used in conversations between mathematicians (and have been guilty of using myself in conversations with non-mathematicians on occasion). Whether you decide to adopt them or not, you’ll find it illuminating to know their meanings.

**Asymptotically**

Mathematical meaning: as the independent variable becomes arbitrarily large.

Colloquial meaning: in the long run; looking at the big picture.

Example 1: Since he’s not staying in academia, having his name on papers is asymptotically irrelevant.

Example 2: They do have a significant age difference, but asymptotically it won’t matter all that much.

**Corollary**

Mathematical meaning: an easily derived logical consequence of a proven result or theorem.

Colloquial meaning: something that follows automatically; something you get for free.

Example 1: If she gets invited to this wedding, her significant other’s presence will be a corollary.

Example 2: I just bought myself a new bicycle, and this water bottle came as a corollary.

**Inflection point**

Mathematical meaning: the point on a curve at which the second derivative changes sign.

Colloquial meaning: a situation where each new unit of effort affects the result less than the one before.

Example 1: I could have stayed up all night to finish it, but I don’t like to work past my inflection point.

Example 2: We’ve been working for ten hours and the inflection point is getting close; let’s call it a day.

**Modulo**

Mathematical meaning: the remainder of the division of a given quantity by another (fixed) quantity.

Colloquial meaning: minor details that must be dealt with as a condition for getting a desired outcome.

Example 1: I will definitely join you at the basketball game tonight modulo finishing this assignment.

Example 2: I got the job modulo the background check and some annoying paperwork.

**Orthogonal**

Mathematical meaning: perpendicular; in probability theory, uncorrelated (refers to random variables).

Colloquial meaning: unrelated; independent.

Example 1: Your observation is very interesting, but it’s orthogonal to the question we are discussing.

Example 2: How important a task is is often orthogonal to how urgent it appears to be.

Are there any other mathematical terms you like to use in everyday life? Share them in the comments!

I use “exponentially” and “parallel” a lot. Also, although it’s not a strictly mathematical word, I had never used “rigorous” before I did some math coursework.

Love your blog. Thank you!

Thanks a lot, Sasha! I already had “exponentially” on my reserve list, and just added “parallel” and “rigorous” as well – once I get enough new terms I will consider doing another post of this kind, provided people find it interesting

Nicely done! I really like this blog.

Did you mean that these are mathematical terms mathematicians use in the their colloquial meaning? Or did you mean since the mathematicians are using them in a mathematical sense while the non-mathematicians hear them in a colloquial sense, there’s some potential for confusion?

Here are some phrases/terms I use a lot in conversation: a priori, maximally, optimizing, in a limiting sense, axiomatically. Also, even though ‘potential’ has several dictionary meanings, when I say ‘maximum potential for’ I tend to picture contour lines.

Thanks so much, Nilima! I was specifically targeting the former, namely, mathematical terms that permeate mathematicians’ speech even in non-mathematical situations, which allows them to acquire a colloquial meaning. However, the latter is probably a very frequent occurrence as well, and could be interesting to write about – one example that springs to mind is “or” which non-mathematicians tend to use as an exclusive or whereas some mathematicians use it in its logical sense.

Thanks for contributing the terms you use in conversation, I added them to the reserve list as well!

Nice blog, Leo!

Transitive

I use it to describe social relations, for example “I know this person transitively” means I know somebody who knows him.

Some rare social functions, such as trust, might be transitive.

Thanks a lot, Lyuda! I am definitely adding “transitive” to my reserve list! Along the same lines I once sent an email to all my West Coast friends introducing them to one another, entitled “towards transitive closure”

Hey Leelee!

So proud of you, and this blog! It’s great!!! Your first date story is cute. I enjoy trying to understand all this stuff!

Much love,

Rox

Thanks a lot, Rox! I wish more people would put in more effort into trying to understand mathematics rather than prematurely giving up on it – then again, the education system also has a role to play in that.

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