When something – or someone – is described as sharp, what’s your reaction? 

The word can carry a warning: Watch out, that knife is sharp! or indicate that there’s a suddenness or quickness about the noun that it’s attached to: I’m feeling a sharp pain in my side! or I like that person because of their sharp wit.

Might just be commentary on someone’s fashion sense: You look sharp today!

You hear the word sharp and think that whatever it’s describing is something to pay attention to because it’s describing something significant.

Well, you have no idea!

In mathematics, the word sharp is used in association with the word: bound. You’d be right to assume that this thing called “bound” (much like the word boundary) indicates some sort of demarcation, a margin, a restriction. A bound can be a number whose value is greater than the value of all the other numbers in a particular set, which, then, qualifies to be called an Upper Bound. Alternatively, if the bound is a number whose value is less than the others, well, you guessed it – that’d be a Lower Bound.

On occasion, though, you’ll see a Sharp Upper (or Lower) Bound. A Sharp Upper Bound is not only at the tops of that set, it has reached its pinnacle. It’s optimal. It allows no room for improvement. It’s the G.O.A.T of bounds. 

And this is why I brought you here today. 

You see, mathematicians don’t throw around the word sharp all willy-nilly and I, for one, appreciate the restraint. How the heck did this one word end up having 25 varied applications of its common definition? And that’s just when it’s used as an adjective.

In math, when a word is used to describe something, it’s very loyal to the context of how it’s first used. 

Though I absolutely cherish how creative math can be, I also deeply appreciate when it puts the brakes on things getting too wild up in (t)here. In other words, I think it’s great that math is the pocket multitool for all types of problem-solving  – while simultaneously serving as a gutter bumper as you bowl your way towards making a decision.

If you tell me something is sharp, I do not care in what context you are using it, I want to believe that that statement is absolute. Nothing subjective going on in your usage of the word. No slang. 

All of that being said: Please do warn me if that knife I’m about to pick up is, in your informed opinion, sharp. Better safe than sorry.