Missing multiplication symbol

From Why start at x, y, z

It's common to omit a multiplication symbol:

\(ab = a \times b\)

But sometimes it's not as clear:

Does \( a(b+1) = a \times (b+1)\), or is \(a\) a function?[1]

When writing a division on one line, does an implied multiplication bind more tightly than an explicit one?[2]

Is \(a/bc\) equivalent to \(\frac{a}{bc}\) or \(\frac{a}{b}c\)?

There seems to be an unwritten rule "juxtaposition is stickier". (See Juxtaposition means combine in the obvious way)

But that might not apply when there are numbers involved: almost everyone would interpret \(2/3x\) as \(\frac{2}{3}x\) instead of \(\frac{2}{3x}\)

The "juxtaposition is stickier" rule only seems to break ties, not override the normal order of operations:

\[ ab^2 = a \times (b^2) \]

Sometimes the ambiguity comes from mistaking a function for an operation:

\[ (a+b) \Phi (a+b)\]

which can be viewed as either \( (a+b)\cdot \Phi(a+b)\), or \(\Phi\) as binary addition-like operation, similar to \( (a+b)\oplus (a+b)\).[3]

Jim Simons reckons we should give up on implicit multiplicatoin altogether.[4]


  1. Tweet by Christian Lawson-Perfect
  2. Twitter thread by Christian Lawson-Perfect
  3. Igor Pak, How to Write a Clear Math Paper: Some 21st Century Tips
  4. The Times, They Are A-Changin', Jim Simons, Mathematics in School, November 2020.