math research conducted in other bases than 10

Question

Is mathematics research generally done in other bases than 10, and is that something that could be of benefit to reach new solutions and ways of thinking? I'm a math novice but into normcritical analysis, and curious if our cultural familiarity of base 10 is a bias that would limit our understanding of mathematics or if it would just be a cosmetic inconvenience.

Answer 1

If the vast majority of the world spoke English, would mathematics research generally done in other languages? Could this benefit new solutions or thinking? Of course not, it would just hinder readability. This is the same reason we rarely venture away from base $10$.

Numerical systems are like languages. “Tree”, “Árbol”, “Baum”, may be said differently in different languages, but they all refer to the same abstract concept. Likewise, $3$, $10$ and $11$ look different in different bases, but they all refer to the same abstract concept, the number three, which satisfies exactly all of the properties we expect it to in any other base.

Of course, there is one exception: sometimes we’re interested in properties of the number system itself. That’s why occasionally, you’ll see research about binary, or ternary, or simple, easy to analyze bases. But if these aren’t the subject, you’ll rarely see them used.

If the Mayans or Mesopotamians were academic forces nowadays, we’d probably write numbers down in base twenty or sixty. But since that isn’t the case, we’ve stuck with ten.

Answer 2

As noted by Asaf Karangla, the vast majority of mathematics doesn't care how you write your numbers, so this is merely a matter of notation.

In abstract algebra, there are plenty of objects that may be considered "doing math in base X". Starting from cyclic groups, you can eventually get up to finite fields of size $p^n$ for all prime $p$.

If that doesn't look sufficiently like "numbers in base $p$", then pass through to the full p-adic numbers.