Proficiency of the week: Numerancy Versus Maths

The reason that overlapping proficiencies exist has a lot to do with the free proficiencies given in certain situations. For example, a human, half-elf, halfling, elf or dwarf born and raised in the city of Misty Cross will have gotten trained in speaking common and elven, reading common (and maybe elven), maths and a rudimentary understanding of politics. This formal training in these things is a result of the city's mandatory educational requirements (this is why when barbarians go into the city they can't get drunk because the pub won't have a sign with a big tankard on it, it will have a sign saying 'pub') which are nearly as severe as the city of Harmony's.

Maths is a formal training proficiency. Your character sat in a classroom, or was tutored, and had homework and lessons. He is assumed to automatically be able to do easy mathematical calculations (dividing treasure among the party, paying a tip) but must make a roll to do more complex operations. If he needs to make a roll, which only happens with difficult situations, it requires an INT-2 roll. He can't do things involving calculus and the equivalents (unless he has higher maths.)

Numerancy is the less formal proficiency. Your character isn't mathematically illiterate, but he's only assumed to understand the most basic of numbers. He will need to roll to do what a person with the Maths proficiency does automatically. With either proficiency, your character is not going to be fooled by simple manipulation of statistics. He will know, for example, the difference between something increasing slower than in the past and something decreasing, which is more than I can say about some people in the real world who only watch one news channel. ahem.

If your character has maths, engineering, accounting, etc., it is assumed he is mathematically literate. This doesn't give you Numerancy for free, it just means that you would not use that proficiency to determine your roll. However, if your character has Numerancy, and later picks up maths, engineering, etc., you do not gain a free slot BACK.

So, Why would a player choose Numerancy over Maths?
For the most part, a player wouldn't. You'd take the 'higher level' proficiency, given the chance. You're much more likely to see Numerancy on an NPC, or as a free proficiency from a character background. However, if you were playing a character with an INT of 6, you might have to weigh which would be better for you, a maths proficiency (with more automatic and less rolling) with a score of 4 (and only a 20% chance of success) or a Numerancy with a score of 6 (and a 30% chance of success.) 

Is there a benefit to the Maths score for the lower level proficiency?
Not mathematically, but your character may've found training easier than his classmates.