A word for 'calculator' (the old meaning)

Back before electronics took over calculations, a calculator was a person's job title (and you needed skill to do that). What's that skill called?

A term for someone who can juggle many numbers, routes, and other information in their head at the same time, while re-arranging / re-assigning them to different workers.

What is your source for the claim that such a job title was 'calculator'? My first job (in the mid-1960s) was at a very distinguished scientific research institution (5 Nobel prize winners on the staff at the time - and more to follow.)

My job was in the computer department. I was a temporary assistant computer, my permanent colleagues (female) were computers, and our boss was the chief computer.

There was a rather eccentric mathematician, in another department, who had an 'electronic computer' and part of my job was to take boxes of punch cards to a big electronic computer in another city.

Your description of the duties of the person you want to call a calculator is in line with those of the head of the computer department in my lab at that time. (She had graduated in mathematics, with high honours in a distinguished university).

There is no such job in the modern world, and therefore no job title that describes it in modern terms. The answer to your question then is that no such word exists.

In our modern admiration for all the things that electronic computing can do for us we should not forget the skills of such people as clerks in the Post Office who could add up a column of figures at a glance, or vehicle schedulers who could sort out in their heads a very good, maybe not universally the best, route to deliver ice cream to shops in awkward-shaped counties like Cornwall.

Wikipedia offers the term mental calculator:

Mental calculators are people with a prodigious ability in some area of mental calculation, such as adding, subtracting, multiplying or dividing large numbers.

Mental calculators were in great demand in research centers such as CERN before the advent of modern electronic calculators and computers.

Human computer is another option:

The term "computer", in use from the early 17th century (the first known written reference dates from 1613), meant "one who computes": a person performing mathematical calculations, before electronic computers became commercially available. "The human computer is supposed to be following fixed rules; he has no authority to deviate from them in any detail." Teams of people were frequently used to undertake long and often tedious calculations; the work was divided so that this could be done in parallel. Frequently, the same calculations were performed independently by separate teams to check the correctness of the results.

Since the end of the 20th century, the term "human computer" has also been applied to individuals with prodigious powers of mental arithmetic, also known as mental calculators.

What's that skill called? [later additional suggestion] if the 17th century "Computer" or 14th century "Calculator" names for master arith/math-matician is not what your looking for then we need to accumulate all your requirements to perhaps find a Greek variant that was commonly used prior to that.

logistician (modern uses, route planner / assigner of labour and resources)
Greek logistikos, skilled in calculating, from logistēs, calculator a variant of logician See current military usage

The first administrative use of the word was in Roman and Byzantine times when there was a military administrative official with the title Logista. At that time, the word apparently implied a skill involved in numerical computations.

Since others have mentioned arithmetic + mathematics and geometry seems not applicable The other applied forms I can think of are

Actuaries may solve your problem, Numerologists and Stasticians a(re)bound by numbers. Strategists and Tacticians logically come close to your target and just for good measure we have Tallymen

As answered above a computer [1] (one who computes) or computor was an early 17th century term. Alternatives include computist possibly used before 1646 [1] or listed at a later date computant. Notable pioneers in this field included Mary Edwards (c. 1750 – September 1815) was a human computer for the British Nautical Almanac Her daughter, Eliza Edwards (1779-1846), also worked as a computer [until...] Civil Service rules made the employment of women very difficult.

Side note The supposed first digital calculator was "The Arithmometer" or Arithmomètre not introduced till Patented in France by Thomas de Colmar in 1820 long after computers.

So for you quiz masters "Which came first the computer or the digital calculator?"

Personal experience. My Great Aunts reputedly lived over the age of 100 and worked with the navy, in The Great War (WWI), but would never disclose what they did, however the family mumbled they were computists. It would have been fun to say they were ComputeAunts!

[1] see alephzero's comment below for citations e.g used by Sir Thomas Browne in PSEUDODOXIA EPIDEMICA, Volume II Third Book, Chapter XIV, Gutenberg EBook "we have the account of a year in 365 days, exact enquirers and Computists will tell us, that we escape 6 hours, that is a quarter of a day." "Now it is manifest, and most men likewise know, that the Calenders of these computers, and the accounts of these days are verry different;" The Oxford calculators including Richard Swineshead "The Calculator" was the name given to a group of lead logical mathematicians founded Early 1300's

In the old days before electronic calculators we used a comptometer.

It was used by a comptometer operator. This was a highly skilled task, a (then) modern version of the abacus. The operator's fingers would form a cradle of fixed shape depending on one operand and dance among the rows and columns to obtain a quick result from the other operand.

I also know the word wrangler which I understand to be someone in the days before electronic calculators, who was proficient in calculating values such as log tables. I can't find a better reference than this.