Erdós is described in Hoffman's biography ('The Man who Loved only Numbers') - I can't recall, nor immediately find by whom - as only being able to count up three numbers: '1, 2, n'.

Reminds me of the "zero one infinity rule"[0] rule for programming. Roughly stated it says that software should be designed around 3 cases: 0/no instance of a situation, 1/single instance, or an infinite/limitless instances.

[0] https://en.m.wikipedia.org/wiki/Zero_one_infinity_rule

I have a degree in maths and I suck at arithmetic. Understanding abstract mathematical concepts has little to do with speed and accuracy of thought and more to do with visualisation. But then again you are much better off with both, I often struggled because I could see how to get to the solution but struggled moving the symbols around accurately and fast enough to get to the correct soln in the required time limit.

That would explain a lot. I am the opposite. Do well at the math that requires number crunching but terrible at things like geometry where I have to visualize stuff. Probably because of aphantasia.

I would say visualisation is great to understand those mathematical concepts that can be visualised well. There are many mathematical concepts for which this is not true. Logic comes to mind.

It's not really important, but the "Grothendieck prime" is 57 according to Wikipedia.

https://en.wikipedia.org/wiki/57_(number)#In_mathematics

True, 51 is "exmadscientist prime".

<boldly updates wikipedia>

...I'll take it.

But, hey, I probably won't make that mistake again. Probably.

> Ironically enough, "someone who likes math but hates arithmetic" isn't a self-contradictory thing.

I didn't even realise anyone would expect there to be a relationship between "liking" arithmetic and actual mathematics. I worked with mathematicians and was called one myself (it was a stretch, I think) but I have no idea who in the lab was or was not proficient in doing numeric calculations by hand. It was just not relevant. There was one guy though who liked to show off doing things like multiplying long numbers in his head, which was amusing.

It would suck to lack the ability to manipulate algebraic expressions efficiently, but you could go quite far without it in many branches. My most interesting results were identifying certain topological features of certain discrete structures of relevance to biology. There was no arithmetic or algebra involved at all except to write down the results formally.

I was in a bit of a weird half-rate math competion team/club where some people who were there to get out of history class and some people who were very much the opposite and were some of the smartest people I've ever talked to. One thing I noticed is that all the power competitors had good calculation ability, but whereas some people were just really fast calculators and, like your lab friend, could calculate huge multiples in their head, others were actually subpar at that type of mental math and instead were just familiar with, for instance, all the perfect squares/cubes/powers of 5 up to 20 and beyond because they've just encountered them a lot.

When i was in university i did a math minor. I definitely remember the people who were math majors tended to be fairly bad at simple arithmatic (or at least just very average)

Which may be because you simply can't do everything good without practice and in pure math, well, there are things you don't do as much. When I go back to the 3rd and 4th degree polynoms we solved back in school, it's a hassle. Back then I was quite good at solving them but nowadays it just takes time to get accustomed to these kind of problems.

"A number less than 100 is prime if it sounds prime, and isn't 51 or 91."

(To me, 57 is too obviously 3 less than the obviously-divisible-by-3 60.)