Well, God created the integers and all the rest is the artifice of humans, and all.
…which quote I liked more when I mistook it for just an appreciation for the elegance and beauty of number theory, before I knew that Kronecker (for all he did a bunch of valuable work), really was a crank on the subject and wanted to kick the irrationals out of mathematics.
I went to Caltech, and the rule whenever a group went out to eat together was that the youngest non-math major was in charge of calculating the tip and figuring out what everybody owed, because math majors were invariably awful at basic arithmetic.
(This was pre-smartphones, of course).
I’m certainly familiar with the “bad at arithmetic” stereotype, but I don’t think I ever knew a mathematician or math major it actually applied to.
I always did put a lot of effort into developing my mental arithmetic skills. Back in elementary school I came to the realiziation that it’s easier to do addition and multiplication left-to-right instead of the right-to-left algorithm we were taught. That way you remember all the numbers in order.
At my low-level government job I’ve been known to impress people in a meeting by averaging a few numbers in my head, or multiplying a three- or four-digit number by 4.3.
Yes, I can do that, too. If I would train that I probably would be pretty good. But I prefer doing other things (for example entertaining math like by Martin Gardner, or programming, etc.)
Are there any mathematicians on the forum?
I started late in life (I was well over the maximum age for a Fields medal when I received my PhD, lol), and retired after a move (long story!), but I am a mathematician. My area is a mix of “enumerative combinatorics” and “special functions”. Enumerative combinatorics deals with “generating functions” like power series and continued fractions. Special functions deals with non-elementary functions (i.e. not polynomials, trig functions, exponentials, logarithms) that come up in classical physics, usually in connection with solving ordinary or partial differential equations.
I also taught a course in the history of mathematics (a bit of a misnomer: maybe “mathematics in a historical context” would be a better title).
I still dabble, but since I don’t have easy access to a research library, it’s hard to keep up with current developments.
I fèel lìkè ťhè phýsìcìśtś aŕe at leàst hònoŕaŕy mațh mìnòrs, givèn thè amòunť of mațh wè arè expectèd tò tàke añd appĺy. Withòut tŕyinģ, I wàs a sìngke cĺaśs awày fŕòm mèetiñg thè reqùiŕemènts fòr a maťh mìnoŕ.
Yes, physics is very math-heavy! Main difference: Mathematicians proof equations, physicists just use them.
If the problem is written down and you write the answer down, then right to left multiplication is easier since the process involved only adding 2 digit number to 3 digit number. The algorithm used is good for mentally multiplying 2 8-digit numbers together.
Multiplication/Division by a single digit would be easier left to right, though. Especially if you don’t have anything written down.
Is there a significance of 4.3? Or is it just a random sample of 2 digit multiplication?
Multiplication by 4.3 is super specific to my job.
Gauss was a physicist and astronomer as well as a mathematician. And Jacobi’s first publication on elliptic functions was published in an astronomy journal. The divide between physics and mathematics didn’t really become a divorce until around the end of the nineteenth century. And the custody problems – is the computer science department in your favorite university party of the college of mathematics, of physics, or of engineering?
My attitude would be that if you regularly do mathematics at least one level beyond calculus in order to make some connections, then you’re probably a mathematician. You might not be a professional mathematician, but you’re a mathematician nonetheless. And if you have a bit of fun doing it, you have the right to claim to be an amateur mathematician as well, and in some cases, a hobbyist or DIY-er as well.
And if you’re a bit weird as well, you might even pass for a professional.
When I was drafted for that position, I quickly saw that people forget sales tax (which in the US is added at the end of the tally). It’s not a matter of being good at arithmetic, but being good both at estimating and taking into account the data that is invariably located in the wrong place.
Some amateur mathematicians have contributed to the world of math:
I got this names (among further names) from a discussion on mathoverflow.net which I can’t link here correctly. OK, I try it anyway:
soft question - What recent discoveries have amateur mathematicians made? - MathOverflow
Does sf writer Greg Egan count, or does the math B.S. cost him his amateur standing?
That can be seen in different ways. I personally wouldn’t count him to the amateurs. Edit: But he is on the list in the link I gave.
I think lawyer Pierre de Fermat (1607-1665) is a good example of an amateur mathematician with an incalculable impact on mathematics.
I would add from a century earlier the Italian physician Girolamo Cardano who first published methods for algebraically solving the cubic and quartic (at a time when algebraic notation was almost non-existent, and when one did not normally even publish results)
Much more recently, in the late 1950s and through the 1960s, Scientific American published the “Mathematical Games” column by Martin Gardner. A number of problems posed in that column generated interest by both amateur and professional mathematicians. Some of these column are still being cited.
Oh, cool, I went to Caltech too (but for grad school, not undergrad). IF really is a small world. I can certainly confirm that mathematicians are terrible with basic arithmetic, but as a topologist, I’m decent at adding mod 2.
Haha! Very advanced arithmetics… 
I had a friend at BSU who was a grad student studying topology. He was self-disparagingly known as Knotboy. It was a running bit when we were out that if it came up we were grad students we’d inevitably be asked what we studied, so each of us would have a full over-the-top technical-sounding description of our studies until we got to Ed, who was then described as some variation of “and Ed here likes to play with knots.” Which was funny, because we all felt he had the hardest maths to deal with, by far, and the guy was sincerely brilliant. Specifically, he was into protein folding, but the bit was funnier.
I saw a talk from the guy who proved this. (And Spectre)
Just randomly throwing my aperiodic monotile into the ring as another mathematician doing IF. I’m not British, so maybe it doesn’t count.
My field is computational algebra but I have been told algebraic geometry on many occasions and one day it’ll sink in. Number theory and combinatorics are cool too.