mttheww asked: I don't really get the dollars joke? maybe I don't know enough about math to get it

There’s a famous “fact” in math that

1 + 2 + 3 + 4 + … = -1/12

Obviously this is false given the usual definition of an infinite series, because the left-hand side keeps getting bigger and bigger without bound — it doesn’t converge to anything, much less to anything negative.  Using the usual definition, the left-hand side does not have a well-defined sum.

However, there are alternative definitions of “the sum of an infinite series,” and according to several of them, that equation is true.

This is useful in certain calculations in physics (in that if you use that equation, the result “works”), though we don’t really understand why.  Of course it doesn’t always work in every context, as the dollars joke makes clear.

John Baez has a fun lecture about this and related stuff here.

verygaygirlfriendfoxmulder-deac asked: right now i'm an english major/women's studeis person, but i've always been passionate about astronomy. math was my weakest subject, but i don't think i'm bad at it. probably now a little bit since i'm out of practice (after having been convinced i was "bad" at math), but i think what i want to do is pursue my passion in astronomy. it's been the only constant in my life since i was about 10. i was going to switch to physics in the spring, but idk... im scared? excited? having low self esteem

tbh anything relevant is welcomed mostly like. lol i just want to do astrophysics and have a degree im proud of and have a challenge??? but i still have this crippling anxiety that i’m not smart enough or ppl will be mean to me or something :’|

[note: part of this ask exchange was lost b/c I replied privately, but basically verygaygirlfriendfoxmulder asked for advice and I wanted to make sure I wouldn’t be giving totally irrelevant advice]

Okay, first of all, as I already mentioned in a private ask, I was pretty sure I wanted to major in physics (or maybe math) when I first arrived in college, and in fact did so.  So I can’t offer any advice about changing majors.  I’m also a cis male and can’t directly speak to gender prejudice in physics (besides the obvious “it exists”).

I did used to think of myself as bad at math – I was several years behind my friends in math for much of high school, and once took a neuropsychological test where the testers told me I would never be good at math.

I started becoming much more interested in math after I signed up for calculus-based physics on a whim before senior year of high school and read the book Calculus Made Easy the summer before senior year.  I was surprised how easy it was to pick up the basic concepts (this was partly because the book is designed to make things easy, as the title suggests), and I started to think that maybe math wasn’t my enemy after all.  After that I did very well in the physics class and found it fascinating, which is what set me on the road to majoring in physics.

So, if I can give any advice based on personal experience, it’s to try to find a good, non-intimidating, preferably entertaining math textbook at whatever level you’re at, and try to read it on your own outside of any academic context.  If you find this fun, that’s a very good sign, and also a way for you to pick up on the concepts you may have fallen behind on.

My personal opinion is that math is so poorly taught at the pre-college level (at least in the U.S., where I live) that a lot of people’s anxieties about the subject, or senses that they aren’t good at it, are entirely the result of the teaching system and not of the subject matter.  I’m not saying that you shouldn’t worry about math being a stumbling block, but that if you’re worried about it being a stumbling block, try to have direct experiences with math outside of class instruction, and see how they go.  Read textbooks, or even just surf Wikipedia, on your own time, and see how you feel about it.

(Paul Lockhart’s passionate essay A Mathematician’s Lament says a lot of things I agree with about how bad early math education is; I wouldn’t go as far as he does in some places but the essay is definitely worth a read.)

As for anxiety, worrying that you’re not smart enough, etc.: you are not alone, it happens to many people studying famously “hard” subjects (see “impostor syndrome”).  It is frustrating, and it will not stop being frustrating – I’m in grad school and I constantly worry that I’m not smart enough to be here or that I’m the dumbest person in the program and everyone knows it, to the point that the worries often interfere with getting work done.  Even though I’ve been here for three years and have passed all my quals and seem to be making good progress in research and so forth.  And, I mean, I have an anxiety disorder that I am medicated for, and, well … I’ve gotten this far, is I guess what I’m saying?  The worries never go away but they do not mean it won’t work out.

I hope that was helpful in some way!