The Royal Institution: Eugenia Cheng — “How To Think Like A Mathematician”

Unexpected great discoveries. Calculating the cosmos: How mathematics unveils the universe. By Ian Stewart.

I'm a physics major who works as a tutor with a bunch of math majors, and today I was explaining differentials to a student and I said to convert the dC/dt equation to one with differentials just multiply both sides by dt and that's the only difference and I could feel them all judging me hfgsgskdhdlhd trust me we know we are wrong but we are too lazy and dumb

Okay, okay, look, all is well.

Yeah mathematicians are gonna cringe a little when people say stuff like this because we know it’s not rigorous, but you know what else? We made that dy/dx notation look like fractions for a reason. Certainly what’s going on here is a little more subtle than division and multiplication and if you’re working with some really weird functions that subtlety could get you in trouble. But for most situations, you can treat that stuff like fractions, and we made the notation that way to highlight that fact and make the symbol manipulation more efficient.

We laid the complicated foundations with rigorous analysis so we would have a robust and efficient tool, and we made it user-friendly, and we gripe about its users using it the way we intended? That’s like complaining that I use my phone without understanding its circuitry or complaining that I eat pop tarts without understanding what’s in them. Those things are true, but my phone was designed to be used by someone who doesn’t understand or need to understand its circuitry and pop tarts were designed to be eaten by people who don’t understand or need to understand what’s in them. I know that someone understands my phone’s circuitry and someone knows what’s in pop tarts and I trust them.

You’re not lazy or dumb. Calculus, as mathematicians passed it off to engineers and scientists, was designed to be used by people who don’t understand or need to understand the rigorous analysis that holds it up. Engineers and scientists trust that we gave them a good tool that we built well, and they use it. It’s nice when they understand it more deeply and it serves them well but it’s not always necessary.

I’m not gonna stop joking about how silly treating dy/dx as a fraction is, because it certainly won’t fly in math circles where doing so might actually screw you over, but even more because that’s what everyone does. Every field cringes and giggles when the out-group uses their tools without deference and deep understanding, as is every field’s right, but it should never be taken too seriously, because guess what!

That’s the anthropocene, babey! That’s specialization of labor! We don’t all have time to understand everything, we just have to understand what we can and trust that someone else understands the rest! That’s science! That’s humanity! That’s beautiful! Joke about it all you want, it is a little weird, but anyone properly hating on it? Cut it out or I’ll cut you out and that’s that!

If u don’t fuck a special relativity then we can’t be friends

No. 447 

A new geometric design every day 

| Solitude |

Shop | Instagram

Almost done with my concentration!

I love solving mathematical problems. They calm me and cheer me up. They are like meditation to me.

I’m missing them a lot this week. I'm currently writting a paper and is quite urgent, so I don't have time for them. It isn't that I hate writting, I actually quite enjoy it. But it's been a terrible week and I miss my maths.

People don't stop things they enjoy because they reach a certain age

“People think of education as something that they can finish. And what’s more, when they finish, it’s a rite of passage. You’re finished with school. You’re no more a child, and therefore anything that reminds you of school - reading books, having ideas, asking questions - that’s kid’s stuff. Now you’re an adult, you don’t do that sort of thing any more. […] You have everybody looking forward to no longer learning, and you make them ashamed afterward of going back to learning. If you have [a system of education using computers], then anyone, any age, can learn by himself, can continue to be interested. If you enjoy learning, there’s no reason why you should stop at a given age. People don’t stop things they enjoy doing just because they reach a certain age.”

— Isaac Asimov  (via 01030104)

“Document the moments you feel most in love with yourself - what you’re wearing, who you’re around, what you’re doing. Recreate and repeat.”

— Warsan Shire (via larmoyante)

dude seeing these Mega high quality images of the surface of mars that we now have has me fucked up. Like. Mars is a place. mars is a real actual place where one could hypothetically stand. It is a physical place in the universe. ITS JUST OUT THERE LOOKING LIKE UH IDK A REGULAR OLD DESERT WITH LOTS OF ROCKS BUT ITS A WHOLE OTHER PLANET?