What do you do on days you just don't feel like studying?

Why did the human species diversify phenotypically so much a few thousand years ago? Why has that process stopped? Why was change needed then, not before, not after? Humans have continuously inhabited Europe for the last 40,000 years

There are a lot of people with math and physics degrees at the Amazon warehouse...

How does not knowing the factors of a large number hide information?
How have we not run out of numbers used to generate private and public keys? There's only so many prime numbers that exist within a 2048-bit number space. And the larger the number the less likely it is to be a prime.
When 2048-bits become unsafe do we just go to something like 4096-bits? Is that the name of the game? Just increase keep increasing the key size? What's the downside, that it takes more time to legitimately use these keys every time you want to encrypt and decrypt a message?
When i'm generating a private key, am I finding two huge prime numbers then multiplying them together to get an even bigger number that takes people a long time to figure out what the two prime factors are?
Obviously there are some fundamental mathematical concepts that I'm not getting that make these questions seem rather stupid.

I’m the DOE spent fuel engineer from a previous thread. Let’s talk nuclear stuff. Fission, fusion, weapons, power, etc.

Heres the situation
>be me
>18 years old
>skipped math classes literally all the time in highschool
>graduated hs without knowing even order of operations
>didn't go to college because neet
>started self studying math
>use jerome kaufman's algebra for college student for a year now.
>my performance is alright, i am at ease throughout the whole book, ace the practice excercises throughout the whole book.
>have one problem: struggling at problem solving

Holy shit..Give me any function, I can easily find its' difference quotient, graph, x and y intercepts, minimum value. Give me any polynomial and I can easily factor it, and enjoy the long process involving fractions with radicals and shit Basically, I am good at paper but struggle at applying the concepts I have learned in word problems and struggle also at setting up proper equations, variables etc.

How did you become good at solving word problems? Books you used, techniques, etc will be appreciated.

Which country/city to live in as a "digital nomad"?

>night before math exam
>painful abstainment from coffee for weeks (2 cups a week), in preparation for big coffee blowout the morning of the exam
>be retarded
>decide to have a small cup in the evening with a signifact amount of dark chocolate, being used to falling asleep like a baby having downed 2 cups back when I was addicted
>now can't sleep
It's fucking over.

America's Rocket edition
Previous: >>14321039

>tfw just proved P = NP
let $A$ be connected graph such that $P$ has a truth table of size $2^{o(\alpha^2)}$. Then $A$ has a truth table of size $2^{o(\alpha^2)}$. We can assume w.l.o.g. that $A$ has no isolated vertices and only one (isolated) cycle. If there are only $p$ components that are not Hamiltonian then, since $A$ has a single cycle, there exists a connected component with at least $p$ vertices. Now, let us define a truth table $\mathcal{T}$ for $A$. In the truth table $\mathcal{T}$, there is exactly one row in each of the $p$ connected components, $x_1x_2\ldots x_p$: the truth table is made with the labels in $V\backslash\{x_1,\ldots,x_p\}$ and the $x_i$ in the truth table correspond to the vertices in the connected component. Since $P$ has a truth table of size $2^{o(\alpha^2)}$ we can have, without loss of generality, the $x_i$ corresponding to the vertices on the cycle (since $P$ does not have isolated cycles). For each of the $p$ rows we label the vertices corresponding to the $x_i$ with $1$ (true) and the other vertices with $0$ (false).

By following each of the first $p$ rows of $\mathcal{T}$ we see that one of the $p$ vertices $x_i$ satisfies $\bigwedge_{1\leq i \leq p}x_i=1$ (since we must make a truth table for each connected component). Now, since $A$ is connected, we must have that $x_i=x_j$ for all $i,j\in \{1,\ldots,p\}$: the $p$ vertices $x_i$ must be identical. This gives us that $x_1x_2\ldots x_p=1$ and, since $A$ has a single cycle, $1$ is a truth table of size $2^{o(\alpha^2)}$ of $A$ contradicting that $P$ is a truth table NP-complete, therefore P = NP.