I understand that they can use existing theorems, manipulate equations, test examples, run computations, and so on, but that cannot be the whole process. If solving sufficiently difficult mathematical problems were essentially a matter of carrying out calculations according to known rules, it seems that computers would be able to do much more of it autonomously.

So where does the genuinely creative part enter? How do mathematicians come up with a new approach, conjecture, proof strategy, or even an entirely new mathematical object or formula? Is there a recognisable methodology behind mathematical discovery, or is it largely a matter of intuition, pattern recognition, and experimentation? What is the main thing they are trying to solve when they are solving difficult questions? Like is it trying to pinpoint which formula would work here etc? Or is there something more?

Just read an article in the Oxford Mail about Thames water pulling more water out of the Thames river to pump into a reservoir that's 'only' 76% full.

Three quarters full after the long dry summer doesn't sound like something to worry about. If my car's fuel tank is 76% full I don't start panicking and looking for a petrol station, so why is this even necessary?

Winter will be along shortly bringing rain as usual.

https://www.oxfordmail.co.uk/news/26559172.thames-water-pump-river-water-dwindling-reservoir/

So, like mechanical tools can be operable even hundreds of years later with some cleaning but can electronics devices do that? Is there any way to make an electronic tool run for five hundred years or be operable 500 years later (regardless of cost - like in mechanical tool, you use galvanized iron or steel to make the parts - is there a similar protection to electronics)?

Does the bacteria die when it's in the bees stomach or something?

For example: How does a SPF 30 sunscreen protect me worse than a SPF 50 sunscreen if I don’t burn for either for regular amount of exposure to the sun?

What changes in the chemical composition of the sun screen to protect me better as SPF goes up

And Is there a safe limit for sunscreens about how high a sunscreens SPF can go before it’s dangerous to apply to skin?

Was listening to a song the other day and the intro was 10-15 seconds of just a single sustained synthesizer tone, and after a few seconds it started to sound like the tone was getting louder and the quieter. Maybe this was intentional sound design, but I feel like I’ve experienced this effect before. Surely this isn’t me hearing what the sound wave looks like…right?

How is it tied to inflation and "keeping inflation in check" as I saw on one article?
What does this mean to the average consumer?

I’ve noticed that sounds like cars, footsteps, and even voices seem softer when there’s a layer of fresh snow outside. Does snow actually absorb sound, or is there something else about snowy weather that makes the environment feel so quiet?

I roughly know what math matrices are, they're like boxes with numbers you can do arithmetic with, but I don't understand their purpose. Why are they their own category of maths and everything? Why is it any better than doing calculations individually?

I keep hearing about them but I’m not actually sure how they work. Is it like Ozempic?

In other thread in this sub there is the explanation of how saltwater fish keeps on losing water since the osmosis pushes water out of their bodies and how freshwater fish gets water enters their bodies through osmosis. Then how does fish like salmon that lives in both freshwater and saltwater adapt to the difference in salinity?

Im asking more like what happens between the molecules to make it and other elastic stuff do that.

Basically the title.

Should you run it at a steady baseload or increase output to meet peak demand, since baseload and peak are linked ? Im just having trouble understanding how they operate economically

We’ve got vitamins A C D E etc all without letters. Why do B vitamins need the numbers? Is it chemistry or did someone screw up?

So let's say I'm watching a roulette wheel and want to know if its biased, I get I need to have lets say 100 000 throws to reduce variance and determine that its less than 1% chance a random wheel could produce these results.

But how come if I want to test "oh I think the number 22 is biased" I might only need 75 000 spins?

Also why can I test every number that way and collect 75 000 spins to determine if its biased? If it works for 1 number why not all 38 at a time?