There's something quite interesting about the problems in number theory especially. The questions/relationships sometimes don't seem useful at all and are later proven to be incredibly useful. Number Theory is the prime example of this. I believe there's a G H Hardy quote somewhere, about Number Theory being obviously useless, but could only find it from one secondary source, although it does track with his views expressed in A Mathematician's Apology[1] - "The theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics."
You can find relationships between ideas or topics that are seemingly unrelated, for instance, even perfect numbers and Mersenne primes have a 1:1 mapping and therefore they're logically equivalent and a proof that either set is either infinite or finite is sufficient to prove the other's relationship with infinity.
There's little to no intuitive relationship between these ideas, but the fact that they're linked is somewhat humbling - a fun quirk in the fabric of the universe, if you will.
> No one has yet found any war-like purpose to be served by the theory of numbers or relativity or quantum mechanics, and it seems very unlikely that anybody will do so for many years.
Less than 100 years later, we stand waiting for nuclear bombs guided by GPS to be launched when the authorization cryptographic certificate is verified.
My bad. You’re right. It was group theory and cryptanalysis. Number theory comes in later in the 1970s for public key cryptography (1976 publicly, early 1970s at GCHQ). So the military work on it really started in the late 1960s.
Number theory appears to be at the core of computability, via Matiyasevich's theorem, which links the behavior of every Turing machine to the solutions (or lack thereof) of Diophantine equations. It’s not surprising to me that number theory constantly ends up being more useful than suspected since in many ways the study of these equations is equivalent to the study of computation.
I actually just left Betterment because over the last few years their Core portfolio has really lagged performance of my non-Betterment investments (largely VTI, VTSAX, VBTLX in approximately 80/20 stock/bond split). Upon ACATS-ing over to another broker, I found they'd purchased some funds with high fees when there were really similar funds available with far, far lower fees. The only reason I can think of to buy a higher expense fund when a much lower expense variant exists is in the name of tax loss harvesting, but even that is a really short-sighted decision.
Another thing that annoys me endlessly: a few months ago, Apple Music introduced animated cover art and then proceeded to animate album covers that shipped decades before Apple Music existed. If modern artists want to use this for their new albums, or if an artist wants to rethink the album artwork for a remaster, fine. But, Apple deciding to do a shoddy job of moving the Beatles to another layer and having it pulse in and out on the cover of Abbey Road? Fuck that.
I'd argue DARE is more akin to abstinence only sex ed than an actual sex ed curriculum. Or at least my DARE experience was much closer to a Mr. Mackey "Drugs are bad, m'kay" than a measured instruction of various drugs and the kinds of harms they posed.
I had a Honeywell smart thermostat that worked entirely locally with Apple's HomeKit. I haven't used Home Assistant but a cursory Google search implies this would work. My recollection is it was a Honeywell T5. Notably it did sometimes fall off the WiFi for brief periods of time, so I couldn't give the product itself a ringing endorsement.
I usually specifically look for smart devices like this because I dislike the idea of them phoning home for "analytics" or "to enhance my marketing experience" and just firewall them off.
I'm not sure if it's explicitly required, but I've yet to encounter a HomeKit device that didn't work when prohibited from talking to anything outside the LAN.
You can find relationships between ideas or topics that are seemingly unrelated, for instance, even perfect numbers and Mersenne primes have a 1:1 mapping and therefore they're logically equivalent and a proof that either set is either infinite or finite is sufficient to prove the other's relationship with infinity. There's little to no intuitive relationship between these ideas, but the fact that they're linked is somewhat humbling - a fun quirk in the fabric of the universe, if you will.
[1] https://en.wikipedia.org/wiki/A_Mathematician's_Apology