Well, I am humbled by the company here.

Godspeed, gentlemen.

M J R:

Yep. That was it!

OBloodyHell (10:40 pm) said, “even if you never ever use the math techniques directly, learning them does do a very very important thing, and that is to give your thinking processes a great deal of rigor and self-checking. The world can always use a lot more of that.”

I am privileged to attest to this via personal experience. I recently wrote in a volume of my own personal reminiscences that

“Preparing for this pure mathematics doctoral oral exam was about the most grueling experience of my life, and passing it with flying colors was one of the most exhilarating. The mental and intellectual discipline I acquired and required of myself was without parallel. I only wish I had better words to describe the profound sense of growth and achievement I experienced.”

I still lack those “better words”. But OBloodyHell is very on-target when writing of “giv[ing] your thinking processes a great deal of rigor and self-checking.”

As far as I can determine, that experience / gift never went away, even after all these decades. At the same time, I fear that those decades do appear to be taking a toll vis-a-vis sharpness, acuity, and the like. No, I ain’t what I once was.

And, now [drum roll] . . .

Understatement Of The Year / Century: “The world can always use a lot more of that.”

Bring it on!!

[I did eventually complete the entire course of study alluded to above, albeit with very unusual twists and turns and sidesteps.]

I do now recall mentioning in some or other context a confectionery near the school. If that’s what you are recalling, I plead guilty as charged!

I found that you can, interestingly, trace your own understanding of math pretty much to the approximate decade of the mathematics being applied.

Oh, yes, I completely agree. A graduate course in complex analysis will generally bring you up to around 1900, Linear algebra to maybe 1920, abstract algebra to 1960 (due to abstract nonsense), model theory to 1960-1970, etc. Of course, those are general classes, specializing will make one more current in some tiny little bit of mathematics. There are geniuses who are on the cutting edge of more than one little bit, Terence Tao for instance, but it isn’t common. As I said, I did a Ph’D more for fun than for a profession. First, 52 is way too old to start climbing the slippery pole of academia, and second, the people making important contributions were younger and more talented than I.

In terms of today’s population, that would be like 1760 people dying of one disaster. Almost literally unthinkable.

Or the 8000-odd toll of the 1900 Galveston hurricane, equivalent to 35,000 in a modern context. The mind boggles at how easy Death was a mere 75-100 years ago.

Today we freak out over numbers that are mere fractions of those.

…Well, we saw how unfair he was, in shutting down gasoline making companies + fossil fuels companies, so you can bet: he , + Vice President Harris, + the Democrats who support him, will be just as unfair:

[in trying to cut the Congress + voters out of making new gun laws, and “assault rifles + assault weapons laws”, to ban or outlaw:

[any models of guns they don’t like, or any laws that allow open carry of guns, or any laws that allow concealed carry of guns], in The United States].

Do you have a Glock pistol that holds more than 10 bullets or 10 bullets in its magazine[?]…too bad for you. Biden will try to outlaw/ban it.

Do you have a semiautomatic rifle that looks like an: AR-15, or an M4, or an M16[?]…to bad for you. Biden will try to outlaw it.

Do you have a semiautomatic rifle that looks like an AK47 or an AKM[?]…to bad for you. Biden will try to outlaw it.

Have you ever gotten a felony conviction, like- disorderly conduct for an act like- tossing a glass of Pepsi on someone when you were mad[?], or does your town or State give you + other people a felony conviction- for a parking ticket…or for driving 5 miles over the speed limit[?]…to bad for you. Biden will likely try to outlaw YOU from owning a gun, for the rest of your life, for getting that felony conviction.

Do you like, target shooting, or having guns to defend yourself or others, or [do you think bullets + guns are interesting?, Or do you think ballistic science is fun?], well- Biden and his new [anti-gun violence] push will probably tell people that you are “sadistic or brainless people” that “don’t care if kids under 18 are killed by guns, or that anyone is killed by guns”.

Yes, US, civilian gun owners care about people being hurt or killed by guns, + they try to teach themselves and others how to use guns- so that innocent + non-violent people don’t get killed or hurt by guns, ever.

Please do what you can to stop Biden from making very unfair [laws or rules] that unfairly target: law-abiding, civilian gun owners, by contacting Congress + any State officials, or town/city officials- and ask them to stop Biden from making these laws, when he tries to make these kinds of laws.

(Also, as a final note- Biden likes to say things like: [20 thousand people are killed in the US by guns each year. Let’s outlaw all guns.]

Yes, and about 20 thousand people are killed by car accidents, + by crimes done with cars, each year in the US- but Biden, + others, don’t see that statistic and say: “Let’s outlaw all the cars”.

Please notice- 20 thousand isn’t the exact number(s) for these two type of fatalities, but I’m just trying to make a point about Biden’s using statistics, in his statements].

Thank you for reading my comment, today.

Cheers.

Here’s a link to a news article about this issue-

https://www.koat.com/article/gun-violence-prevention-federal-office-announcement/45263781

They refused to let me (some BS about it being “independent study”, and I was supposedly not “mature enough” @ 15, despite the summer class being mostly limited supervision, with the teacher spending most of his time hanging out in the TLounge…). One reason I have ALWAYS despised public schools, their apparent purpose is to HOLD BACK anyone with any ability at all. 🙁 I honestly believe I could have been doing Calculus by the time I was 12, had they not been spoon-feeding me math.

Needless to say, This Crap did not Stop Me for a minute. I went to the local public library, found a college level textbook which had the answers in the appendix, and started teaching myself… quite successfully, I will assert. When queried, one of the teachers who had rejected me spoke of reversing himself the beginning of the next term.

As a result of my mother’s financial situation, however, I wound up transferring to a different school a mid-term, and the teacher who Taught Calculus was kind of jerk who was — in the mid 1970s, still using (literally) 1950s-era teaching methodologies. As an adult, I appreciate and understand where he came from more, but it was not the kind of teaching style that worked with me in any regard, so… when my senior year rolled around I just took fewer HS hours and went to the local JuCo to take classes in Calculus and Physics w/ Calculus — actual credit — rather than get “AP” credit. As a result of that, I pretty much ran 3y ahead of my official Class in college, with regards to math — taking 4000 level classes as a Freshman, 5000 level grad classes as a soph, and 6000 level classes as a Junior.

I found that you can, interestingly, trace your own understanding of math pretty much to the approximate decade of the mathematics being applied. And, similarly, to the sophistication of the techniques used to manipulate concepts to get from “what you don’t know how to deal with” to “what you do know how to deal with”. I pretty much broke off around 1850 or so…

Gauss was, as you suggest, an absolute genius… Laplace was right up there with him.

It’s interesting how every single technique used in Differential Equations class are limited and utterly useless. Laplace Transforms are among the first such concepts and can actually deal with some moderately realistic problems, if still simple ones.

My two fav early classes were Laplace Transforms and Applied Boundary Value Problems, both ca. 1710 in math. I was quite self-pleased when I foresaw the techniques being taught as a way to solve the problems in the next classes — first, the extension of the Factorial concept into the Gamma function, and the usage of Difference Equations to create a generalized solution for the Fibonacci sequence. Most people here are going, “Huh?” but that’s ok. I independently saw the application, and that’s no small feat.

After that, my favorite class was Complex Variables and the notion of Conformal Mapping.

I generally never liked theory, but Abstract Algebra was just melt-in-your-mouth theory for me. Had I gone into teaching, it would have been a prime candidate, along with Applied Math.

*sigh* It’s been decades, though, I’d have a hard time doing an integration by parts, as I segue’d into doing computers, instead.

But don’t regret my experience at all, as I think, at the very least — even if you never ever Use the math techniques directly, learning them does do a very very important thing, and that is to give your thinking processes a great deal of Rigor and self-checking. The world can always use a lot more of that.

Hey, I picked up a Ph’D in mathematics at age 52, for the fun of it. Have managed 31,000+ citations, depending on who is counting, since then for two joint math adjacent papers that I didn’t even need to write, though I was first author on one. The citations are somewhat wasted on me, as I am not an academic and retired in any case. But they do offer some bragging rights 🙂

Irving Reed was a family friend, and his thesis advisor was E. T. Bell (pseudonym) for a dissertation in functional analysis. Which is a bit odd as his fame is in electrical/computer engineering (Reed-Solomon codes). He once opined that there were three good mathematicians at USC, and one of them was in the math department.

Apropos Gauss and publication, he also discovered the fast fourier transform (1805), but never published the monograph that contained it. A good reference on the history of the FFT is here. It was rediscovered in different forms several times after, but never made a big splash until 1965, when the Cooley-Tukey algorithm was published. It is now one of the most important numerical methods.

For a good, but short, discussion of the development of non-Euclidean geometry, see this.

Gauss was a very smart guy.

Sure thing!