A good foundation in understanding scientific claims and evaluating proofs seems essential in such times. Maths is an essential part of that.
Rather, as the US Constitution has bluntly put it, if we want to keep democracy, "the right of the people to keep and bear Arms, shall not be infringed." The above examples seem to support this.
In fact, I believe that the invention of firearms democratized military might by making the professional soldier (knight, man-at-arms or Swiss style mercernary) obsolete. In a time where military might was determined by how many men could be drafted into service, a government could only retain power through the support of those drafted men.
A rule by "all drafted men", in other words, is the foundation of democracy. Like most societies, a democracy is rule by the predominant warrior caste. In the greek democracies, all male citizens were serving as hoplites. That was teh basis for their "democracy". The Roman republic had legions of citizens (until Marius), enabling another form of citizen rule. Then came the Marian reforms, with professional soldiers controlled by the elite. Almost directly after, Sulla, Caesar and Octavian introduced the Roman Empire.
500 years later, the Romans in Western Europe were overrun by Germanic chiefs. Their elite soldiers became the armored knights of the Medieval Europe, and they introduced Feudalism, where power was held by the nobility (and sometimes shared with a king, who was often quite weak).
Then came the age of the pike armed Swiss mercenaries and similar non-noble military formations more similar to the legions of Imperial Rome. This gave many European monarchs full controls.
The founding fathers saw this, and rightly predicted that armed citizens was an ingredient in ensuring governance by the people. In Europe it would take another 150 years or so for this to play out.
Many on the left will not realize this. They think that democracy is self-sustaining regardless of potential for the elites to be corrupted and sieze the power.
The founding fathers had studied their history. They knew about Marius and Sulla and how the Roman elites quickly had taken control once the citizens were no longer the backbone of the army.
The founding fathers were not "common people", but rather highly educated members of the elites. Their existence had been made possible by a monarchical system, and they bore many similarities with the elites of the Roman empire (the senators).
The guns may give the power to rule, but not the wisdom, and people like Thomas Jefferson understood this. And this is where the understanding of the populist right falls short.
Thomas Jefferson in particular was a proponent of quality education for the citizenry, he thought that "no other sure foundation can be devised for the preservation of freedom and happiness".
In other words, not only guns but also books were needed to keep the people free (and happy).
https://en.wikipedia.org/wiki/Thomas_Jefferson_and_education
When citizens completely lose the ability to understand the world in which they live. He promoted the teaching of "Science and Virtue", but was concerned about intellectuals from "tyrannies" in Europe.
Maybe he anticipated something like the Frankfurt School?
The only way to prevent demagogues (like Ceasar) who promise to people that which is impossible to deliver, is to: 1) Make sure the people know enough Science to be able to know the possible from the impossible. 2) Make sure people know enough history to recognize what values are true Virtues that lead to healthy societies, and which are hollow lies, more suitable for use by would-be-dictators to gain control.
But I do hold the concern you hint at, and with an increasing tendency towards fewer, more expensive and soon maybe automated weapons platforms, the risk may increase of some kind of move towards some alternative system. (Monarchy, Aristocracy, Oligarchy, Theocracy, Autocracy, etc)
Which is why I (who used to be too liberterian to like the idea of a forced draft) now support a system based on the draft, simply because of the stability it provides.
But if and when the most effective type of military once again becomes wieldable by a small minority, it will become harder and harder to prevent a shift.
The Civil War was the ultimate aim of the Second Amendment. State militias banded together to fight the United States. It was never about ensuring democracy.
The interpretation that the Second Amendment is about enabling individuals to protect their personal interests with guns is very new. And this idea that the Second Amendment is supposed to be about guns maintaining democracy is a perversion of even that. Coercion via the threat of violence from random, unelected strangers doesn't feel very 'democratic' to me.
I'm not American, and I'm not writing specifically for the US. But after reading up on most periods of Western history, I did notice that whatever group of people served as the core of the army, tended to be the same group that controlled the country. And that this pattern seems to be older than history itself.
> And this idea that the Second Amendment is supposed to be about guns maintaining democracy is a perversion of even that.
The idea itself is almost certainly not new. Around the time of the American Revolution, Europe had been through a period of around 1800 years of mostly some form of tyranny.
For most of that period, the "right to bear arms" (which tended to mean military grade weapons and armor) was restricted to the nobility or other privileged group, who would often take advantage of the monopoly for coercive purposes. (Kind of like the Sheriff of Nottingham in the Robin Hood legend.)
People living 200-250 years ago were certainly aware of that, as it was recent history for them. The concept that was new to them, was that of "democracy". Instead, they tended to care about "liberty" vs "tyranny".
For instance, St. George Tucker in 1803:
"A well regulated militia being necessary to the security of a free state, the right of the people to keep, and bear arms, shall not be infringed. Amendments to C. U. S. Art. 4. This may be considered as the true palladium of liberty ... The right of self defence is the first law of nature: In most governments it has been the study of rulers to confine this right within the narrowest limits possible. Wherever standing armies are kept up, and the right of the people to keep and bear arms is, under any colour or pretext whatsoever, prohibited, liberty, if not already annihilated, is on the brink of destruction."
People at that era, just as now, had many different opinions, and I don't know the discussions well enough to know the precise intent of the Second Amendment.
But whether it was the intent or a side effect, I believe one effect of an armoed populace (privately armed or drafted), is that it makes it harder for a would-be tyrant to take away all liberties.
One example that may be more relevant than the USA, right now, is Russia. Russia still has a system partially based on the draft. But Putin is not willing to pull in all reserves the way Ukraine has done. A reason for that may be that it could increase the risk of the army turning against him.
I don't claim simply learning maths is sufficient - I mean math in the form of what is a proof, statistical reasoning, things like that.
In general I don't think we ever even looked at a paper or "study" and tried to find tell-tale signs of bad science. That should change.