dkural

It's because Texas is the OG of human suffering. Texas gave up territory than end slavery: This is why Oklahoma looks so weird (the "panhandle"). After the so-called Missouri compromise, in order to remain a slave-state, Texas gave up that piece of land. Also, Texas declared independence not once, but twice, to remain a slave state. First, from Mexico: "Many Anglo-American settlers were from the southern United States and brought enslaved workers, using legal loopholes like indentured servitude to bypass Mexican restrictions against slavery. They feared Mexico would abolish the practice entirely". And then, famously, of course, fighting to remain independent during the Civil War.

Copper is a well known antimicrobial and copper paint is used on ship hulls as an anti-fouling layer.

"every novel result is broadly perceived as a big deal" is not at all true. AI companies hype any novel result as proof that AI is good for mathematics, but professional mathematicians write tens of thousands of papers every year, and for 99.99% of them, nobody cares or writes it up. Mathematicians certainly don't go around saying each and every novel proof in their papers are a big deal. Do you have any evidence supporting your statement that it is "broadly perceived" (by whom?) as a big deal?

Most fields, in the aggregate, produce a lot of pointless work, but if you judge mathematics by its best examples, as judged by the field itself, and also by the outside intellectual community, it is a coherent body of work (& brilliantly creative). It is not pointless puzzles at all. William Thurston's geometrization theorem, Klein's erlangen program, Witten's work in physics-inspired mathematics, Langlands program, the Grothendieck school of Algebraic Geometry are deep and abiding intellectual achievements of true understanding. If you don't understand the meaning behind this work, it speaks to your ignorance, not to their significance. The "obvious practical problems" are not solved. Fluid Dynamics is wide open. Non-perturbative quantum theories are wide open. Heck, there are open mathematical problems in General Relativity. Dynamical systems are very poorly understood. Go read a book or something.

There's actually a lot of math trying to describe the types of space you mention - non quantized, non 'granular', they're not made of points, or distances (metrics). One deep idea is to define space through which symmetries hold (Klein's Erlangen program). Topology itself is not interested in distances per se, only properties of a space invariant under homeomorphisms (a fancy way of saying you can continuously deform a cup to be a donut). Thurston's Geometrization Theorem outlines the 8 geometries that a closed 3 manifold can have. Topos theory studies space in a very general setting that connects logic to it. You may like the books "The Shape of Space" and "Surreal Numbers". The Numbers 1, 2, 3 is not the only in which mathematicians abstract reality.

Spot on! Love Diaspora. This is honestly such a gem of a comment. To some extent, if the AI ever gets "so far ahead" of humans, the most productive aspect will be the frontier visible to humans. We're focused on translating mathematics to lean at the moment, but it'll be as important to translate it to humanese - to the human language of structure, number, geometry. I also completely agree with LLMs being essentially blind to visual reasoning. They really struggle reasoning with Floer Heegard diagrams for example.

Your example of the Italian school is well taken, although most of their results were later proven to be correct in the right setting. Severi's example is particularly egregious and I think a major reason this became a thing is Severi's refusal to course-correct and accept that some of the results were not correct. It has echoes of Mochizuki, and I fear, once you dig deeper, some issues around the initial declaration of "We've proven the Classification of Finite Simple Groups". There were many genuine gaps, and a lot of lore taken for granted. The sociology around how this happened is interesting - rushing to announce that it was done was the major mistake, it took away almost all incentive to actually write up the proofs and take them through proper peer-review. Genuine mathematical work was falsely reduced to "write up".

Some of the Istanbul earthquakes felt like that for me.

This part: Let's now adjust for inflation so you can see the budget squeeze. $19.2 billion in 2016 dollars is worth $26.4 billion and change, once adjusted for inflation, in March 2026. Feel free to do it yourself. Magic of compounding.

24.4 for 2026 is notably less than 26.4. Budget squeeze.

I agree with you - I was saying that members of the military & their families have treaty-defined standards of being in the country & thus required to behave a certain way, whereas a regular visitor or student visa comes with a different set of rules and not regulated by a military cooperation treaty.

Different rules apply to members of the military stationed on a treaty-based foreign military base.

However, as a thought experiment, let's go with your flawed analogy: Even then, this person was acting like a guest -- it is a long-cherished American tradition to exercise our constitutionally-protected right to free speech, assemble, and yes, protest. Nothing's more American than speaking against Government oppression and overreach.

The government is not your owner. The government is not your father. You are a participant in the affairs of your country, and take responsibility in its direction. Civic engagement and right to protest are important tools to make our government accountable. These are fundamental American values. And you're welcome to bring friends. It's legal.

One of the attractions of a country for scientists and scholars, and visitors generally, is an atmosphere of freedom. The right to protest is a constitutionally protected right. He was well within his rights. The current administration is purposefully curtailing freedoms to intimidate ordinary people to keep quiet as they plunder the country. Google is now going along with it. Your advice is to just study and enjoy the experience, which is what most people do. Luckily there are others who can be loud for those who can no longer speak, their cities bombed and families killed; with the hope that the world will eventually notice and listen. Civic engagement, and a free press is one of the most important tools at our disposal to fight those who seek to exploit the weak - that is why every wanna-be dictator and corrupt politician is so keen to curtail these rights.

"The area is so remote that, since no regular marine or air traffic routes are within 400 kilometres (250 mi), sometimes the closest human beings are astronauts aboard the International Space Station when it passes overhead.[23][24] "

You realize that is far too recent to show up in cancer death rates for under-40 year olds right? It takes 10-15 years for a change-in-behavior to show up in incidence and even longer for deaths. As a classic example, see the shift (i.e. the delay) in curve of reduced smoking and reduced lung cancer.