"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".
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]
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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.
How much of the rise do the listed later on (endurance athletes, obesity, sugary drinks, sedentary lifestyle) explain the relative youth rise? After all, some of this was an issue in 2006 as it is in 2026. Does it explain most of the relative rise, or is there a major missing piece / a mystery still to be explained? I doubt the % of endurance athletes changed meaningfully population-wide, to be a major contributing factor, for example.
I don't doubt translators face massive job losses. I hate this "personal interest" style anecdotal news stories though, because it gives me no actual sense/data on how fast/slow this transition is, how widespread etc. It's basically junk food.
A lot of viruses insert themselves into your DNA, they may mess up the 3D structure, or during DNA repair result in misrepair / duplications, or simply insert somewhere and break something important. All of these are ways that can contribute to kickstarting or accelerating cancerous growth.
I've really seen both I suppose. A lot of devs don't take accountability / responsibility for their code, especially if they haven't done anything that actually got shipped and used, or in general haven't done much responsible adulting.
Look up Jevons Paradox, when something becomes more efficient, consumption can goes up, often due to price elasticity.
Think of like this: Imagine car prices go from $200,000 to $$20,000 - you wouldn't sell 10x the amount of cars, you'd sell --- In fact I just looked up the numbers - worldwide only 100K or so cars are 200K & higher, whereas roughly 80 million cars are in that affordable category.
So a price drop of 90% allowed sales to go from 0.1M to 80M!! I think this means we need more engines, tires, roads, gas, spare parts.
I think the biggest lever is completely overhauling healthcare. The USA is very inefficient, and for subpar outcomes. In practice, the federal government already pays for the neediest of patients - the elderly, the at-risk children, the poor, and veterans. Whereas insurance rakes in profits from the healthiest working age people. Given aging, and the impossibility of growing faster than the GDP forever, we'll have to deal with this sooner or later. Drug spending, often the boogeyman, is less than 7% of the overall healthcare budget.
There is massive waste in our military spending due to the pork-barrel nature of many contracts. That'd be second big bucket I'd reform.
I think you're also right that inflation will ultimately take care of the budget deficit. The trick is to avoid hyperinflation and punitive interest rates that usually come along for the ride.
I would also encourage migration of highly skilled workers to help pay for an aging population of boomers. Let's increase our taxpayer base!
I am for higher rates of taxation on capital gains over $1.5M or so, that'll also help avoid a stock market bubble to some extent. One can close various loopholes while at it.
I am mostly arguing for policy changes to redistribute more equitably. I would make the "charity" status of college commensurate with the amount of financial aid given to students and the absolute cost of tuition for example., for example. I am against student loan forgiveness for various reasons - it's out of topic for this thread but happy to expand if interested.
Global datacenter spending across all categories (ML + everything else) is roughly 0.9 - 1.2 trillion dollars for the last three years combined, I was initially going to go for "quarter of the federal budget", but picked something I thought was more conservative to account for announced spending and 2025 etc. I pick 2022 onward for the LLM wave. In reality, solely ML driven, actual realized-to-date spending is probably about 5% of the federal budget. The big announcements will spread out over the next several years in build-out. Nonetheless, it's large enough to drive GDP growth a meaningful amount. Not large enough that redirecting it elsewhere will solve our societal problems.