Is mathematics over, or just graduating?

vouaobrasil

> It will grow into a full-scale industry and become the true infrastructure of all scientific and technological progress, a foundation that every other field stands on rather than a quiet corner of academia. Sounds revolting. Everything being turned into the industry is soulless and uninspiring. I know a lot of people worship this future but I for one hate it. I for one don't see the point in creating this intellectual power where there will always, always be someone to abuse it simply because of our instinct to be greedy.

shiandow

The notion that mathematics would be over just because it's slightly easier to find proofs is like the idea that astronomy would be over because of telescopes.

caaqil

This is probably the inescapable conclusion that most in the current panic-filled era of Math research discourse will come to, one way or another.

gobdovan

Not sure why people are stopping at 'AI can do advanced math!' and calling that the field is gonna transform due to LLMs specifically. Pretty much any meta-formulation of math gives you some initial rules and a goal. From natural deduction and sequent calculus to dependent type theory and whatever flavour of category theory you choose, at a sufficiently abstract level, you'll end up with some form of search problem. ATP folks foresaw machines doing automatic proofing for decades, but it seems that noone had enough incentive in pursuing it at the cost of suffering the tediousness of the encoding process. Now AI labs took the opportunity to do something impressive and have shown that it's possible to close the ergonomics gap. But the deeper achievement is the decades of ATP and proof-assistant work that make machine-generated proofs mechanically certifiable in the first place. I am pretty sure in the next couple of years we'll see more evolved sledgehammers [0], maybe with LLM-like tech playing a role in encoding theorems, that will allow us to prove deeper than we can do manually, then help with the archeology and extraction of learnings from observing the 'trace' of certified proofs. So instead of explore -> understand -> solve, we'll get solve -> compress -> understand. [0] e.g. https://isabelle.in.tum.de/website-Isabelle2025/dist/Isabell...

paulorlando

This piece reminded me, of all things, of Gandhi's essay "Hind Swaraj." He was pretty anti-technological-driven change. He was anti: - Machinery replacing handicraft (skill disappeared and poverty followed) - Labor-saving machines replacing human workers (workers became expendable) - Doctors replacing consequences (people lost self-control) - Railways replacing constraint and slowness (harm spread faster) But he loved the sewing machine. Gandhi’s test for whether to accept tech-driven change was whether it satisfied primary needs. Interpretation of those needs was certainly not universal. As he wrote: "...it is not the primary need of man to traverse distances with the rapidity of a motor car. The needle on the contrary happens to be an essential thing in life, a primary need.” That's the airplane in this post. Excitement or fear of the AI airplane is either judged as helping mathematicians (sewing machine) or doing something not quite right (the above machinery/doctor/railway)...

suopspaces

https://www.youtube.com/watch?v=92WHN-pAFCs

randallsquared

Ironically, "graduating" is how vtubers announce retirement.

cloudbonsai

The author uses airplanes as an analogy. I want to add a few historical facts here: - First, airplanes in the first 30 years were extremely rough and dangerous. When Dole hosted a contest for the first transpacific flight in 1927, 6 out of 8 teams failed. Ten people died as a result. - Second, people made a lot of silly predictions about this new technology. The New York Times extrapolated that people would soon start commuting to New York using personal airplanes. - Third, people made capital investments based on these wild guesses. For example, the architects of the Empire State Building installed a huge spire to prepare for the upcoming age of airborne traffic (intended to be used as an airship docking station!) The bottom line is that predicting the trajectory of a new technology is often impossible. As a society, we are currently in the experimental phase of LLM-based AI, testing all the possibilities one by one. Who knows which path leads where.

flowerlad

We are entering an age when intelligence is no longer a scarce resource. Bill Gates believes that in 20 years, we will reach an age of abundance [1]. But the next 20 years will bring tremendous social upheaval as we learn to adapt. https://www.nytimes.com/2026/08/26/technology/bill-gates-ai-...

but_the_aeropla

Sure, don't bet against the airplane. Have you utilized an airplane recently? - Only a tightly regulated industry permits you to buy a single-use ticket before the brief upheaval your personal privacy. This isn't a one time scan, it's one for each ticket generally! - You don't ride airplanes every day, it's a tightly controlled portal to far away. Maybe some "very special" people have job subsidized commuter flights daily, but they're a minority. Are we suggesting, and supporting, that commercial AI unfolds the way commercial air travel has? Yikes!!! This is not the future of commercial AI. We need to toss this airplane analogy and use something more accessible. Radio. Radio changed the world 100 years ago, now a significant portion of the human population is armed with at least one radio device they use daily. Side ponder: developing the applications of radio arguably led to a slew of intermediate and sibling developments resulting in the machines we used to build machine learning. Prove me wrong! If you're still with me, then we can attempt to extrapolate together: if 100 years of radio applications cumulated into the smartphone, then, what will 100 years of AI accumulate to? What is the "smartphone" of AI in the future? Electricity is to the SoC pocket or desktop computer. Radio is to the machine learning and LLM. Smartphone is to, what? Complete the puzzle and win the prize of enlightenment! The radio analogy is the best way to speculate and extrapolate about our future. Another automation if you don't like the radio analogy is refrigeration. Remember all the industry of ice workers that were displaced by the refrigerator? What happened to them? What about all the immigrants that built railroads in America during the 19th century? What happened to them? They settled in the towns that grew the result of the railroad work and hopefully found purpose using the railroads they helped build. You know, if they didn't die first. All the programmers and engineers who were laid off "because of AI" need to settle in one of the "AI railroad towns" and get to work. The railroad is built, the next one is built automatically, so make your living using the railroad you helped build. FWIW I have one of these railroad job towns, but, I didn't help build the first railroad.