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- Hacker News
- As the famous British mathematician Alfred North Whitehead wrote 111 years ago, "Civilization advances by extending the number of important operations which we can perform without thinking of them."
This now includes the proving of theorems.
He went on to write "Operations of thought are cavalry charges in a battle - they are limited in number, they require fresh horses, and must only be made at decisive moments."
Mechanization also demolished that institution, which had also survived for thousands of years.
by pfdietz - anyone else already experiencing this in a corporate environment? I know I am. Its not just between teams either, its within them.by Ancalagon
- In science and math, too often only the final result gets credited or published.
Maybe we should start crediting and publishing our intermediate results and attempts.
Humans would gain credit for providing a part of the solution to tough problems, LLMs would profit from the resulting data flywheel.
by niemandhier - I devised an algebraic representation of music composition. This enables me to mass produce musical scores without ever touching artificial intelligence.
It took me 10 years to develop the system, and I intend to ride it out as much as I can. By act 3 of my life sure I will publish the math. But in this economy, I would be a damn fool to publish my equations just to let the LLMs write better music.
by song_synth - Universities should be providing university hosted llms to their faculty and students. No student or faculty member should be using public llms for their work. They can share info directly with other people or in non-public forums to keep it away from commercial llms. It is going to have to be against the rules to submit anyone else's work to a commercial llm. Businesses are going to have similar policies.
Universities can host the llms just like they hosted any other computer lab or web service on campus. This is what universities are supposed to be doing. Universities should be involved in open model research and should offer models that are not datamined.
- Make the proof from LLMs with the same constraints as human mathematicians have:
The proof must be as succinct as possible so that it's reviewable. It's ok for the same LLM to publish repeatedly, but it's not Ok to drop a bulk 600kb Lean proof.
The proof must build on other works that are similarly bite sized and published before (so that it's incrementally reviewed)
The proof must be published as soon as fully formed, and not in bulk like current LLMs proofs.
by philprx - I have seen two worries recently:
1. People will publish so much frontier mathematics, humans won't be able to understand it all
2. Frontier mathematics will all be kept secret
Fortunately, these seem like they can't both happen at once.
by lacker - This will not happen. The fear comes from the real problem: publication as a measure.
The mathematics itself will only benefit from the discovery of cross links from the human created literature. Think about these LLM as infinitely patient and very long attention experts in what was already done.
So on one side, for a few years at least, it will become normal to publish tens of articles. The article inflation is what scares the present system.
On the other side, after a while, when all the existing mathematical corpus will be mined and most of buried connections will be explored, we shall have a much more better foundation for future mathematics.
It is very naive or misleading to think about mathematics as if it were chess or go.
In few year these (future) tools will be in standard use.