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Math is still catching up to the genius of Ramanujan

quantamagazine.org

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Re: Math is still catching up to the genius of Ramanujan

#401

Post by philiplu »

dxbydt wrote: post #393
sourcepluck wrote: post #306

This thread is a good example of one of the perhaps overlooked reasons it can be hard to discuss education in our societies - any attempt at making a general point, or a meta-observation of some kind, quickly gets swallowed in a massive influx of personal anecdotes about things that happened to people during their education. Maybe there are other topics where the same phemonen exists. I'm not sure if off the top of m…

> it can be hard to discuss education in our societies I found it quite ironical how the whole topic has been hijacked into this side discussion. For the record, Ramanujan is NOT a product of the Indian education system. In fact, that system was quite cruel & off-putting to him. He was a self-taught math prodigy. Apart from the well known 2 big biopics, there are numerous TV soaps telecasted in India in various langu…

> I found it quite ironical how the whole topic has been hijacked into this side discussion

Indeed. I submitted this post, because I found the article's discussion of the math involved fascinating, along with biographical details of Ramanujan I hadn't heard about before. I'm surprised to see how popular the post is, but also that there's maybe 5 or so posts that engage with the actual mathematics.

I probably shouldn't be surprised - generating functions pointing out unexpected connections between different restricted integer partitions is pretty niche.

Re: Math is still catching up to the genius of Ramanujan

#402

Post by dharma1 »

bombastry wrote: post #386
IAmGraydon wrote: post #75

The stories of mathematicians like Srinivasa Ramanujan, who claimed to have derived complex partitions and identities in dreams, have always captivated me. It's as if their minds were tapping into some hidden reservoir of knowledge. I'm curious what drives these intuitive leaps. Was Ramanujan's brain quietly processing patterns during sleep, leveraging its default mode network in ways we're still struggling to unders…

The recent book Mathematica by David Bessis attempts to describe this exact topic. One core theme of the book is that math is done by building mental models and using our intuitions that come from. Formalism is then used to shape and refine these models. By spending time developing these models, insights eventually become obvious. These mental models are the essence of mathematics, not theorems. The author explicitly…

thanks, will be checking the book!

My intuition is that some people are able to develop abstractions on top of abstractions (compression is a key part of intelligence) that allow them to traverse the search space much, much faster than without these, and with enough repetition this becomes routine, even faster in the brain.

I don't think we have a good theory of how this works, or at least I haven't come across it.

Neural network guided search is somewhat similar but I think we are missing several key pieces

Re: Math is still catching up to the genius of Ramanujan

#403

Post by sourcepluck »

ok123456 wrote: post #361
sourcepluck wrote: post #306

This thread is a good example of one of the perhaps overlooked reasons it can be hard to discuss education in our societies - any attempt at making a general point, or a meta-observation of some kind, quickly gets swallowed in a massive influx of personal anecdotes about things that happened to people during their education. Maybe there are other topics where the same phemonen exists. I'm not sure if off the top of m…

Trama mostly.

Trauma-drama? :)

Re: Math is still catching up to the genius of Ramanujan

#404

Post by astrange »

willy_k wrote: post #185
drilbo wrote: post #180

Earlier quoted context omitted.

In the past, when I've heard the 'less additive form', it was in contrast to nicotine from tobacco, where there are other chemicals and compounds at play. While it's true ROA can be a big part of habit formation, I'd argue it's a stretch to call it different form when it's the same chemical in either case. tbf tho, I am somewhat contradicting another comment I made about bioavailability on this very gp thread so suff…

I mean they quite literally come in completely different forms of products, but I get your point. I thought nicotine vs tobacco was mostly important for health risk, with the exception of cigarettes which IIRC have all sorts of nasty stuff added or in trace amounts.

That's also my understanding, and nicotine has some other strange health benefits - for instance, it's a better schizophrenia treatment (for symptom relief) than the actual medications for it, which is why almost all schizophrenics smoke.

On the other hand, I just looked at Twitter and saw two different people get ~$3000 payments from a class action lawsuit against Juul, which is by far the biggest payment I've ever heard of from a class action signup, so I suspect they're about to die.

Re: Math is still catching up to the genius of Ramanujan

#405

Post by hilux »

babyent wrote: post #5

That was a fun read. What really stuck out to me was how R failed in a bunch of other subjects except math because he wasn’t interested in them. I know society and norms expect students to learn all these other subjects. But what if those just aren’t interesting to someone? I wonder how many geniuses we skip on because doing the chores of homework and getting through boring classes is busywork and memorization for th…

What better system do you propose to identify and nurture the one-in-a-million genius (the productive genius, not the crazy genius) while also serving tens of thousands of smart strivers, as well as the vast majority of the rest?

I don't think we can or should design a system optimized for that one-in-a-million genius. It would be worse for everyone else, and ultimately for society.

Re: Math is still catching up to the genius of Ramanujan

#406

Post by dharma1 »

chucknthem wrote: post #400
dharma1 wrote: post #398

I often think about Ramanujan in the context of AI, if reasoning is type 2 thinking how did he (apparently) come across a lot of his ideas as intuitions

I wonder if you can train a neuronetwork to have the kind of intuition Ramanujan had. How incredible would it be for math discoveries. Then separate AIs to try and prove or disprove the insights.

probably but we don't know how to build that type of intuition. in humans or in machines.

AlphaProof does do some kind of neural network guided search and automated theorem proving to validate it https://deepmind.google/discover/blog/ai-solves-imo-problems...

But it's still fairly brute force and inefficient

Re: Math is still catching up to the genius of Ramanujan

#407

Post by recursive »

circlefavshape wrote: post #281
scotty79 wrote: post #262

Earlier quoted context omitted.

I absolutely disagree. Adulthood is freedom. It's when you decide what you choose to do. Sometimes things feel like you have to do them but that's just remnants of the conditioning you were moulded by as a child. When you are pressed to the wall you are eventually forced to understand that you don't really have to do them, you just choose to, because however hard they may be it's easier for you than the available alt…

> Adulthood is freedom. Freedom? That has not been my experience of adulthood. To me adulthood is about making responsible choices based on their consequences for you and the people around you ... which means that the majority of my time is spent doing things that other people need rather than because I want to do them

> To me adulthood is about making responsible choices based on their consequences

What is freedom, if not the ability to make those choices?

Re: Math is still catching up to the genius of Ramanujan

#408

Post by hilux »

HarHarVeryFunny wrote: post #302
maeil wrote: post #177

Earlier quoted context omitted.

In the New World, the Ramanujans' lives are spent optimizing high-frequency trading, ads or video recommendation algorithms. This is arguably even worse for society than them not being discovered altogethrt.

People like Ramanujan are on a different planet compared to your everyday PhD working stiffs. There's smart (PhD), there's genius (Einstein, Feynman, von Neumann), and then there are freaks of nature like Ramanujan.

Do you know the saying "comparison is the thief of joy"?

It was intended to apply to oneself, but seems just as true when appreciating the genius of others. No need to diminish von Neumann, etc., AND doing so just diminishes your own credibility.

Re: Math is still catching up to the genius of Ramanujan

#409

Post by PlattypusRex »

returnInfinity wrote: post #144
anonzzzies wrote: post #141

Earlier quoted context omitted.

I have always been only interested in the 'exact' sciences since I was a little kid; I did not do other things even if I had to. I just didn't turn up; I was doing 'more important stuff'. I graduated with a special letter from the queen; all aces for exact sciences and the rest massive fail. It turned out that this made me a good programmer and employer, so I made a shitload of money (in eu terms; pocket change compa…

What we need to do is, make the subjects interesting to learn with tech. It may now be possible with Videos, Games and VR.

No, the subjects are already interesting. What we need is to pay teachers a good, above-average wage, and to continuously invest in their professional development throughout their careers. Only a good, well-trained teacher can make a subject interesting and engaging.

Re: Math is still catching up to the genius of Ramanujan

#410

Post by PlattypusRex »

kiba wrote: post #100
coliveira wrote: post #57

Earlier quoted context omitted.

> and do so with relative competency I dispute this on the grounds that students are going through American schools and many of them don't even know how to read.

92% of adults know how to read to varying level.[1] The number, while high, is not satisfactory. Clearly, we also want adults to be functionally and not pass a super low bar of being able to read a sentence which 92% does not care to distinguish, but it is not fact true that "many of them don't even know how to read". 1. https://en.wikipedia.org/wiki/Literacy_in_the_United_States

Over 20% of American adults have a literacy proficiency at or below Level 1. This is defined as "difficulty using or understanding print materials" and "may struggle to understand texts beyond filling out basic forms." So 1 out of every 5 Americans is functionally illiterate. I would say that counts as "many of them don't even know how to read."
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