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Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

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Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#361

Post by woodruffw »

dublin wrote: post #357
andrepd wrote: post #346

Earlier quoted context omitted.

Attributing science and freedom of religion to Christianity? That's a bold thought.

And a correct one. There is a reason these things did not develop until when and where they did...

Pinning concepts like "science" and "freedom" to a specific era is a silly endeavor. But if you had to, neither would originate in Christian Europe: science as a concept predates Christianity by at least 800 years; the thing we call "freedom" today didn't take shape until 1600 years into Christian Europe's development.

Christianity, like just about every religion, has made invaluable contributions to philosophy. But it's ahistorical, to an embarrassing degree, to attribute such broad concepts and bodies of inquiry to it.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#362

Post by ConceptJunkie »

s1artibartfast wrote: post #158
robomartin wrote: post #140

Quoted post unavailable.

It's not really remarkable because governments rarely come up with nasty names. Even then the cultural revolution isn't an inherently positive. Culture can be good or bad and so can revolutions

Of course they don't. But what's remarkable, and the U.S. is no exception here, is that the names they come up with are quite often the diametric opposite of what effects they actually have. The "Inflation Reduction Act of 2022" is but one recent example.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#363

Post by wikfwikf »

andrepd wrote: post #347
wikfwikf wrote: post #303

Earlier quoted context omitted.

I don't think this is the whole story. Of course, it is a tragedy when people who had undeniable raw talent are neglected or passed over and don't get to achieve as they might. It's also sad and disappointing when we observe structural injustices in our society. However, isn't it possible that giving great teaching resources to people who aren't already at the top level in terms of raw talent, allows them to succeed…

> If so, it's not a zero sum game - the 'averagely clever people who have received great tuition' and who go on to succeed might be a sign of the education system working, not its failure. The failure is that mediocre students which come from an environment which helps them (good school, private tutors, stable home life) can be successful, while "naturally gifted" yet disadvantaged students don't. The basic fact that…

> The failure is that mediocre students which come from an environment which helps them (good school, private tutors, stable home life) can be successful, while "naturally gifted" yet disadvantaged students don't.

I think you have rephrased what I said to again push the idea that it's a zero sum game. If mediocre students can be successful, given the right educational inputs (for some definition of 'successful' and 'mediocre'), isn't this a huge opportunity? Perhaps we should improve society as well as social justice by trying to promote mediocre students from poorer backgrounds to this same level of success, rather than by working on the problem of undiscovered genius.

> The basic fact that parental income is still the best predictor of educational achievement should tell you everything you need to know.

My whole point is that this does not tell you everything you need to know. If low-parental-income and high-parental-income students had exactly the same potential to succeed, the fact that parental income is a good predictor of achievement might be telling you either (or any combination) of two things: that wealthier students are achieving beyond what should be expected (and so we are ending up with incompetent people in very senior positions because they did not get them on merit), or that poorer students are achieving below where they should be (and so we are wasting the potential of talented people). These are really different problems! And probably have quite different solutions.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#364

Post by radford-neal »

andrepd wrote: post #347
wikfwikf wrote: post #303

Earlier quoted context omitted.

I don't think this is the whole story. Of course, it is a tragedy when people who had undeniable raw talent are neglected or passed over and don't get to achieve as they might. It's also sad and disappointing when we observe structural injustices in our society. However, isn't it possible that giving great teaching resources to people who aren't already at the top level in terms of raw talent, allows them to succeed…

> If so, it's not a zero sum game - the 'averagely clever people who have received great tuition' and who go on to succeed might be a sign of the education system working, not its failure. The failure is that mediocre students which come from an environment which helps them (good school, private tutors, stable home life) can be successful, while "naturally gifted" yet disadvantaged students don't. The basic fact that…

I certainly agree that talented students from disadvantaged backgrounds ought to be helped. But thinking parental income is the causal factor behind the observed correlation of student success with income may be mistaken.

Two other hypotheses are that the money itself is not important, but rather the familial transmission of certain cultural traits (which also often lead to high incomes), and/or that, similarly, the causal factor is genetic transmission of some cognitive or personality traits. Note that a factor being genetic does not mean it is immutable - for instance, there could be a genetic factor that leads to students doing poorly in school because they are intolerant of sitting still for hours in desks, which would become irrelevant if one stopped requiring them to sit still for hours.

A mistaken idea of the causal explanation for the correlation with income would lead to interventions that don't actually work.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#365

Post by ConceptJunkie »

treeman79 wrote: post #165
bdhe wrote: post #150

Earlier quoted context omitted.

> It's the old "I'm from the government and I am here to help" joke. What else is the government for? I understand it's a popular Reagan talking point but I don't really grok it. If you assume the govt doesn't work for us, particularly if you're in politics, it becomes a self-fulfilling prophecy.

The idea is that government is inherently bad. But no government is worse. People in government will abuse their positions as much as possible. So limiting government as much as possible is the goal. Good example is pandemic. Governments saved a small number of people by collapsing economies. Quit possibly killing more people then were saved. There is a very good argument that the best thing governments could have do…

Government is the worst possible way to solve any problem. Therefore, we should only let it solve those problems that absolutely cannot be solved any other way. There are plenty, and this is not a statement that all government is bad, but that it needs to be tightly constrained.

People constantly rail about the evil wrought by big business, and they're right to do so, but what is the government (in the US anyway), but the biggest (and perhaps most corrupt) business of all? Except it's not constrained by the requirement to turn a profit, so it doesn't suffer the bad consequences of failure, because you can always print more money.

And you're absolutely right about the pandemic response.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#366

Post by naasking »

gavagai691 wrote: post #5

Two additional notes: 1. Zhang posted an attempt at solving this problem in 2007 that he later more or less admitted was flawed: https://mathoverflow.net/questions/131221/yitang-zhangs-2007... . But speaking with mathematicians who are intimately familiar with Zhang's previous work, there seems to be good reason to be optimistic nevertheless. First, the idea behind Zhang's proof is similar to the zero-repulsion ideas…

> 2. Zhang is 67 years old. If the paper is correct, then Zhang constitutes a strong counterexample to G.H. Hardy's famous claims that "mathematics is a young man's game" and nobody alive today could say, as Hardy did, that "I do not know an instance of a major mathematical advance initiated by a man past

I think the actual truth is more like, "big breakthroughs mainly happen early in one's career". Most mathematicians start their careers young, therefore they publish breakthroughs while young. Zhang started quite late so his innovations are later in his life, but still early in his career.

And it makes sense, everyone has a slightly unique way of thinking, and long-standing problems will only yield to unique thinking. Eventually someone will come along that has just that right type of unique thought process that will find a hole to solve such a problem.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#367

Post by rcarr »

fredley wrote: post #295
zimpenfish wrote: post #260

Brings to mind Gould's quote - "I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops." https://www.goodreads.com/quotes/99345-i-am-somehow-less-int...

I think about this often. Having studied mathematics, it's a field where there is a huge range of talents, even at 18 (and younger). There are genuinely gifted people who stride ahead, but the sad reality is that even at top institutions most of the undergraduate cohort will be merely averagely clever people who have received great (often private) tuition. In a field where finding every genius really matters because…

This is the problem right here. The solution is that Maths teaching needs to be brought online Duolingo/Brilliant style (with in person teacher support obviously). We can completely standardise the curriculum and do A/B testing to find out what is the most efficient way to get the information into students’ heads.

The data could be analysed further to see if there were certain mathematical learning styles (I suspect there are). One cohort of students might be better off on the visual/geometry heavy track, one might be better on the abstract track etc.

It should be initiated at the national government level and mandated to use in schools but the actual building of the application should be contracted out to a company from Silicon Valley/Roundabout/$COUNTRY_TECH_HUB.

Until this happens or something similar we’re just going to continue having this grossly unequal and unfair state of affairs where access to good mathematics education is complete geographical potluck for anyone whose parents can’t afford tuition. The amount of wasted potential is staggering.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#368

Post by rcarr »

germandiago wrote: post #300
hoseja wrote: post #293

Earlier quoted context omitted.

It's also a major failure in didactics. It feels like very little of the new knowledge since twentieth century has been truly digested for easy teaching. Why isn't general relativity taught in elementary school? It should be possible.

FWIW I notice how remarkably bad I was taught math at school. When I started to go to university I really noticed how bad it was. At university the jump forward was really noticeable. For example, at school they would show you a couple of simple explanations about derivative math or integrals, briefly and start with all the formulas. At university I used to have a teacher that started with: history of mathematics, wh…

This! Identical situation in the UK from my experience. Why maths is taught completely separated from its history and its purpose is baffling. Well actually it’s not: it’s because it serves the teachers. You hammer the formulas and patterns into the kids so they can pass the exams. Your school gets good grades and the principal is happy because he can now market his school as successful and the government inspectors are happy because the school is hitting its metrics. Meanwhile, the kids haven’t actually learned anything. As soon as the exam is passed they forget the formulas and go on with their lives.

We should be explaining the story of maths and how it benefitted society. We should be asking kids about their interests and then showing them how mathematical tools can be used in those areas. We need to show kids how maths is tied to real life rather than just presenting them with a boring formulas to memorise.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#369

Post by rcarr »

dheera wrote: post #297
pa7x1 wrote: post #78

Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…

> we may reach a point where a mathematician's intellectually productive life is not sufficient to contribute Arguably the same could have been said in the 1700s when people lived till a mean life expectancy of about 40 and they would have perhaps been concerned that at some point in their future nobody would be able to make scientific advances in their lifespan. Yet here we are, living till 80s and beyond, making ac…

Or just make mathematical education more efficient which seems like the Occam’s Razor answer to me.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#370

Post by unsupp0rted »

ConceptJunkie wrote: post #358
unsupp0rted wrote: post #251

Earlier quoted context omitted.

I can easily imagine an Earth with no philosophers after say Aristotle that is functionally identical to our current one.

Wow. I guess you're not familiar with any philosophers other than Aristotle, otherwise you could never make such a statement.

Please elaborate
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