[HN Gopher] After 20 years, math couple solves major group theor...
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After 20 years, math couple solves major group theory problem
Author : isaacfrond
Score : 355 points
Date : 2025-02-20 10:09 UTC (12 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| thih9 wrote:
| This is about McKay conjecture
|
| https://en.m.wikipedia.org/wiki/McKay_conjecture
| alberto_ol wrote:
| Non mobile link
|
| https://en.wikipedia.org/wiki/McKay_conjecture
| ChrisMarshallNY wrote:
| Damn. That's some dedication. I really like the personal story,
| therein. You don't always see that, in STEM stuff.
|
| I hope that their relationship deals well with the new reality,
| now that their principal goal has been achieved.
| nthingtohide wrote:
| I think experts in all kinds of fields should write more about
| their thinking process. Just showing final result often feels
| like it was easy for them and discourages other from even
| attempting to understand and contribute. Especially in
| mathematics, the ideas are simple (they have to be because no
| one would be summing infinite series in their head like
| Ramanujan) but they are hidden behind lot of symbolic jargons.
| grandempire wrote:
| It's always less impressive to know how it works and fewer
| people care.
| nthingtohide wrote:
| Here's an example of what I meant
|
| Lecture by Douglas Hofstadter: Albert Einstein on Light;
| Light on Albert Einstein
|
| https://youtu.be/ePA1zq56J1I?si=7WuiRa3GNSmMXArZ
| lo_fye wrote:
| Way to go, Math!
| socceroos wrote:
| What a mathive achievement!
| yamrzou wrote:
| "While working together on the McKay conjecture, Britta Spath and
| Marc Cabanes fell in love and started a family."
| Out_of_Characte wrote:
| They found their succession
| anthk wrote:
| Intersection set with genes from set A and B.
| inglor_cz wrote:
| With the kids being homeomorphic to the parents.
| echoangle wrote:
| Wouldn't it be more like a subset of the union of A and B?
| Intersection set sounds like the child only has the genes
| that both parents share.
| anthk wrote:
| True; that would be dangerously close to incest. Subset
| of a union, then.
| veidr wrote:
| FFS you nerds, get a room
|
| (and then form a working group to devise an algebraically
| provable disincentive to incestuous calculation)
| Out_of_Characte wrote:
| Way ahead of you, pal. I am my own grandpa.
|
| https://youtu.be/eYlJH81dSiw?si=NNPDjaWV-OzrP2JU
| thaumasiotes wrote:
| https://www.youtube.com/watch?v=BipvGD-LCjU
| charlangas wrote:
| How do these kinds of advancements in math happen? Is it a
| momentary spark of insight after thinking deeply about the
| problem for 20 years? Or is it more like brute forcing your way
| to a solution by trying everything?
| getnormality wrote:
| In this case, a ton of progress had already been made. The
| conjecture had been proved in some cases, reduced to a simpler
| problem in others. This couple went the last mile of solving
| the simpler problem in some particularly thorny cases.
|
| You're really standing on the shoulders of giants when you rely
| on the classification of finite simple groups.
| btilly wrote:
| _You 're really standing on the shoulders of giants when you
| rely on the classification of finite simple groups._
|
| Giants whose work has (dirty little secret) never truly been
| verified. The proof totals about 10,000 pages. At the end of
| the effort to prove it there were lots of very long papers,
| with a shrinking pool of experts reviewing them. There have
| been efforts to reprove it with a more easily verified proof,
| but they've gone nowhere.
|
| Hopefully, the growing ease of formalization will lead to a
| verification some day. But even optimistically that is still
| a few years out.
| isotypic wrote:
| > There have been efforts to reprove it with a more easily
| verified proof, but they've gone nowhere.
|
| My understanding was that the so called "second generation
| proof" of the classification of finite simple groups led by
| Gorenstein, Lyons, Solomon has been progressing slowly but
| steadily, and only the quasithin case had a significant
| (but now fixed) hole. Are there other significant gaps that
| aren't as well known?
| btilly wrote:
| Huh. Looking at it, they have made a lot more progress
| than I was aware of. I will correct my opinion.
| https://mathoverflow.net/questions/114943/where-are-the-
| seco... was very informative on this.
|
| Still they have a couple more books of proof left, and I
| have to wonder how carefully it will be reviewed. This
| will still be a massive improvement, but I'd be a lot
| happier if the entire proof could be formalized.
|
| Plus there is still a possibility that there proves to be
| another significant hole.
|
| If any theorem needs to be formalized, this is the one.
| No other theorem is this big, this hard to prove, and
| this important to get right.
| getnormality wrote:
| At the moment we seem to have exactly one guy equipped to
| do this, and he'll be busy with something else for the
| next few years: https://www.reddit.com/r/math/comments/17
| 6vtju/kevin_buzzard...
| jebarker wrote:
| My experience from proving a moderately complicated result in
| my PhD was that it's neither. There wasn't enough time to brute
| force by trying many complete solutions, but it also wasn't a
| single flash of insight. It was more a case of following a path
| towards the solution based on intuition and then trying a few
| different approaches when getting stuck to keep making
| progress. Sometimes that involves backtracking when you realize
| you took a wrong path.
| sweezyjeezy wrote:
| Yeah agreed - there are actually many, smaller flashes of
| insight, but most of them don't lead to anything. I once
| joked that you could probably compress all the time I was
| actually going in the right direction in my PhD down to about
| a month or two. That's a bit glib, often seeing why an
| approach fails gives you a much better idea of what a proof
| 'has to look like' or 'has to be able to overcome'. But many
| months of my PhD were working on complete dead-ends, and I
| certainly had a few very dark days because of that. Research
| math takes a lot of perseverance.
| jebarker wrote:
| > Research math takes a lot of perseverance.
|
| Yup, I think stubbornness/perseverance is the most useful
| transferrable skill I got from doing research math. It's a
| double-edged sword though as I often just can't give up
| working on something when I really should in my tech job.
| bloomingkales wrote:
| The structure of DNA was seen in a vision in James Watson's
| dream. Some say it's subconscious problem solving and I think
| most down to earth people agree with that, but some less down
| to earth people will absolutely attribute it to god (I'm in the
| latter). If we were to entertain a silly proposition, something
| in the universe could just move our story along, all of a
| sudden. These paradigm shifts just seem to appear.
| FartyMcFarter wrote:
| Subconscious problem solving is definitely a thing as far as
| I'm concerned.
|
| It's happened several times that I struggled with a bug for
| hours, then suddenly came up with a key insight during the
| commute home (or while taking a shower or whatnot), while not
| actively thinking about the problem. I can't explain this any
| other way than some kind of subconscious "brainstorming"
| taking place.
|
| As a side note, this doesn't mean the hours of conciously
| struggling with the problem were a waste. I bet that this
| period of focus on the problem is what allows for the later
| insights to happen. Whether it's data gathering that alows
| the insights to happen, or even just giving importance to the
| problem by focusing on it. Most likely it's both.
| fsckboy wrote:
| an alternate hypothesis is that all thinking is unconscious
| with consciousness being the sum of many unconscious
| processes. So, while it's true as you say "that some kind
| of subconscious "brainstorming" taking place", that would
| just true all the time, and you only notice it when your
| conscious thoughts are of something else.
|
| (n.b. historically speaking in the literature,
| "subconscious" was the word used to describe Jung's "woo-
| woo" ideas about a collective subconscious shared across
| populations, and unconscious was the word used for ideas
| about a single brain a la Freud which is what we are
| talking about here)
| y33t wrote:
| > The structure of DNA was seen in a vision in James Watson's
| dream
|
| I believe this is apocryphal. Watson likely said this because
| he stole Rosalind Franklin's research.
| bloomingkales wrote:
| I can only think of that example because it's the only one
| I know of where the scientist admitted to something divine.
|
| This is probably something I need to research more, because
| the questions scientists are dealing with are too deep to
| ignore the one big question, and I wonder who struggled
| with it.
| selimthegrim wrote:
| Kekule?
| Philpax wrote:
| Ramanujan is another great example of divine inspiration.
| hcs wrote:
| Not divine specifically but I like the Wikipedia List of
| Dreams: https://en.wikipedia.org/wiki/List_of_works_based
| _on_dreams#...
| btilly wrote:
| I disagree. What he stole was the pictures she took. He
| really did come up with the structure.
|
| Mind you he was helped by a nice coincidence. Franklin knew
| all 230 space symmetry groups, and so had to sort through
| them. Watson only really knew one - his PhD thesis was on a
| protein with the same group as DNA.
| Jun8 wrote:
| Hah, serendipity: I was reading the Groups part of the Infinite
| Napkin after it was posted on HN recently. I understand the
| definitions, etc. but still haven't grasped the central
| importance of groups.
|
| For example, article says there are 50 groups of order 72
| (chatGPT says there are 50 non-Abelian, 5 Abelian), this seems to
| be an important insight but into what?
| Chinjut wrote:
| Don't listen to ChatGPT. There are 44 non-abelian and 6 abelian
| groups of order 72. I wouldn't say these particular numbers are
| terribly important, but they are correct.
| Imustaskforhelp wrote:
| Don't listen to ChatGPT.
|
| As someone "junior programmer" , I think I should just keep
| this information . Many times I have tried to not use
| chatgpt. but its just so lucrative.
|
| I really need better control of myself. Going to block
| chatgpt at a dns level.
| jandrese wrote:
| Definitely don't use ChatGPT to try to learn about something
| you have no knowledge of. It's impossible to separate the
| bullshit from the truth if you don't already have some
| foundation in the field, and chatbots often try to sneak some
| bullshit in there.
| grandempire wrote:
| Many mathematical structures are groups so understanding them
| helps you get insight into the concrete situation you are
| trying to solve. For example is the problem I am seeing
| abelian? If so then it must look like X or Y.
| __MatrixMan__ wrote:
| I've only taken three (undergrad) classes involving groups so
| I'm far from an expert but my feeling is that their underlying
| structure is a bit like prime numbers.
|
| Nobody bothers explaining why the primes are spaced like they
| are, rather people explain other phenomena by pointing out that
| certain things about it are prime or not.
|
| For instance, there's this thing about having a nice neat
| formula for factoring second degree polynomials (the quadratic
| formula). One also exists for cubics and quartics (though they
| don't usually have you memorize these) but none exists for
| quintics. It took mathematicians a while to prove that such a
| thing doesn't exist (how to prove a negative?) but they managed
| it by arguing that all such things have an underlying finite
| group smaller than a certain size and look, we've listed them
| here, and there's no such group corresponding to a quintic
| formula, therefore there is no quintic formula.
|
| So they're useful as a sort of primordial complexity that can
| be referenced without extensive explanation since properties
| about the small ones can be checked by hand. And as it turns
| out, quite a lot of things form groups if you bother you look
| at them that way.
| BlackFingolfin wrote:
| > Nobody bothers explaining why the primes are spaced like
| they are
|
| I take it that means you also haven't taken (m)any number
| theory classes then ;-). Because people _wildly_ care about
| that.
|
| This is in a sense the background of another well-known
| conjecture, the Riemann conjecture...
| __MatrixMan__ wrote:
| Fair point, and correct (just one class). Myself, I'm fine
| with a field being important because well it's a mystery of
| the universe and well we just couldn't not scratch the
| itch. But I know that not all askers want answers like
| that, so I was attempting to dust off the "it's also
| useful" neurons :)
| ndriscoll wrote:
| Groups are important because they are the algebraic way to
| describe symmetry: if you have some operation that leaves a
| thing invariant (e.g. rotating an equilateral triangle so that
| a vertex lands on where another started), then the operation is
| invertible and the inverse leaves the thing invariant. You can
| compose such operations and the composition will still be
| invariant. The identity function always leaves everything
| invariant. So your symmetry operations form a group.
|
| Slightly trickier is that every group is a set of symmetry
| operations for something. So groups _exactly_ capture the idea
| of symmetry. To a mathematician, "group" and "symmetries" are
| synonymous.
|
| Finite groups can be interesting as the symmetries of e.g.
| molecules (e.g. rotating atoms around onto each other), which
| can tell you something about molecular structure, energy
| levels, spectra, bonding potential, etc. Infinite groups appear
| in physics (e.g. the laws of physics are the same when you
| rotate or translate your coordinates by arbitrary amounts).
| Symmetry also comes up as a way to study other mathematical
| objects, and mathematicians might just want to know what all
| possible groups look like.
| w0de0 wrote:
| With the right photo, this could be an Onion headline poking fun
| at lonely math nerds.
| PhillyPhuture wrote:
| "There was a risk that such a single-minded pursuit of so
| difficult a problem could hurt her academic career, but Spath
| dedicated all her time to it anyway."
|
| I feel like this sentence is in every article for a reason. Thank
| goodness there are such obsessive people and here's a toast to
| those counter-factuals that never get mentioned.
| Der_Einzige wrote:
| Unfortunately the average persons hatred of autistic or nerdy
| people implies that many believe the world would be a better
| place if "obsessive types" didn't exist.
|
| Hans Asperger could only save his Austic children from nazi
| death camps by convincing the nazis that they had value to
| produce rockets and bombs.
|
| It's quite remarkable that the USA is so advanced given how
| deep and ruthless our anti-intellectualism goes.
| veidr wrote:
| Isn't it basically the same? Nazi Germany in 1934 was
| relatively advanced, too.
|
| I think the difference is^W was that USA celebrated it in a
| Homer Simpson kind of "Ha ha! NERDS!" way, while meth-Hitler
| was like "let's sterilize them but try to extract math from
| them to... (whatever batshit goal)"
|
| Anti-intellectualism seems to be a thing when the
| intellectual/moderately-competent people have already brought
| success. (Until then it's more like anti-witchcraft, or
| whatever...)
| Gud wrote:
| I don't think the average person hate autistic or nerdy
| people.
| throwpoaster wrote:
| Yes, they do. They wouldn't say it, but look at how
| autistic people get treated by their peers, teachers, and
| bosses.
| jonnybgood wrote:
| How do you know their peers, teachers, and bosses aren't
| autistic too? Autistic people can't be peers, teachers,
| and bosses? Autistic people can be assholes too. Maybe
| that's what it really is: some people are just assholes.
| yifanl wrote:
| Extreme category error, try again.
| parineum wrote:
| They absolutely don't.
|
| The average person is probably uncomfortable around
| autistic people because they don't know how to deal with
| them and, when you see someone like that, it's usually best
| to avoid interacting with them. Not because autistic people
| are dangerous but people acting out of the ordinary
| sometimes are.
|
| The lumping in of nerdy with autistic is ridiculous too.
| The average person just doesn't care about your interests
| unless they are in common. Nerdy typically just means
| having a niche interest or hobby.
|
| Your parent reeks of a persecution complex.
| Der_Einzige wrote:
| It's shocking that you can just bury your head in the
| sand about the colloquial usage of "autist" (often
| happening at the same time as "Incel") replacing "retard"
| in the lexicon of the average zoomer.
|
| It's not a persecution complex to identify the ways that
| hate gets used, deployed, and repackaged for a new
| generation. Putting your head in the sand about stuff
| like this is why Trump winning the election was SO
| shocking to some and extremely obvious to others.
| mike_ivanov wrote:
| I guess you never studied in a school and therefore not
| aware of bullying and its stereotypical targets.
| MattGrommes wrote:
| Obviously everything is a spectrum but I agree. If
| anything, "a touch of the 'tism" is the new "I have OCD"
| because you like a clean desk, something people are fine
| with saying without regards to it being true.
| jonahx wrote:
| "the average persons hatred of autistic or nerdy people"
|
| This is a _wildly_ inaccurate picture of the average person.
| I don 't even think this is true of 10% of people.
| lanstin wrote:
| Probably enough for 90% of such folks to be tormented quite
| effectively during childhood.
| bear141 wrote:
| This is a great point. If a small percentage of the
| population is openly and aggressively negative towards
| another part of the population, it makes sense that they
| would both artificially appear as if they are a larger
| part of the population, to each other. I think it goes
| both ways.
| macbem wrote:
| Anyone who's a bit different has a high chance of having
| been bullied at some point. It doesn't mean that society
| hates this specific group of people.
| LPisGood wrote:
| I _highly_ doubt 90% of nerdy people were tormented
| during childhood. Have you spent time in/around academia?
| These people are massive nerds and horrendous childhood
| torment is pretty rare.
| ted_dunning wrote:
| It was 100% in my personal experience.
| LPisGood wrote:
| I'm not saying it doesn't happen. I'm not even saying it
| doesn't happen at all higher rate than the general
| population.
|
| But 90% is just too much to be feasible.
| MrMcCall wrote:
| Our son was specifically chosen to be in his 4th Grade
| class because it spent part of the day hosting the spectrum
| kids within their "regular" class. He was chosen for that
| honor because of his kindness.
|
| He has been taught to love others since he was born, and
| the Path of Love has borne fruit for all those around all
| four of us.
|
| All the people who say it can't be done have never tried
| consciously evolving with Divine help.
|
| {Complete lyrics} --Sinead O'Connor in Massive Attack's
| "What Your Soul Sings"
| tim333 wrote:
| US intellectualism is patchy. Sure a lot of people are not
| into it but on the other hand you probably have more well
| paid academic posts than any other country.
| manoweb wrote:
| What are you talking about, why do you think that autistics
| are treated better in Europe, Africa, Asia? Also, people do
| not "hate" them, people in general hate everybody, don't play
| the victim
| BobaFloutist wrote:
| Probably the most powerful man in the world right now openly
| self-identifies as autistic. Obviously there are very many
| autistic people who get treated very badly, but I don't think
| it's reasonable to say that the average person "hates"
| autistic people.
| harrison_clarke wrote:
| that guy is arguably causing branding problems for less
| powerful autistic people
| BobaFloutist wrote:
| Yeah I wouldn't want to be an autistic person that
| doesn't suck right now.
|
| I imagine it's a lot like my experience of having ADHD
| and being trapped between wanting leeway and support but
| also wanting to be held accountable and considered
| capable of improving and watching the Tiktokification of
| my disorder force me to argue that actually people with
| ADHD _can_ do things and no having it doesn 't fully
| excuse you from ever meeting commitments or doing the
| fucking dishes, especially if you're rejecting all and
| any treatment or strategy.
| manoweb wrote:
| There are tens of millions of people doing a repetitive work
| every day, instead of being entrepreneurs. Just let them be,
| not everybody needs to dedicate their existence to maximizing
| their career opportunities, at any level.
| chowells wrote:
| This isn't being an entrepreneur. This is solving a problem.
| The two almost never overlap.
| godelski wrote:
| > Just let them be
|
| As someone who's research goes against the grain, I just
| request the same. I have no problem with people maintaining
| the course and doing the same thing. In fact /most/ people
| should probably be doing this. BUT the system discourages
| going of course, exploring "out of bounds." The requests of
| these people have always been "let me do my thing."
|
| Just make sure "let them be" applies in both directions
| tomcam wrote:
| I worked at a pro audio company where one guy spent 5 years on
| a power supply. It succeeded, and I always appreciated the
| management for supporting him.
| lemonberry wrote:
| Do recall the specific problem he was trying to solve?
|
| It's amazing to me how much thought and work has gone into
| the seemingly trivial things we encounter on a daily basis.
|
| I think of this every time I see a blue LED. Or a rice
| cooker!! So easy to take for granted.
| yujzgzc wrote:
| And you can thank this guy for the LEDs that made it possible
| for you to even read about it on a screen
| https://youtu.be/AF8d72mA41M
| Xcelerate wrote:
| I want financial independence for the sole reason that I can
| work on interesting problems like this without any outside
| nagging or funding issues from anyone else (there might still
| be some judgment, but I can ignore that).
|
| Personally I think governments should fund more moonshot solo
| or small team efforts because high risk / high reward pays off
| when you reduce the variance by spreading it out over so many
| people. But it looks like we're going headstrong the other
| direction in terms of funding in the U.S. right now, so I'm not
| optimistic.
| godelski wrote:
| > I want financial independence for the sole reason that I
| can work on interesting problems like this without any
| outside nagging or funding issues from anyone else
|
| Ditto. This is literally the only desire I have to be
| wealthy. It is not about having nice things, a nice house, or
| any of that. It is about letting me do my own research.
| jereees wrote:
| I bet there's a good number of us. How do we make this a
| reality? :)
| drivebyhooting wrote:
| Last decades? Work in ad tech. Now? Work on LLMs.
| godelski wrote:
| > I feel like this sentence is in every article for a reason.
|
| Breakthroughs, BY DEFINITION, come from people going against
| the grain. Breakthroughs are paradigm shifts. You don't shift
| the paradigm by following the paradigm.
|
| I think we do a lot of disservice by dismissing the role of the
| dark horses. They are necessary. Like you suggest, there are
| many that fail, probably most do. But considering the impact,
| even just a small percentage succeeding warrants significant
| encouragement. Yet we often act in reverse, we discourage going
| against the grain. Often with reasons about fear of failure. In
| research, most things fail. But the only real failure is the
| ones you don't learn from (currently it is very hard to publish
| negative results. Resulting it not even being attempted. The
| system encourages "safe" research, which by its nature, can
| only be incremental. Fine, we want this, but it's ironic
| considering how many works get rejected due to "lack of
| novelty")
| globnomulous wrote:
| > Breakthroughs, BY DEFINITION, come from people going
| against the grain. Breakthroughs are paradigm shifts.
|
| This is wrong. It's not inherent in the meaning of the word
| "breakthrough" that a breakthrough can occur only when
| someone has gone against the grain, and there are countless
| breakthroughs that have not gone against the grain. See: the
| four-minute mile; the Manhattan Project; the sequencing of
| the human genome; the decipherment of Linear B; research into
| protein folding. These breakthroughs have largely been the
| result of being first to find the solution to the problem or
| cross the theshold. That's it. That doesn't mean the people
| who managed to do that were working against the grain.
|
| > Yet we often act in reverse, we discourage going against
| the grain. Often with reasons about fear of failure.
|
| I don't know which "we" you're referring to, but just about
| everybody would agree with the statement that it's good to
| think creatively, experiment, and pursue either new lines of
| inquiry or old lines in new ways, so, again, your claim seems
| clearly wrong.
|
| If you're discussing just scientific research, though, sure,
| there are plenty of incentives that encourage labs and PIs to
| make the safe choice rather than the bold or innovative
| choice.
| pinoy420 wrote:
| Yea but this is HN where everyone is a disruptor and
| doesn't play by the rules
| MrMcCall wrote:
| > Breakthroughs, BY DEFINITION, come from people going
| against the grain.
|
| They are what Gladwell calls, in "David and Goliath", being
| _unreasonable_ in the face of so-called "prevailing wisdom".
| inetknght wrote:
| > _Often with reasons about fear of failure._
|
| If that were it, I would agree.
|
| But I don't agree. I think people who discourage going
| against the grain are more fearful of the loss of economic
| input. It's unproductive to do something you _know_ will
| fail; it 's very expensive to encourage that failure.
| isaacfrond wrote:
| So what the McKay conjecture is saying is this.
|
| Suppose I'm interested in representing a Group as matrices over
| the complex numbers. There are usually many ways of doing this.
| Each one of them has a so-called character, which is like
| fingerprint of such a representation.
|
| Along another line, it has been known that all groups contain
| large subgroup having an order which is a power of a prime--call
| it P. This group in turn has a normalizer in which P is normal--
| call it N(P).
|
| The surprising thing is that the number of characters of G and of
| N(P)--which is is only a small part of G--is equal.
|
| *technical note in both cases we exclude representation the
| degree of which is a multiple of p.
| antonf wrote:
| Did you miss definition of G, or I didn't have enough caffeine
| yet?
| throwpoaster wrote:
| I assume from context it's the original group, but I'm only a
| cup deep.
| looofooo0 wrote:
| Correct
| jmount wrote:
| > When the couple announced their result, their colleagues were
| in awe. "I wanted there to be parades," said Persi Diaconis
| (opens a new tab) of Stanford University. "Years of hard, hard,
| hard work, and she did it, they did it."
|
| That sort of positive support was one of the elements I really
| liked in working on combinatorial problems. People like Persi
| Diaconis and D.J.A. Welsh were so nice it makes the whole field
| seem more inviting.
| MrMcCall wrote:
| All our acts are butterfly wing beats that influence those with
| whom we interact, for either good or ill. And those waves
| resonate back within our being as happiness or its opposite,
| depending on our intentions and actions.
|
| "Positive vibration, yeah." --Bob Marley
| xenago wrote:
| What an awful webpage. They hijack the click and right click
| actions. Can't triple click to select a paragraph. Can't drag
| selected text. Ugh
| PunchTunnel wrote:
| What browser are you working in? I'm not having any trouble in
| Brave, Chrome, or Opera.
| xenago wrote:
| Edge and Firefox both replicate the issue. It is on all
| browsers
| Imustaskforhelp wrote:
| on zen , it works
| justinpombrio wrote:
| The paper: https://arxiv.org/abs/2410.20392
| rurban wrote:
| Their proof: https://arxiv.org/abs/2410.20392 (2024)
| wglb wrote:
| This is a terrific article. It led me to a couple of hours
| tracking articles about related efforts, not the least of which
| was John Conway's work.
|
| Mind you, my math is enough for BSEE. I do have a copy of one of
| my university professor's go-to work books: The Algebraic
| Eigenvalue Problem and consult it occasionally and briefly.
| racl101 wrote:
| The couple that maths together stays together.
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