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Glen_b
Glen_b
12:27 PM
@Geomatt I closed it probably about the time you posted about it. But why go to ask someone in person when you can just get people on the internet to do your work for you without you even needing to get out of bed? Sure you won't learn anything, but hey, you can be maximally lazy in the meantime, which is apparently what university is for now. We might not answer this person's question but some sites will ...
 
 
1 hour later…
Jenkar
Jenkar
1:56 PM
@GeoMatt22 To be fair, some universities (around the world) are really bad on guiding students to getting help. IE teachers give the content of their lecture and that's it and exercises are made and answered without much check of if the student has understood.
 
 
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Antoni Parellada
Antoni Parellada
5:02 PM
@whuber I found a copy of Differential Geometry And Statistics / Murray
Chapman Hall, 1993 for $77 through Biblio.com If it is too advanced, at least it will serve as a road map for things to look up. I found [this series Norman Wildberger](https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP), which sounds promising, and have listened to the first lectures. However, I am always on guard with Wildberger's lectures - after having listened to a lot of them I started to realize how idiosyncratic he is.
I don't know if you are familiar with Norm Wildberger, but I would be very interested to hear your opinion if you happen to know his work / teaching perspective. If you are not familiar, but now you feel some curiosity, this video says it all. So without real numbers, transcendental functions, and stuck with polynomials, his proofs tend to be tedious. And my gut feeling (unsubstantiated) is that at some points he may be a bit fringe.
 
 
4 hours later…
Kodiologist
Kodiologist
9:13 PM
@AntoniParellada I've never heard of this guy before, but rejecting the existence of irrational numbers is more than a bit fringe. It's the mathematical equivalent of geocentricity.
 
Antoni Parellada
Antoni Parellada
9:25 PM
@Kodiologist I am sure he is an excellent mathematician, and it is normal for people who are experts in a field to start questioning the most fundamental underpinnings. And if I had a chance to edit my prior post, I would change the word 'fringe'. But it is difficult to continuously be on the lookout for things he may say that are strictly his 'asymptotic' bias, and separate them from what is more of a consensus view, while still trying to learn the fundamental ideas. Your comment reinforces
my take on the issue.
Thank you.
 
 
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Glen_b
Glen_b
10:38 PM
@Antoni Norm Wildberger? I'm currently writing a paper with a colleague whose daughter is doing mathematics there. She's either in one of his classes now or was last semester. [Actually I think I briefly met him one time but it would have been years ago.]
He seems to be an interesting fellow but yes, idiosyncratic might be a suitable term.
I really don't know his work that well, I merely took a look at some of his stuff once or twice. ... but a long time ago
I think people like that (real, trained experts who question fundamental orthodoxies) are essential, and can do really important work. Not to say the two are comparable in any direct sense, but for example take Brouwer who was definitely unconventional in rejecting ideas others see as fundamental but made major contributions
This guy
L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer ForMemRS (/ˈbraʊər/; Dutch: [ˈlœy̯tsə(n) ɛɣˈbɛrtəs jɑn ˈbrʌu̯ər]; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis. He was the founder of the mathematical philosophy of intuitionism. == Biography == Early in his career, Brouwer proved a number of theorems that were breakthroughs in the emerging field of topology. The most celebrated results were: his fixed point theorem, the topological invariance...
The Brouwer fixed point theorem, for example -- which is probably the thing he's most widely known for
 
Glen_b
Glen_b
10:56 PM
However while I see such people as important, when first learning a topic, I'd generally try to learn it from someone with more conventional ideas.
Someone out of the mainstream might be good for a second take, though, once you understand what everyone else is talking about
I remember working with another iconoclast -- a guy in finance who utterly rejects the notion of risk premium (which is pretty much fundamental to the whole edifice). He really knows his stuff, too. A very interesting fellow to chat with.
Such people can make their own careers difficult but I think we need them.
(In this case by "working with" I mean "in adjacent rooms"; I don't know that we taught any of the same subjects)
...
 
Antoni Parellada
Antoni Parellada
This is absolutely mind-blowing! Earth has shrunk into a parochial society with the development of the internet. Just imagine, it's 1720, and CV MathOverflow is bursting with activity. User Eule(xp)r just answered a question by the highly ranked Daniel B., a mathematician from Switzerland insisting on using only his first name... Wait, wait... AppleManNewton is putting the question on hold...
All in Latin.
Were would mathematics be is those towering figures had had access to SE? R, Matlab?
BTW I just discovered (thanks to Norm W.) a beautiful (and free) toy: geogebra.org/graphing
 
Glen_b
Glen_b
11:14 PM
Sometimes with such people it can be hard to tell them apart from the cranks with their REVOLUTIONARY THEORIES... but having actual publications in real journals the relevant areas in spite of highly unconventional views is a pretty strong test (that's a pretty high bar since getting published will be more difficult than if you take a conventional stance)
@Antoni Newton ... if he wasn't running a place like MathOverflow ... would be regularly running the risk of getting suspended from it
 
Antoni Parellada
Antoni Parellada
Terence Tao was something like 10 on the site a few months ago.
 
Glen_b
Glen_b
Imagine CV with Fisher (er... Ronald, not Nick) in it. Yikes. You might get some interesting stuff but sheesh there'd be a lot of drama
@Antonia yeah but Tao is one of those people who plays well with others, unlike either Newton or Fisher.
He's also a good "explainer", making him a good fit for such sites.
 
Antoni Parellada
Antoni Parellada
How much brain power has to be piled up on these communities when he is not number 1, even though whenever he opines, everybody agrees...
 
Glen_b
Glen_b
He's too busy to spend the time it takes to be right near the top (and his fame helps with the reputation, since everyone knows who he is)
In his case he knows so much stuff that he's able to draw a lot of connections between things. That can be especially useful for such collaborative sites
But yes MO has a large number of smart cookies
Ah, dammit, I did it again. Got up in time to do something and then forgot about it
 
Antoni Parellada
Antoni Parellada
Norman Wildberger... Respek!
 
Glen_b
Glen_b
11:28 PM
Yep, though I believe that first one is self-published. However, there's a lot of stuff that gets through tough peer review.
(And the less mainstream the tougher that would be)
I'm also brought to mind of unconventional artists (like Picasso or Van Gogh)... those guys could do the conventional stuff (and did) before they did their own thing
Van Gogh was doing impressionist painting and pointillism and so on when he was younger.
And he was pretty good at it
 

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