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DrBen
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Re: Philosophy of Mathematics

July 25th, 2021, 10:38 pm

Hardy, A Mathematician's Apology
In my teen's I treasured this book, I also inherited the anti-applied math slant, with the probably unhelpful idealism (but we are all young once). Would also add 'Discourse on the Method' by René Descartes, a must for all! The motto, 'the world is the encyclopedia of life' I have tried to adhere to since.
 
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Cuchulainn
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Re: Philosophy of Mathematics

July 26th, 2021, 8:14 am

Hardy, A Mathematician's Apology
In my teen's I treasured this book, I also inherited the anti-applied math slant, with the probably unhelpful idealism (but we are all young once). Would also add 'Discourse on the Method' by René Descartes, a must for all! The motto, 'the world is the encyclopedia of life' I have tried to adhere to since.
I never liked number theory.
The world's greatest mathematicians got their inspiration from the world around them, Hardy was a dead-end.
I think the schism applied/schism is silly. Unfortunately, maths has gone downhill since Henri Poincaré.

I liked Cartesian geometry at school. Many years later I wrote a C++ OOP library for CAD, graphics and optical technology.
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Cuchulainn
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Re: Philosophy of Mathematics

July 26th, 2021, 8:22 am

Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics.[citation needed] British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton (see Cambridge Mathematical Tripos). Hardy was more in tune with the cours d'analyse methods dominant in France, and aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics that was an important part of Cambridge mathematics.
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DrBen
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Re: Philosophy of Mathematics

July 26th, 2021, 12:11 pm

Hardy, A Mathematician's Apology
In my teen's I treasured this book, I also inherited the anti-applied math slant, with the probably unhelpful idealism (but we are all young once). Would also add 'Discourse on the Method' by René Descartes, a must for all! The motto, 'the world is the encyclopedia of life' I have tried to adhere to since.
I never liked number theory.
The world's greatest mathematicians got their inspiration from the world around them, Hardy was a dead-end.
I think the schism applied/schism is silly. Unfortunately, maths has gone downhill since Henri Poincaré.

I liked Cartesian geometry at school. Many years later I wrote a C++ OOP library for CAD, graphics and optical technology.
Henri Poincaré, now you are taking his work around the nature of Mathematical creativity is also a must read: L'Enseigement Mathematique (1902). Since I was 12yo, the single question above all others which I would like "to know" (not sure "to know" make sense in this context) is "what is the nature of mathematical creativity?" That reminds me, Plato's 'Theory of Forms' which comes up many times in his works ('The Republic' my Plato go to text), which is where all us pure math's guys go when we are in a trance (nice place too). A rather topical historical text, bit of outlier in normal times but now rather insightful to know is what lifestyle choices did the greatest scientist that ever lived make during the plague, can just dip into "The calculus wars...." by Jason Bardi to get an idea. Shame Newton is dead really, since BOJO could give him a call and ask who (on risk adjusted basis) should crack on and go down the pub and who should get in the bunker. You guy's got a thread here talking about this, I mocked up a SEIR model for us on the IoM, we 2,375 per 100K, but that nothing compared to British Virgin Island's. But that another story I guess, and I probably should not but here is a shameless plug: 
https://sites.google.com/webcabcomponen ... l?authuser
Cuchulainn, let me know where should post this in DM. In mean time, if I have made a complete messed this up on this, please DM, not keen to make myself look like a complete muppet in the local press or bring disrepute onto our beloved mathematics, and more importantly cause confusion for others trying the make risk adjusted decisions regard what is right of them and their circumstances.
 
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DrBen
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Re: Philosophy of Mathematics

July 26th, 2021, 2:12 pm

Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics.[citation needed] British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton (see Cambridge Mathematical Tripos). Hardy was more in tune with the cours d'analyse methods dominant in France, and aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics that was an important part of Cambridge mathematics.
G.H.Hardy reformed Tripos, so course better reflected training of a research mathematician. I read few students before this used to get trained by a coach for the tests (like Olympiads now I assume). Can you imagine someone like Henri Poincaré being in this system, very possible if he was born in UK (not France) would have got to Cambridge and then at some point said stuff this and went off to the City or similar. With regards to Newton, back in the day (early Summer 1996 I assume just after my years Part III exams) I expressed view to Graeme Segal who was one for my lecturers for Part III regarding atmosphere around exams was perhaps unhealthy (at least for some), and he told me "if it is good enough for Newton it is good enough for you".  
 
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Paul
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Re: Philosophy of Mathematics

July 26th, 2021, 3:02 pm

Graeme Segal and Nigel Hitchen were my pure maths tutors. They put me off for life. I saw Segal not that long ago. He was wearing mostly brown; if you know him you’ll understand my surprise.
 
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Cuchulainn
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Re: Philosophy of Mathematics

July 26th, 2021, 3:36 pm

Graeme Segal and Nigel Hitchen were my pure maths tutors. They put me off for life. I saw Segal not that long ago. He was wearing mostly brown; if you know him you’ll understand my surprise.
I see. My topology lecturer (who was a PhD student of Hodge (Atiyah's supervisor)) put me off topology as well.
If you ask a topologist to explain, they start drawing pictures of things with holes.

like in Penrose's book that many wax lyrical about.
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Paul
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Re: Philosophy of Mathematics

July 26th, 2021, 5:33 pm

I would take them seriously if they could show me how to untangle a kite string.
 
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Cuchulainn
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Re: Philosophy of Mathematics

July 26th, 2021, 6:49 pm

Another interesting observation is to reflect on the "styles" (elegance, nitty gritty) of one's lecturers. Our algebra lecturer was a grandchild of Cayley and gave very elegant lectures, the functional analysis lecturer had an approach in between algebra and analysis (from GH Hardy). Then the pinnacle was real/complex/probability analysis from department head (PhD student of W. Feller).
Only 2 years ago did I find out that the Statistics prof worked in Hut 6 and invented ISBN.

Still, even at the time most of my class went on to do pure maths or physics research. Not much pdes or numerical analysis. Maybe because Ireland had no nuclear arms, oil or semiconductor programmes.

And in 2000 the String Theorists' hype took over. Madness.

It's sad but quite a few succumbed to dementia. Maths is no antidote..
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platinum
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Re: Philosophy of Mathematics

July 31st, 2021, 2:13 pm

Another book for this collection - came across it in a used bookstore earlier this month; first edition is 2002, second is 2016:

The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford Landmark Science) - Roger Penrose

He covers the basic principles of physics, cosmology, mathematics, and philosophy and discusses AI in depth. Nice explorations from a gracious and open minded scientist and interesting to revisit the original ideas twenty years later.
 
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Collector
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Re: Philosophy of Mathematics

August 5th, 2021, 11:59 am

For every action there must be a equal and opposite reaction (the beginning of the end of fake imaginary math ? or the beginning madness? Scream? )

YYProduct(Number1, Number2, optional Principal, optional OutputDirection)
Screen Shot 2021-08-05 at 1.55.21 PM.png
)

"Written in faint pencil lines on the corner of the world-famous painting is the phrase: "Could only have been painted by a madman!"" (or perhaps only bought by a madman, price tag 120 USD M) Madness can always get worse, price likely up!
 
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katastrofa
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Re: Philosophy of Mathematics

August 6th, 2021, 7:17 am

The true title of the quartet is "Four maths students shown complex arithmetic".
Image
 
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platinum
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Re: Philosophy of Mathematics

August 20th, 2021, 10:58 pm

Came across this today in Quanta Magazine:

Map of Mathematics

Could be augmented maybe and many areas of math not included this version, but an interesting start.
 
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Collector
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Re: Philosophy of Mathematics

August 28th, 2021, 2:35 pm

Killing Imaginary Numbers? From asymmetric number system to symmetric
Screen Shot 2021-08-27 at 12.52.35 PM.png
 
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Collector
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Re: Philosophy of Mathematics

August 31st, 2021, 9:40 am