> Grothendieck spoke of problem-solving as akin to opening a hard
nut. You could open it with sharp tools and a hammer, but that was
not his way. He said that it was better to put the nut in liquid, to
let it soak, even to walk away from it, until eventually it opened.
This is a lovely way of looking at solving hard problems as a
life-project, instead of a rushed performance. There's a pernicious
pressure in academia for students to be world-class before they're 25,
whereas I think the best insights seem to pop out quite naturally
after putting them in the background for 10 or 20 years.
I have not met many brilliant mathematicians, but a few do seem
especially sensitive to wounding by the ugliness in the human
condition. It's a shame both Alexander Grothendieck and Theodore
Kaczynski didn't find ways to tough it out against the ugliness
instead of succumbing to withdrawal or anger - because truth is the
greatest weapon against the violence of ignorant tyranny.
> truth is the greatest weapon against the violence of ignorant tyranny.
Do you see this work in practice?
All I see is a dead internet filled with AI-generated fake detritus-like content, attention and behaviour manipulation, all sorts of dark patterns.
Truth alone doesn’t come close to protect you against ignorant violence. Ignorance is multiplied by tech at much higher multiple, simple because there is often little profit in spreading the truth.
Sure. I see it in every child cured of cancer because the truth of
Fourier means that Positron Emission Tomography can zap a tumour. I
see it when people dance to music because the truth of electrodynamics
and sampling theory mean artists in a studio can make a record for
millions of others to enjoy. I see it when people are warm in their
homes because Einstein's truth about matter and energy means they have
electricity. The world around us is literally a triumph of truth.
> All I see is a dead internet filled with AI-generated fake
detritus-like content, attention and behaviour manipulation, all
sorts of dark patterns.
You're looking at it wrong. What you see is a group of sad little
people who betrayed technology to assuage their own inadequacies.
They mostly took what other much smarter people invented to make
sordid little businesses out of leveraging ignorance. The world is
catching up with them and their deeds, mark my words.
"...he described scientists and mathematicians as the most dangerous people on the planet, because they carelessly put destructive technological power in the hands of politicians."
This is indeed true. There's another side however, in that scientists and mathematicians have also put creative technological power in the hands of ordinary people. Perhaps a more nuanced view is that authoritarian states controlled by politicians are the most dangerous systems of all.
Anyone have a good suggestion of a mathematics textbook that would help me learn 'from the ground up so to speak' like how the article mentions, "He spoke of his mathematical work as the building of houses, contrasting it with that of mathematicians who make improvements on an inherited house or construct a piece of furniture."?
I am curious why a curriculum in the US includes four courses on calculus. Why isn't this just part of maybe three analysis courses for undergraduate studies?
Those are practical courses, meant to prep for linear algebra and differential equations — and various STEM tracks. As I recall, there were some proofs (eg, limits showing derivative rules; limits showing sums for integral rules).
We covered all the proofs in real analysis 1 (derivatives; sequences) and 2 (integrals; measure).
This textbook (work in progress but mostly complete) is an attempt to do exactly that: start at foundational math like group theory and topology and build up to higher and higher levels of math.
I worked through the first few chapters a while ago, and it's very good. My only issue is that sometimes he assumes knowledge of things that I didn't know about, but cursory googling was good enough for those situations.
>Grothendieck almost never worked with specific examples. It has been said that once, when he was asked to use a prime number to demonstrate something on the blackboard, he said, “You mean an actual number? O.K., take fifty-seven.” Fifty-seven is not a prime number—it’s nineteen times three—and it is now known as Grothendieck’s prime.
I've had a few professors over my years in academia who took a similar approach to mathematics and I have to say I really benefited from it. I found that if you can do high level math with a,b,& c instead of 1,2,& 3 you can do any problem your going to run into.
I also left the story oh his Grothendieck’s prime in because I find it quite charming, the idea that this exceptional mathematician couldn't think of a prime when asked makes me feel a lot better about some of the sillier mistakes I've made over my career.
This is a lovely way of looking at solving hard problems as a life-project, instead of a rushed performance. There's a pernicious pressure in academia for students to be world-class before they're 25, whereas I think the best insights seem to pop out quite naturally after putting them in the background for 10 or 20 years.
I have not met many brilliant mathematicians, but a few do seem especially sensitive to wounding by the ugliness in the human condition. It's a shame both Alexander Grothendieck and Theodore Kaczynski didn't find ways to tough it out against the ugliness instead of succumbing to withdrawal or anger - because truth is the greatest weapon against the violence of ignorant tyranny.