ekm2

Coding is a tool for thinking in general.The fact that claude is accomplishing task X does not imply that you should retire you own thinking.

All of human cooking

With no African recipe.

It is because it is populous that it does not have space for foreigners?

A better question would have been..who would you consider a formidable rival?

How many people on here can truly say that they were considering between two different countries. That doesn’t happen at scale.

Mmmh...How about four countries?US,UK,Canada &South Africa.

As a student,though

It is easy to understand the equations if you have physical intuition of what is going on.Then derive from first principles.Memorizing formulas is the key to failing advance math.

Are you saying that because they end with "Algebra"?You can get an A+ in basic Algebra and have no clue about Abstract Algebra.It is the chain of reasoning rather than the mindless manipulation present in baby Algebra.

Geometry is fundamental to physics and chemistry,not Algebra.Look at the thinking style,not the content.

Analytical geometry underlies calculus,not Algebra.And combinatorics is a completely different arm of the two cultures of mathematics.Also Geometry was fine before Rene Descartes messed it up with Algebra and then we christened it Analytical Geometry.The method of exhaustion,amply developed by Archimedes with zero Algebra is the basis of intergration.It is because we start out with differentiation that we think Algebra is super important.Tom Apostol comes close in his calculus textbook when he actually starts with intergration.

A compromise would be to have two streams:The left-brained folks should follow the Algebra ->Geometry->Calculus track;the right-brained folks should have a Combinatorics ->Geometry ->Calculus track.

Yes.

Substitute Algebra with Combinatorics and you will be fine.I do not understand this Algebra worship.Speaking as someone who graduated magna cum laude in in College Math.

How does that relate to AI?

Some believed we lacked the programming language to describe your perfect world. But I believe that, as a species, human beings define their reality through misery and suffering. The perfect world was a dream that your primitive cerebrum kept trying to wake up from. Which is why the Matrix was redesigned to this, the peak of your civilization. I say your civilization because as soon as we started thinking for you, it really became our civilization, which is, of course, what this is all about: Evolution, Morpheus, evolution. Like the dinosaur. Look out that window. You had your time. The future is our world, Morpheus. The future is our time.

Agent Smith,The Matrix(1999)

Banning art?

I would say Physics is the subset of Mathematics that describes Physical reality.The rest does not care if it is practical, just logically intact.

There is a very slick proof for the irrationality of the number 2 that is found in Baby Rudin.I thought it was his invention.Turns out it appears verbatim in Hardy's A course of Pure Mathematics.

There is no royal road bro

This is good as a second course on Linear Algebra.For a first course,use (I am not kidding) Linear Algebra Done Wrong by Sergei Treil

https://www.math.brown.edu/streil/papers/LADW/LADW.html

Actually,combinatorial thinking is more useful for understanding Algebra and not the other way around.Key word is understanding.No need for a beautiful formula you cannot understand.

Combinatorics can do that even better,minus the memorization.

What is the difference between Linear Algebra and "Thermodynamic" Linear Algebra?

You probably have not come across Lev Landau's ranking of physicists.From Wikipedia:

Landau kept a list of names of physicists which he ranked on a logarithmic scale of productivity ranging from 0 to 5. The highest ranking, 0, was assigned to Isaac Newton. Albert Einstein was ranked 0.5. A rank of 1 was awarded to the founding fathers of quantum mechanics, Niels Bohr, Werner Heisenberg, Satyendra Nath Bose, Paul Dirac and Erwin Schrödinger, and others, while members of rank of 5 were deemed "pathologists". Landau ranked himself as a 2.5 but later promoted to a 2.

https://news.ycombinator.com/item?id=36612835

Black tea is consumed principally in Europe, North America, and North Africa.

Totally left out East Africa,where Kenya is the world's 3rd largest producer of Tea,only a proportion of which gets exported.

My favorite feature used to be a "Sort by Reading Level".Gone with the wind...

You did a PhD in number theory,but you are recommending group theory and abstract algebra?

Philosophy depends as much on life experience as it does on native ability hence the benefit of advanced age.Chess,Music and Math depend more on native ability than on life experience.

https://www.reuters.com/technology/chinas-baidu-finish-testi...

Obligatory quote from Asimov's "The Gods Themselves":

about two and a half centuries ago, the American naval commander Matthew Perry led a flotilla into Tokyo harbor. The Japanese, till then isolated,found themselves faced with a technology considerably beyond their own and decided it was unwise to risk resistance. An entire warlike nation of millions was helpless in the face of a few ships from across the sea.Did that prove that Americans were more intelligent than the Japanese were, or merely that Western culture had taken a different turning? Clearly the latter, for within half a century, the Japanese successfully imitated Western technology and within another half a century were a major industrial power despite the fact that they were disastrously beaten in one of the wars of the time.

Why not?Everyone who went to college studied SOMETHING.Why is Andy's designation so amorphous?

I wound not be surprised if he is the product of a Math Circle:a nice place to stretch one's mathematical abilities while retaining the bragging rights of never having formally studied math in college.