#paulhalmos — Public Fediverse posts

@ajcain

I agree with you in terms of substance and usefulness, of course. Yet I also have to admire the autor's Chuzpah. "Read my book, Reader, I have a story to tell. Read it, I will take you along."

That kind of style was still quite common, say thirty or fourty years ago, among historians and art historians. The same people whose lectures or conference talks would be read out from perfectly written notes. In some cases, it even worked.

At the other extreme is the excessive structuring adopted in many science texts, where we may have to keep track of sub-sub-sub-sections.

Paul Halmos in his books as ever got it right. Three levels: parts, chapters, sections within chapters. Each section has 1-2 pages; each chapter is a handful of sections, no other headings except flags for Theorems. The section titles are extremely brief, almost serving as index lables. The perfect merger of self-sustaining narrative and formal section structure.

#typography #BookDesign #PaulHalmos

1/2

@DrYohanJohn
@davidjamesweir

An anecdote from Paul Halmos's autobiography:

In class. The lecturer works through a proof, on the blackboard. At some point he says "It is obvious that ..." and then states the relationship he relies on in his proof.

One student asks: Excuse me, Professor, I don't see why this is obvious. I don't understand it.

The lecturer nods, turns back to the blackboard, looks at the previous steps, thinks, chalks up some calculations in a corner, thinks some more.

Then he turns back to class. "Yes, as I said, it is obvious."

[Quoted from memory, details in the book will differ.]

#PaulHalmos #ItIsObvious #proofs #HigherEducation

@troublewithwords

Oh, but Linear Algebra is love! The purest human reflection on the exercise of simplicity in the apparent chaos of the world.

I am only half joking! :-) I appreciate your post is about LLMs. They are an obscene misuse of a sacred practice.

My worn-out copies of Paul Halmos's Finite Dimensional Vector Spaces and Emil Artin's Geometric Agebra --- these are the most treasured books in my personal library. (After The Magic Mountain, of course, but _that_ battered volume sits on a different shelf.)

#LinearAlgebra #PaulHalmos #EmilArtin #SimplicityIsLove #LLMsAreBlaphemous

@ZachWeinersmith

I'm not up to date on recent Linear Algebra textbooks, but hey! Strang's book is uniquely beautiful, and uniquely effective in conveying deep structural insights elegantly and with concrete examples that stay with the reader. Perfect for a class setting, but also eminently suitable for self study. The right choice for your project! (imho)

Each field has a textbook that is accessible to inexperienced readers yet true to the deeper structures of the subject. That book ought to be written in every field, but in most fields it never is written. It requires a gifted author to come along and do the deed. Gilbert Strang's writing of his book was one of these special and rare events.

As it happens, linear algebra had another such event, a generation before Strang, in the shape of Paul Halmos's Finite-Dimensional Vector Spaces. Another beauty, on the abstract side of the spectrum, and perhaps the perfect complement to Strang.

#LinearAlgebra #GilbertStrang #PaulHalmos

A two-part lecture course on Topology, by Professor N. The first part is in the spring semester, the second part in the following autumn semester; between them is the long summer break.

First week of the autumn semester, first lecture. Professor N comes into the room. He walks to the blackboard and picks up the chalk. He turns to the class and starts:

"Hence, ... "

---
[Anectdote told by Paul Halmos in his autobiography. I quote from memory, so the details will vary.]

#lectures #HigherEducation #pedagogy #PaulHalmos

@darkling

Indeed. And another re-arrangement of the axioms.

Paul Halmos in his autobiography reports on one of his colleagues who taught a course in measure theory (I quote from memory). He set out the axioms in lecture 1. Come lecture 2, and he explains that actually, the right axioms should be such and such. And so the semester progresses, each week a new, better axiom system, with no time left for any derivations.

I love that story, on so many levels.

#PaulHalmos #axiomatics #teaching #procrastination #TakeYourTime #yesthestudentswillhavelearntmoreinthislecturethaninanyother