Other What are you reading now? (STEM only)

[Auto-Didact]

That's precisely what I meant before. The Bourbaki books an some of the textbooks of the members of Bourbaki are closer to scientific research work, and without doubt excellent research work, but they are lousy as textbooks. I'm sure that all these brillant mathematicians didn't come to the results presented in the waybof these books but in creative acts of thinking. Of course at the end the finding must be formalized in this way to be true pure math.

Indeed, real open ended creative mathematics - i.e. pure mathematics in the classical sense - is always messy and conceptual, while technical definitions through rigourous axiomatic formalization almost only always come after the actual discovery has already taken place.

Formalism, a bastard of logicism, championed by Hilbert in the pure mathematics community started to drive away many of the greatest late 19th century pure mathematicians, from Poincaré - famously the last univeralist (generalist), because of his creative instead of rigorous mind - onwards towards physics and applied math. Both Poincaré and Hadamard wrote on this subject.

Formalism then, during the 20th century, came close to culmination in Bourbakianism, driving generalists almost fully into applied mathematics. This drive-away was in peak effect mid-century - during the time of Mandelbrot et al. - firmly making their contributions to pure mathematics to instead incorrectly be viewed as physics and applied mathematics.

Incidentally, the last great theoretical and mathematical physicists - Feynman, Wilson, Anderson, Dyson, Mandelbrot, 't Hooft and Penrose - all recognized and spoke out against these developments in mathematics, but very few listenend i.e. taking their warnings at face value as critiques of mathematics itself, when they were actually criticizing formalism and axiomatics.

In classical pure mathematics - and therefore in physics as well - formalism is useless in discovering novel concepts, because it already presupposes full completeness of theory; this is why formal pure mathematics is purely deductive opposed to classical pure mathematics. To paraphrase Atiyah and Weyl: Hilbert and his followers killed creative pure mathematics. Bourbaki however made things severely worse by imposing the formalist ideology on students as well through the rewriting of curricula and textbooks.

This caused a severe widening of the divorce between pure mathematics and physics, worsening extremely with the professionalization of academia and overspecialisation of the sciences. The love between physics and mathematics would only be rekindled somewhat late in the 20th century, for somewhat wrong reasons, i.e. in string theory. It is happening again though, but now between applied mathematics and physics - while the formalist scoffs at both.

In any case, it should be obvious why formalism does more harm in mathematics than good; it is a self-imposed censorship of the mind borne out of the idea that mathematics must be reducible to logic, axioms and deductive reasoning alone. This is also exactly why to the physicist - today seen as a non-mathematician by most mathematicians - axiomatics are at best an afterthought; its a shame that many physicists seem to have forgotten this.

 

[gleem]

Formalism, a bastard of logicism, championed by Hilbert in the pure mathematics community started to drive away many of the greatest late 19th century pure mathematicians, from Poincaré - famously the last univeralist (generalist), because of his creative instead of rigorous mind - onwards towards physics and applied math. Both Poincaré and Hadamard wrote on this subject.

Isn't it interesting that Hadamard was Weil's dissertation adviser.

Anyway because of this discussion I have become inclined to reread "Mathematics: Queen and Servant of Science" by Eric Templeton Bell (1951) which discusses the contributions of mathematics to scientific knowledge.and more about the math than the science.

 

[Demystifier]

The Bourbaki books an some of the textbooks of the members of Bourbaki are closer to scientific research work, and without doubt excellent research work, but they are lousy as textbooks.

I think the standard terminology in this case would be textbook vs scientific monograph. Bourbaki books are monographs, not textbooks.

 

[Auto-Didact]

Quantum Information and Coherence, 2014

Link here, but behind a paywall

 

[Auto-Didact]

"Social Network Analysis: Methods and Applications" by Wasserman and Faust, 1994.

I actually learned some very nice pure and applied mathematics from this book, among other things Galois lattices and a method to carry out principal component analysis on non-quantitative data.

It is a basically a book on applied graph theory/network theory for researchers and data scientists out in the field. It gives a perspective at all levels: from pure and applied mathematics, to scientific, to practice.

Despite describing mostly social networks, I would highly recommend this book to any student/researcher wanting to learn to use any kind of network analysis in practice.

 

[Jimster41]

@Auto-Didact And... thanks for the link here. Don't know how I missed this thread.

 

[romsofia]

"Essays in honor of the 60th birthday of Bryce S DeWitt" and "Quantum concepts in space and time".

I really like the writing styles of most of the papers from these two books. They feel more informal to me, which I enjoy. For anyone who enjoys fundamental physics, these two books are truly a treat.

 

[Demystifier]

N. Johnson, Simply Complexity
https://www.amazon.com/dp/1851686304/?tag=pfamazon01-20
Complexity theory explained at a popular-science level.

 

[MidgetDwarf]

Artin: Algebra. Really nice book. Author is very careful with his explanations, good problems, and very enjoyable read.

 

[BPHH85]

Just for fun, I'm reading "the theoretical minimum - what you need to know to start doing physics" by Susskind and Hrabovsky. It's fun to read lighter stuff before sleeping.

For less lighter stuff, I'm reading "Quantum confined laser devices" by P. Blood.

 

[pinball1970]

Just for fun, I'm reading "the theoretical minimum - what you need to know to start doing physics" by Susskind and Hrabovsky. It's fun to read lighter stuff before sleeping.

For less lighter stuff, I'm reading "Quantum confined laser devices" by P. Blood.

Which one? There are 3 now, Classical, QM and SR. I found parts of the Classical difficult especially the "Action" section. I still do not really understand that despite following a few thread on PF on the subject.

I always take Lenny and George on the plane, guaranteed to help me forget about my fear of flying.

 

[BPHH85]

Which one? There are 3 now, Classical, QM and SR. I found parts of the Classical difficult especially the "Action" section. I still do not really understand that despite following a few thread on PF on the subject.

There seems to be two editions of the first part about classical physics, one from penguin books one from basic books. I'm reading the second one but to answer your question...it's part one :-)

 

[opus]

How to Prove It by Velleman.
Trying to learn how proofs and logic work in mathematics. So far have learned about truth tables and how to determine if a statement is valid- that is, using truth tables to see if a conclusion can only be true if all the premises are true.

 

[Auto-Didact]

"High-Field Electrodynamics" by Frederic V. Hartemann, 2002.

 

[Auto-Didact]

"High-Field Electrodynamics" by Frederic V. Hartemann, 2002.

Less exciting than hoped, put it down for now.

Finally got my hands on "Quantum Techniques In Stochastic Mechanics" by John Baez (and Jacob Biamonte), 2018.

It's a bit confusing that in the book they created and christened a new field of research in mathematical physics called 'stochastic mechanics' seeing that there is actually already an existing field of research in physics also called stochastic mechanics (a Bohmian interpretation of QM) created by Nelson et al. a few decades ago.

In any case, reading Baez is as always a pure delight; he fearlessly takes his readers with him on a unique intuitive journey, thereby exposing them to a vast array of genuine creative applications - going far beyond just physics - even backed up by the necessary mathematical rigour.

This is simply a must-read for (aspiring) mathematical physicists, applied mathematicians and physicists & mathematicians more generally.

 

[Demystifier]

stochastic mechanics (a Bohmian interpretation of QM) created by Nelson et al.

Bohmian interpretation of QM is not stochastic mechanics.

 

[Auto-Didact]

Bohmian interpretation of QM is not stochastic mechanics.

No, I meant that there is an existing line of research called Stochastic Mechanics & Stochastic Electrodynamics (SM & SED) going back to at least Nelson 1965.

SM is a semiclassical stochastic theory of mechanics which is mathematically deeply consistent with the Bohmian interpretation i.e. the existence of a quantum potential, namely through the Madelung equations (see e.g. de la Peña et al. 2014 section 3.6, pp 26, 27).

SED on the other hand, is where the real meat is; an extension of the Bohmian interpretation with the ZPF as the quantum potential, claiming to explain quantization and supersede QM and QED all in one go.

A little while ago I read all recent papers on SED, but I can't really recall which one was the best one. However, the best books I have read on these theories are "The Emerging Quantum", de la Peña et al. 2015 and "Fluctuations, Information, Gravity and the Quantum Potential", Carroll 2006 (by the way, the latter one heavily references your work).

 

[n3pix]

I'm now reading, Introduction to Rocket Science and Engineering, Taylor S. TRAVIS.

And having some physics/astronomy issues, I will now ask these questions :)

 

[Demystifier]

Just reading the 2nd edition of L.E. Balentine, Quantum Mechanics A Modern Development. It differs from 1st edition by having a chapter on Quantum Information, so I am actually reading only that chapter, as the rest I have been reading a long time ago.

 

[Demystifier]

J. Baggott, Quantum Space
- A popular-science book on loop quantum gravity.

 

[Klystron]

I'm well into Algebraic Number Theory, third edition, by Stewart and Tall; suggested IMS by a PF member on a math forum. The authors organize the text as a corollary to the long search and proof of Fermat's Last Theorem but I find it a decent intermediate review of algebraic numbers considering I'm more used to set theory. Makes me want to know more advanced abstract algebra.

Almost finished reading The Master Algorithm by Pedro Domingos. Quite a fun introduction to machine learning with several good chapters on probability and stats. Not a textbook; more popular computer science with easy equations.

 

[Andy Resnick]

I've recently received a short stack to review:

World According to Quantum Mechanics, The: Why the Laws of Physics Make Perfect Sense After All (Second Edition)
Group Theory in Physics: A Practitioner's Guide
Methods in Molecular Biophysics: Structure, Dynamics, Function for Biology and Medicine 2nd Edition

The first one seems interesting- it's not exactly a physics textbook, it was written for a "philosophically oriented course of contemporary physics to higher secondary and undergraduate students" who are not necessarily Physics majors. The second is a straight-up applied mathematics text, but seems fairly comprehensive. The third is a fairly straightforward handbook of single-molecule biophysics experimental methods.

I'm so far enjoying all three.

 

[Jimster41]

I've recently received a short stack to review:

World According to Quantum Mechanics, The: Why the Laws of Physics Make Perfect Sense After All (Second Edition)
Group Theory in Physics: A Practitioner's Guide
Methods in Molecular Biophysics: Structure, Dynamics, Function for Biology and Medicine 2nd Edition

The first one seems interesting- it's not exactly a physics textbook, it was written for a "philosophically oriented course of contemporary physics to higher secondary and undergraduate students" who are not necessarily Physics majors. The second is a straight-up applied mathematics text, but seems fairly comprehensive. The third is a fairly straightforward handbook of single-molecule biophysics experimental methods.

I'm so far enjoying all three.

Why that first one got to be 150 bucks? That ain't right.
No, I don't want the Kindle version.

 

[lomidrevo]

Recently, I realized that I need to refresh the basic concepts of theory of probability and statistics. I have found this free textbook very interesting:
Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik

The content is easy to follow and I am having lot of fun solving the included problems. I like it so much that I have bought the printed version
I wish I could have this book back then during my studies..

 

[Auto-Didact]

Einstein's Unfinished Revolution: The Search for What Lies Beyond the Quantum by Lee Smolin

 

[DarMM]

Just reading the 2nd edition of L.E. Balentine, Quantum Mechanics A Modern Development. It differs from 1st edition by having a chapter on Quantum Information, so I am actually reading only that chapter, as the rest I have been reading a long time ago.

I found that extra chapter pretty good for conveying the highlights of the area as best as one can in a general account of QM. However I do feel Quantum Information is better served via a textbook on its own in the context of being a generalization of Classical Information Theory.

 

[Demystifier]

However I do feel Quantum Information is better served via a textbook on its own

What's your favored book on this?

 

[DarMM]

What's your favored book on this?

My personal preferences are:

Barnett, S. (2009). Quantum Information, Oxford: Oxford University Press

D'Ariano, G., Chiribella, G., & Perinotti, P. (2017). Quantum Theory from First Principles: An Informational Approach. Cambridge: Cambridge University Press.

The first is a nice introduction to Quantum Information, but the second is a much more detailed approach to the subject that provides a very different way of looking at QM.

 

[smodak]

Einstein's Unfinished Revolution: The Search for What Lies Beyond the Quantum by Lee Smolin

How is it?

 

[CJ2116]

When I was in Seoul I stopped into a bookstore and found a copy of Wangsness' Electromagnetic Fields. It has been just sitting on my shelf for a few months, but I picked it up last week to supplement Zangwill's book. Totally hooked on this book. His is the only one I have seen that explicitly solves for $\mathbf{r}$ and $\mathbf{r'}$ instead of resorting to slick symmetry arguments right off the bat.

 

[Dr Transport]

When I was in Seoul I stopped into a bookstore and found a copy of Wangsness' Electromagnetic Fields. It has been just sitting on my shelf for a few months, but I picked it up last week to supplement Zangwill's book. Totally hooked on this book. His is the only one I have seen that explicitly solves for $\mathbf{r}$ and $\mathbf{r'}$ instead of resorting to slick symmetry arguments right off the bat.

Exactly what I been saying for years on this forum, Wangsness is by far the best intermediate electromagnetics book written in many years, far better than Griffiths in my opinion.

 

[CJ2116]

Exactly what I been saying for years on this forum, Wangsness is by far the best intermediate electromagnetics book written in many years, far better than Griffiths in my opinion.

It's a bit too early for me to judge fully, but I definitely think I'm inclined to agree.

I also really like the fact that everything is broken down into small chapters. I'm kind of kicking myself that I didn't start reading this sooner!

 

[Auto-Didact]

How is it?

I'm still at the beginning, too early to give commentary; I will say the beginning chapters are probably the most lucid popular description of core QM I have ever read, i.e. if you know little about physics and want to get a good feel for how QM essentially works as a physical theory, there aren't many better descriptions.

 

[SamRoss]

I'm reading Inside Interesting Integrals by Paul Nahim. As I read through other math and science books, I noticed that where I got stuck the most was on integrals; I definitely needed a refresher. Nahim's book is basically him working through zillions of integrals, one after another. I'm three-fourths of the way done and definitely feel more confident.

 

[Auto-Didact]

How is it?

Halfway through now. This is the most lucid account of the different interpretations and foundational issues of QM that I have ever read. It is important to realize that foundations of QM is the most abstruse field in physics. Lee Smolin really has a knack for steering through these overtly complex waters as if they were as calm as a pond on a sunny day.

I have read countless far more comprehensive texts, books, articles and threads on this topic, but in my experience none of the above make the case as clear or as brief as Smolin manages to do. In my opinion this is very much a positive point, because the sheer volume of largely non-essential and repeated information in the literature is clearly weighing the entire field down, even causing students and non-foundations practicing physicists to avoid it.

Perhaps my prior knowledge of and exposure to the subject makes me appreciate Smolin being able to cut through to the core of the issues without getting bogged down in trivial or irrelevant details; if that is so, it may mean that those well versed in the literature may find Smolin offers a well thought out argument based on enough information, while others - not so well-read - might actually find his presented argument lacking enough background information.

Incidentally, if someone (semi-)well-read on the QM foundations literature does seem to find this book explicitly lacking in information, I would presume that they are precisely bogging themselves down in trivial or irrelevant details, and do not actually have a working understanding of the core issues i.e. they are literally making themselves incapable of seeing the forest for the trees.

 

[Demystifier]

Just reading Grensing, Structural Aspects of Quantum Field Theory (2 volumes, more than 1600 pages).

 

[Auto-Didact]

Just started Infinite Powers, by Steven Strogatz (April 2019). Its a history of calculus.

Just reading Grensing, Structural Aspects of Quantum Field Theory (2 volumes, more than 1600 pages).

How is it?

 

[Demystifier]

How is it?

Contains some topics that cannot easily be found in other books, like lattice regularization, Weyl quantization, ...

 

[Auto-Didact]

Just started Infinite Powers, by Steven Strogatz (April 2019). Its a history of calculus.

Halfway through now. The book so far is both an informal history of mathematics and its key discovers. Around the middle is where he arrives at Newton and Leibniz. Along the way I have learned a few things e.g. that Fermat actually invented the Cartesian plane before Descartes did and he even almost invented the derivative as well.

Strogatz does a very good job of balancing contributions for every major historical step, the two key figures which were involved in the invention and how the stark contrast in their thinking based on completely different viewpoints of the subject leads to two very different approaches to some mathematical idea. The miracle of mathematics is that these dual approaches - logically often the complete opposite - are capable of converging to a single idea.

These two different approaches are key to understanding both the practice of mathematics and the subject of calculus, i.e. both actually discovering new mathematics and refining what is discovered as well as understanding what infinity can do for us. Strogatz manages to illustrate the very different nature of symbolic mathematics as mathematics progressed through the centuries, giving an introduction to the concept and primacy of mathematical creativity based on synthesis in contrast to proof by formal analysis.

Synthesis is an informal method/subject invented by the ancient geometers and used since by many mathematicians (and physicists) based on physical intuition. Synthesis as a method tends to be entirely overlooked or ignored in modern math education; this is starkly clear in that calculus is seen as part of analysis with no mention of synthesis whatsoever.

Together with analysis, synthesis enables the possibility of finding answers and proving that the found answers are correct. The problem is that synthesis has been almost universally rejected in public by mathematicians and in mathematics education after Hilbert. It helps very much that Strogatz is one of the greatest applied mathematicians alive and willing to speak so casually about this, both in public, in his textbooks and in his popular books.

@A. Neumaier and @fresh_42, I recall having discussions on this with you on this topic before: the distinct usage of synthesis and symbolic mathematics is why Newton can truly be considered to be the first mathematical physicist, and not Kepler or Galileo despite their physics being presented in mathematical form.

Being in mathematical form is a necessary but not sufficient condition for something to be deemed part of 'mathematical physics' (or analogously 'mathematical biology' or 'mathematical economics', etc); if this were sufficient then any physics argument based on statistical argument would be considered to be 'mathematical physics'.

Kepler's laws were based on non-synthetic reasoning but instead result from statistical analysis of measurements. This is in stark contrast to Newton who derived Kepler's laws from first principles based on his concept of force. It is the qualitative leap in thinking i.e. the usage of synthetic methodology which makes Newton's work to be a new subject called mathematical physics.

 

[A. Neumaier]

It is the qualitative leap in thinking i.e. the usage of synthetic methodology which makes Newton's work to be a new subject called mathematical physics.

But this new subject is called theoretical physics.

Mathematical physics is treating questions from theoretical physics as mathematical problems, i.e., at the level of rigor customary in mathematics - which most of theoretical physics does not have. It may perhaps be taken to have started with Kolmogorov 1933 (Solution of the 6th Hilbert problem).

Actually, it dates slightly earlier, with Courant and Hilbert's 1924 treatise Methods of Mathematical Physics, which might perhaps be the earliest use of the term. (Before that, there was no clear demarcation line.)

 

[Auto-Didact]

But this new subject is called theoretical physics.

Mathematical physics is treating questions from theoretical physics as mathematical problems, i.e., at the level of rigor customary in mathematics - which most of theoretical physics does not have. It may perhaps be taken to have started with Kolmogorov 1933 (Solution of the 6th Hilbert problem).

That is modern mathematical physics, i.e. after the divorce of mathematics and physics around 1880. Before that time mathematical physics and theoretical physics were one and the same subject. (I should probably start a new thread.)

Beforehand what we now see as mathematically mundane was very much cutting edge mathematics. Newton was not coincidentally the best mathematician of his time. After him and before Kolmogorov there were certainly other masters such as Hamilton.

 

[CJ2116]

My copy of Advanced R, 2nd Edition by Hadley Wickham finally arrived last night. Just started reading/working through it.

I spent a while learning various programming languages (C++, Python and Javascript), but for some reason I never felt comfortable in any of them. I gave up in frustration. A few years ago one of my coworkers, who came from West Point as a math instructor, turned me onto R. I totally fell in love with it.

All this to say that I've spent years learning it as a data science tool, but not so much from a deeper computer science level. This book is one of the few that seems to fill this gap. Definitely recommend this to other R users!

 

[fresh_42]

Actually, it dates slightly earlier, with Courant and Hilbert's 1924 treatise Methods of Mathematical Physics, which might perhaps be the earliest use of the term. (Before that, there was no clear demarcation line.)

I came across the following quote these days:

Physics is becoming too difficult for the physicists.

but before the physicists will complain, he also said

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

Beforehand what we now see as mathematically mundane was very much cutting edge mathematics. Newton was not coincidentally the best mathematician of his time. After him and before Kolmogorov there were certainly other masters such as Hamilton.

I think we should not forget Leibniz here. Physics and mathematics evolved pretty much hand in hand. What were new mathematical techniques at their times were often inspired by the search for solutions to physical problems. Hamilton might even be a bad example, since he searched for a field extension without having an application in mind. But there are many others, Bernoulli, Cauchy, Graßmann, and so on and so on. And not to forget Descartes!

The lack of symbiosis nowadays reflects in my opinion the fact that physicists ran out of problems. Since Riemann and Noether (and with her Lie) we seem to have all necessary tools at hand to describe physical problems, so from a physical point of view, mathematics has become a toolbox. This wasn't the case in former times. The latest instance where mathematics was driven by physics was probably string theory, but grading Lie algebras didn't need new concepts, just a bit more research of given constructions.

 

[gleem]

Let's not forget Fourier.

 

[Auto-Didact]

The lack of symbiosis nowadays reflects in my opinion the fact that physicists ran out of problems.

I don't think we have actually ran out of problems at all, instead it seems that no one is really up to the challenge; this is because our collection of (approximative) techniques and the ability to idealize have made us complacent, even blinding us to some obvious limitations of our current theories. Moreover, due to overspecialization, non-communication between different branches and a preference for a premature naive kind of certainty, physicists have begun to accept non-answers as answers.

This cuts both ways which can be seen in that many are overvaluing pseudoproblems such as overt skepticism of a theory purely because it lacks a high degree of formal mathematical rigour and respecting half baked solutions because of practiced familiarity, while simultaneously undervaluing real problems (e.g. pretending that there are no problems in the QT foundations) and ignoring real possible routes to solutions because they seem too unorthodox.

Don't get me wrong, the mathematician's toolbox is a wonderful thing and we should take advantage as much as we can; I feel that most physicists however prematurely stop doing this and then instead only end up learning about a few techniques which they believe are essential, while ignoring the rest.

The mistaking of mathematics as essentially axiomatics - because of how many mathematicians talk and behave - is counterproductive and shifts the burden of inventing new mathematics to the physicist, who again pushes the burden of responsibility further across the chain; indeed, at the end of the day, both the problems and burdens are pushed so far out of sight that "there are no problems" and "that was already solved".

 

[fresh_42]

I don't think we have actually ran out of problems at all

With respect to descriptive methods? Of course we have enough problems, but neither requires new methodical mathematics as far as we know. We discuss whether the small Lie groups need to be replaced by larger ones, we grade Lie algebras for string theory, we even use cohomology, and of course all takes place on Riemannian manifolds with sometimes strange pseudo metrics like Minkowski, or very difficult differential equations like Navier-Stokes. However, all those things can easily be described by what we have. In this sense physics ran out of problems as a necessity to build new branches in mathematics.

 

[atyy]

With respect to descriptive methods? Of course we have enough problems, but neither requires new methodical mathematics as far as we know. We discuss whether the small Lie groups need to be replaced by larger ones, we grade Lie algebras for string theory, we even use cohomology, and of course all takes place on Riemannian manifolds with sometimes strange pseudo metrics like Minkowski, or very difficult differential equations like Navier-Stokes. However, all those things can easily be described by what we have. In this sense physics ran out of problems as a necessity to build new branches in mathematics.

How about the KPZ equation? I think even Landau damping was not firmly founded until recently. And 4D QFT is still undefined.

KPZ: https://arxiv.org/abs/1109.6811
Landau damping: http://smai.emath.fr/cemracs/cemracs10/PROJ/Villani-lectures.pdf
4D QFT: https://www.claymath.org/millennium-problems/yang–mills-and-mass-gap

 

[DaveC49]

Evolution The Whole Story Ed Steve Parker (https://thamesandhudson.com/evolution-the-whole-story-9780500291733)
Selected papers on Quantum Electrodynamics julian Schwinger (https://store.doverpublications.com/0486604446.html) historical persepective on development of QED.

 

[atyy]

https://mitpress.mit.edu/books/broken-movementBroken Movement: The Neurobiology of Motor Recovery after Stroke
By John W. Krakauer and S. Thomas Carmichael

https://www.cambridge.org/core/book...tter-physics/F0A27AC5DEA8A40EA6EA5D727ED8B14EModern Condensed Matter Physics
By Steven M. Girvin and Kun Yang

Girvin and Yang's book was mentioned by @fluidistic in the STEM Bibles thread.

 

[martinbn]

Don't know if this counts, but since Landau damping was mentioned it reminded me that I just finished Cedric Villani's "Birth of a Theorem: A Mathematical Adventure".