Shouldn't the year the article was written (2014) be included in the title?
Mathematicians are chronically lost and confused (2014)
31–40 of 147 posts
Re: Mathematicians are chronically lost and confused (2014)
#32What a great blog post! Totally agree with him. And, personnaly, it is why i'm having so much fun doing maths. Everytime it's a new exploration, a new challenge. My best math teacher I had was seeing math with this philosophy in mind and his class was like discovering new lands every time. I'm sure that if we explained in a way that failing a math problem is as normal and challenging that failing a Mario Bros Level, more people would be in peace with it.
Re: Mathematicians are chronically lost and confused (2014)
#33To me, this is about "mathematical maturity". My observation is that many programmers, especially those who have come of age by working in startups, tend to value ability and sometimes experience over formal education. This is a result, I believe, of noticing that they can outperform many people who have a classical education, and also seeing that many of the people to whom they look up also do not have much in the w…
This is very well-written. The prosody of it illuminates the topic you're speaking about. Being so rare, I wonder what makes you different.
Re: Mathematicians are chronically lost and confused (2014)
#34As an undergrad who recently became serious about math (thanks to its importance in areas I am interested in) this is very inspiring. I have been trying to grok mathematics for some time and sometimes being too frustrated with problems I can't handle. I have experienced the phenomena of giving up on something and coming back to it and finding it trivial. This is exactly what I needed.
Re: Mathematicians are chronically lost and confused (2014)
#35I have a great personal story that highlights how long the journey of understanding mathematics is. I took linear algebra my freshman year of college. It was the non-math major course, so it didn't require proofs. I got an A+ in the class. Not just an A, an A+. I was able to obtain such a high grade by taking tons of practice tests, and since the actual tests were basically mildly veiled calculations, I just had to m…
Linear algebra is the sort of topic where it seems like you can always go deeper. I also got an A in my linear algebra class in college. When I got to grad school for math, I took the first year graduate course on algebra and saw linear algebra in terms of algebraic things like modules and representations. I decided that I hadn't really known linear algebra before, but that I did then. Then I took differential geometry, which involves studying infinite collections of vector spaces parameterizes by points on a manifold. I realized I still hadn't know linear algebra, but after that I certainly did. Then I took a functional analysis class, where we did infinite dimensional linear algebra, where a lot of the finite dimensional theory has analogues but everything is more complicated (e.g. instead of finite bases and dot products, you consider things like Fourier analysis and Hilbert spaces).
The same realization that I don't know linear algebra came when taking a Lie algebras class, and again when learning homological algebra, and probably a few other times as well. There are certainly lots of areas of math that I've never explored that take linear algebra in some other direction (for example, I don't have any idea what the applied math guys do with....).
It's really an amazingly vast subject, especially considering that it's usually just thought of as a tool used to study more advanced topics.
Re: Mathematicians are chronically lost and confused (2014)
#36To me, this is about "mathematical maturity". My observation is that many programmers, especially those who have come of age by working in startups, tend to value ability and sometimes experience over formal education. This is a result, I believe, of noticing that they can outperform many people who have a classical education, and also seeing that many of the people to whom they look up also do not have much in the w…
I disagree that mathematics itself is difficult to engage with outside of academia. There are some academic mathematicians who think mathematics has to be hard because it was difficult for them to understand. There are others for whom sharing their insights is more important than searching for new ones. I think that the set of mathematicians together have done a rather good job in the 20th century of producing mathem…
> proof of weak fairness
Interest piqued. Do you have a good link for an intro to this?
Re: Mathematicians are chronically lost and confused (2014)
#37"mathematicians don’t work like this"? Sure they do. Reading textbooks is normal. As a mathematician, this post is foreign.
Re: Mathematicians are chronically lost and confused (2014)
#38To me, this is about "mathematical maturity". My observation is that many programmers, especially those who have come of age by working in startups, tend to value ability and sometimes experience over formal education. This is a result, I believe, of noticing that they can outperform many people who have a classical education, and also seeing that many of the people to whom they look up also do not have much in the w…
I think math is "easier" to learn while it still holds a clear practical value, up to calculus and linear algebra. Past that, when you start to enter the world of "pure" mathematical s, it can be muh more difficult. The practical value of earlier subjects allows a student or what have you to draw connections between what they already know and this new concept. Something like group theory however is more difficult to find a "use" for, outside of solving problems in your text book.
There are some good texts out there for learning by yourself. I currently own 7 or so Dover Books on Mathematics, and I could understate my appreciation of them.
Re: Mathematicians are chronically lost and confused (2014)
#39Does anybody know a good guide on where to begin? Resources are not the issue here, but usually the overwhelming amount of information regarding all those topics and areas of mathematics. I was always very interested but got discouraged rather quickly, even after a semester at university. So far my favorite access to math was through philosophy.
Step 1: Read Lockhart's Lament: https://www.maa.org/external_archive/devlin/LockhartsLament.... Step 2: Download the Book of Proof: http://www.people.vcu.edu/~rhammack/BookOfProof/ You read through it and do all the odd numbered exercises (the solutions are at the end of the book). Step 3: Get a book called Real Mathematical Analysis by Charles Pugh and you work through that and attempt as many problems as you can, w…
I don't find calculus and lin alg very interesting, school ruined those for me forever I guess. I am mostly interested Logic and Information Theory but I guess the latter doesn't go with a good calculus base.
Thanks for the links, I will read the book of proof and try the exercises, though mostly studied those topics already.
Re: Mathematicians are chronically lost and confused (2014)
#40Earlier quoted context omitted.
Step 1: Read Lockhart's Lament: https://www.maa.org/external_archive/devlin/LockhartsLament.... Step 2: Download the Book of Proof: http://www.people.vcu.edu/~rhammack/BookOfProof/ You read through it and do all the odd numbered exercises (the solutions are at the end of the book). Step 3: Get a book called Real Mathematical Analysis by Charles Pugh and you work through that and attempt as many problems as you can, w…
I'd also recommend Hubbard & Hubbard for a beautiful and beginner-friendly mix of algebra and analysis. My preferred starter kit is Rudin plus Halmos or Axler, but treating Rudin as a summary. So a helper would be needed, like Counterexamples in Analysis. This is what Math 55 used to do.
I don't really recommend Rudin for a true beginner at all (unless, by "as a summary," you mean not really digging into the proofs themselves, in which case any good analysis book will do). Rudin will always try to take the most elegant route to the theorem, regardless if that route goes anywhere near where the rest of the text has been. The result, for me, has been that many of his proofs seem to just meander about for a little while until, at the very end, you arrive at the theorem. It's a bit like driving to work on auto pilot, and just as disconcerting to me.