Jordan Ellenberg

Some followup conversation in the comments at Ellenberg's blog: http://quomodocumque.wordpress.com/2014/05/30/should-andrew-gelman-hav…

Here is Ellenberg's own list of books he has read in the last few years: https://quomodocumque.wordpress.com/the-booklist/

Criticism: https://quomodocumque.wordpress.com/2013/01/05/do-we-really-underestim…

The more mathematically-inclined HNers might be interested in Brian Conrad and Terrence Tao's comments at the bottom of this previous HN article: http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc Edit: Minhyong Kim's initial thoughts seem very interesting as well! http://mathoverflow.net/questions/106560/what-is-the-underlying-vision… And for the less mathematically-inclined: http://news.ycombinator.com/item?id=4477241

Your interpretation is right, and those minima are interesting in themselves. For example, when http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/ was posted, the very first comment was about that. "It almost looks as if the method doesn't (as presently written) produce explicit constants. Hopefully as the ideas become more widely understood, effective constants will be able to be extracted."

http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/ [edit - linked the wrong discussion]

That link is old and was posted a few years before the final paper. The more recent discussion is here: http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/

You're not stupid. At least, there is very little chance that the math you're trying to work on right now requires super-normal cognitive abilities of any sort: it's more about learning to be comfortable with the ambiguity or lack of comprehension that the process of learning entails. Here's a grab-bag of stuff that have helped me (and still do) lift myself out of "damn I'm dumb" situations such as the one you seem to find yourself in. "Does math have to be ambiguous or cryptically written? That doesn't sound right." Well, no. Sometimes, the solution is just "get a better book" (although, see [-1]). However, even extremely well-written books will skip over certain details (which ones they elide depends on the target audience), for the simple reason that it a) massively shortens the book b) maintains the "flow" well, instead of stopping every few sentences to distract the reader with ideas not directly relevant to the argument c) acts as a natural method to help people choose materials: if you're hitting things you can't understand or even parse every two lines, maybe you'd be better served by coming back to it a while later? In other words, the skipped details and "why would that be the case?" are going to be there even in books that are considered masterpieces of mathematical writing, and everyone encounters them and learns to deal with them. So what do you do when you hit the inevitable "yeah, right, that's trivial, suuuuuure" next time? To paraphrase someone I can't…

Related to your comment, not the original post/book: - On Knuth’s idea (which seems good to me), see http://quomodocumque.wordpress.com/2012/05/29/knuth-big-o-calculus-imp… but also the last two comments by David Speyer. - And see also http://cornellmath.wordpress.com/2007/08/28/non-nonstandard-calculus-i… and http://texnicalstuff.blogspot.in/2011/05/big-o-notation-for-calculus.h… that seem to have tried teaching along somewhat similar (but different) lines. - See https://terrytao.wordpress.com/2022/05/10/partially-specified-mathemat… for a further formalization of O notation. (These links via comments I left to myself at https://shreevatsa.wordpress.com/2014/03/13/big-o-notation-a-couple-of…

I will spam you with my uncurated collection I've hoarded for just from the past few months here on HN: CS 20SI: Tensorflow for Deep Learning Research http://web.stanford.edu/class/cs20si/syllabus.html https://news.ycombinator.com/item?id=13781067 A visual introduction to probability and statistics http://students.brown.edu/seeing-theory/ https://news.ycombinator.com/item?id=13735714 Mathematicians becoming data scientists: Should you? How to? https://quomodocumque.wordpress.com/2017/02/26/mathematicians-becoming… https://news.ycombinator.com/item?id=13739687 good beginner tutorials for Stan or probabilistic programming in general http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesi… https://news.ycombinator.com/item?id=13742102 Supporting the AI Talent Pipeline https://medium.com/@mark_riedl/supporting-the-ai-talent-pipeline-5ae0f… Georgia Tech Offers Online Master of Science in Analytics Degree for Under $10K https://news.ycombinator.com/item?id=13382263 Practical Deep Learning For Coders http://course.fast.ai/ https://news.ycombinator.com/item?id=13224588 https://news.ycombinator.com/item?id=13599074 (learn or be a dinosaur) https://news.ycombinator.com/item?id=13605222 ($1k machine) https://news.ycombinator.com/item?id=13588070 (oxford deep nlp) Coding The Matrix: Linear Algebra Through Computer Science Applications http://codingthematrix.com/