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Today was the first day that I could definitively say that #GPT4 has saved me a significant amount of tedious work. As part of my responsibilities as chair of the ICM Structure Committee, I needed to gather various statistics on the speakers at the previous ICM (for instance, how many speakers there were for each section, taking into account that some speakers were jointly assigned to multiple sections). The raw data (involving about 200 speakers) was not available to me in spreadsheet form, but instead in a number of tables in web pages and PDFs. In the past I would have resigned myself to the tedious task of first manually entering the data into a spreadsheet and then looking up various spreadsheet functions to work out how to calculate exactly what I needed; but both tasks were easily accomplished in a few minutes by GPT4, and the process was even somewhat enjoyable (with the only tedious aspect being the cut-and-paste between the raw data, GPT4, and the spreadsheet).
Am now looking forward to native integration of AI into the various software tools that I use, so that even the cut-and-paste step can be omitted. (Just being able to resolve >90% of LaTeX compilation issues automatically would be wonderful...)
Out of curiosity, are you sure that GPT did it correctly? If yes, is it because you were able to "spot check" it in a few places? Or have you used GPT enough that you trust it with a task like this? Or is this for some kind of internal use where a few small errors is unimportant, and you only need the broad strokes to be correct?
I have fairly little experience with GPT, so I'm not sure if there are some things that it always does correctly, and some things where it has to "guess".
@hallasurvivor Yes, yes, and yes. (There were some obvious checksums, for instance by computing the total number of speakers several different ways.)
@tao @hallasurvivor it is amusing (is it?) that there are distinct levels of validity for proofs of theorems and for output of computer softwares.
(A friend of mine had to compute eigenvalues of symmetric random matrices; he was surprised at my question of how he was certain of what Mathematica had computed. In fact, Mathematica had given non-real eigenvalues, of course with a very small imaginary part.)
@antoinechambertloir Oh, that is rather funny! How confident was your friend in the real part of the eigenvalues being correct?
@highergeometer it's like he even didn't notice the imaginary parts, so total confidence...
On the dangers of floating point computation leading to an almost wrong theorem in linear algebra, see that blog post of mine https://freedommathdance.blogspot.com/2021/04/growth-of-gaussian-pivoting-algorithm.html
@antoinechambertloir @highergeometer
in Gaussian elimination one needs pivoting, otherwise it's not even polynomial running time, in the classic bit complexity model.
Small imaginary parts in eigenvalues of real symmetric matrices are usual, when one does not use a procedure which takes the advance knowledge of realness into account.
@antoinechambertloir @highergeometer needless to say, one can easily run into precision problems with algorithms like this - and it's a typical bogus argument of Matlab fanboys: "engineers only care about machine precision floats"; I heard it from otherwise perfectly respectable numerical analysts such as Nick Trefenten.
I guess they invested so much effort in squeezing everything possible from machine precision floats that they prefer to be in denial about the sorry state of affairs in this department. (and keep all these computer algebra people they don't like away from the funding pie, too :-))
@dimpase @antoinechambertloir Supposing I was to need to do decent numerical work in the future, since I'm moving into industry, and may have some freedom to direct the choice of software, what would you recommend for modelling and so forth?
@highergeometer @dimpase I can imagine that industry has its own habits, which are impossible to completely ignore when you work with people. I have heard good things about R, though.
@antoinechambertloir @dimpase As I said, I might have some freedom to determine what tool I use, and learn. I'm not sure R will fit the bill, though! Thanks anyway.
@highergeometer @dimpase In any case, I summon @HydrePrever for his advice.
@antoinechambertloir @highergeometer @dimpase R, and most packages developed for R, are heavily oriented towards data analysis. So it really depends on what kind of "numerical work" you intend to do... For many things, python (with scipy and others - I'm not an user, and can't be more specific) seems the best way to go.