11–20 of 33 posts
He's a superb lecturer, and I owe him a debt of gratitude for his recorded classes.
I think it would be quiet interesting to crowdsource a math-to-english interpreter (a la 'explain shell' [0]) for math equations. [0] https://explainshell.com/
This is not possible, at least not without a very sophisticated AI. One thing that novices seem to not get about mathematics, especially those coming from programming languages, is that the syntax of mathematical formulae is not divorced from the natural language that surrounds it. Different authors use different symbols for the same concept or the same symbol with different meanings. That is, mathematical symbols ha…
The bigger problem is that there is often not a simple English description for math terms, whose meaning might involve understanding concepts that take books to explain.
For example, consider the simple sentence "Let x be an arbitrary vector". What is a vector? There is no clear answer to this question. Formally speaking a vector is simply an element of the set V where V is the underlying set for some vector space. You could try to say that V is an ordered pair of n real numbers, which is true up to isomorphism for finite dimensional vector spaces over the real numbers. But, x could also be the function f(x)=x^2, or the matrix [3, 4; 7, 1+i]. In some contexts, the translator might be able to tell from context what vector space is being worked in. But if the source is a general statement about vector spaces (even if made in support of a more concrete point), there is no way to explain it without explaining the concept of a vector space. To explain vector spaces one would need to, at a minimum, explain fields.
There is also a question of which description to use. For example, suppose we needed to define complex numbers. In some contexts, it is most natural to think of them as points on the xy-plane, which is simple enough (although does not give intuition above what multiplication means, which is arguably an essential component of the "true" meaning of complex numbers). In other contexts, it is more natural to think of them as matrices of the form [a -b; b a]. Attempting to show all the (equivelent) meanings would likely overwhelm the intended user of the service.
I think it would be quiet interesting to crowdsource a math-to-english interpreter (a la 'explain shell' [0]) for math equations. [0] https://explainshell.com/
This is not possible, at least not without a very sophisticated AI. One thing that novices seem to not get about mathematics, especially those coming from programming languages, is that the syntax of mathematical formulae is not divorced from the natural language that surrounds it. Different authors use different symbols for the same concept or the same symbol with different meanings. That is, mathematical symbols ha…
If you haven't heard of Shai Simonson I suggest checking out his ArsDigita University[0] lectures[1] (from which I studied Theory of Computation[2] back in late 2011). He's a superb lecturer, and I owe him a debt of gratitude for his recorded classes. [0]: http://www.aduni.org/ [1]: https://adunivids.neocities.org/ [2]: https://www.youtube.com/watch?v=Pt6GBVIifZA
The most amusing part about him was that he wore those tight biking shorts and shoes while he taught.
Here's an audio clip of Shai introducing Richard Stallman at a talk where Stallman gets pretty annoyed[0]
[0]: http://audio-video.gnu.org/audio/rms-speech-arsdigita2001.og...
I think it would be quiet interesting to crowdsource a math-to-english interpreter (a la 'explain shell' [0]) for math equations. [0] https://explainshell.com/
This is not possible, at least not without a very sophisticated AI. One thing that novices seem to not get about mathematics, especially those coming from programming languages, is that the syntax of mathematical formulae is not divorced from the natural language that surrounds it. Different authors use different symbols for the same concept or the same symbol with different meanings. That is, mathematical symbols ha…
And in machine learning idiots mix lambda for hyperparameters and eigenvalues....
Earlier quoted context omitted.
This is not possible, at least not without a very sophisticated AI. One thing that novices seem to not get about mathematics, especially those coming from programming languages, is that the syntax of mathematical formulae is not divorced from the natural language that surrounds it. Different authors use different symbols for the same concept or the same symbol with different meanings. That is, mathematical symbols ha…
Exactly. And in machine learning idiots mix lambda for hyperparameters and eigenvalues....
I've always loved math, but as things get more complex I stop thinking in math and start thinking in code.
Mathoverflow and math.stackexchange soft-questions tag has lots of mini-essays, e.g. https://mathoverflow.net/questions/143309/how-do-you-not-for...
and https://math.stackexchange.com/questions/617625/on-familiari...
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For proofs, books by Polya, Velleman, Hammack etc
Prof Baez' reading lists for math and physics: http://math.ucr.edu/home/baez/books.html
There's a few books on how to approach books and problems, e.g. don't strain on first seeing new material. Lara Alcock wrote 2 books on studying math which seem to have the same ToC, a lot of undergrad programs have materials on proofs and how to transition from high school problem solving: http://web.archive.org/web/20150319020039/http://www.maths.c... Mathoverflow and math.stackexchange soft-questions tag has lots…
http://www.staff.science.uu.nl/~gadda001/goodtheorist/ (sidebar for specific areas).
