Timeline for What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?
Current License: CC BY-SA 3.0
30 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2017 at 15:14 | answer | added | Francois Ziegler | timeline score: 14 | |
| Oct 29, 2014 at 3:32 | history | protected | François G. Dorais | ||
| Oct 29, 2014 at 3:21 | answer | added | Nathan | timeline score: 6 | |
| Oct 29, 2014 at 0:28 | answer | added | Gerry Myerson | timeline score: 6 | |
| Oct 28, 2014 at 22:38 | answer | added | Lennart Meier | timeline score: 9 | |
| Aug 11, 2014 at 9:43 | comment | added | Mikhail Katz | @BenCrowell, the notation ${}_{\ulcorner\!\urcorner}$ appears in Leibniz but not in Fermat. For a discussion of this see ams.org/notices/201307/rnoti-p886.pdf | |
| Jul 12, 2014 at 23:58 | comment | added | user21349 | related: math.stackexchange.com/questions/865559/… | |
| Jul 12, 2014 at 16:29 | review | Close votes | |||
| Jul 12, 2014 at 21:36 | |||||
| Jul 12, 2014 at 16:05 | answer | added | user21349 | timeline score: 22 | |
| Jul 12, 2014 at 14:45 | comment | added | user21349 | @AndrejBauer: but when you say that dy/dx refers to the standard part, you're dragging in Robinson's non-standard analysis Check out the link in my earlier comment, p. 10. Fermat and Leibniz had a notation, ${}_{\ulcorner\!\urcorner}$, and a term, "adequality," that expressed essentially the same notion as Robinson's standard part (subject to the limitations of the development of mathematics at that time). The idea is much more generic than NSA. | |
| Jul 12, 2014 at 11:34 | comment | added | Andrej Bauer | @ZhenLin: the context in this case should be local, i.e., we require an abstraction so that we can write $\int\int x y \,dx\,dy = \lambda x y \,.\, \frac{1}{4} x^2 y^2$ or some such. For consider the case $x \cdot \int \int x y \, dx \, dy$, what is the answer, and should it be the same as the answer to $x \cdot \int \int z y \, dz \, dy$? You can't resolve the mess until you introduce proper abstractions and bound variables. | |
| Jul 12, 2014 at 11:11 | comment | added | Benjamin Steinberg | How goes the program to call a ring without identity a rng and a semiring (ring without negatives) a rng. | |
| Jul 12, 2014 at 8:01 | comment | added | Zhen Lin | What's wrong with writing $x$ for a projection? I suppose you might prefer $x, y \vdash x$, but contexts are supposed to be, well, contextual. | |
| Jul 12, 2014 at 7:38 | comment | added | Andrej Bauer | I don't really want to get into a flame war, but when you say that $\frac{dy}{dx}$ refers to the standard part, you're dragging in Robinson's non-standard analysis, which may not be everyone's favorite, especially physicists might prefer nilpotent infinitesimals. Regarding $x$ being the identity function: how about $\int \int x y \, dx \, dy$, do I get two identity functions $x$ and $y$, which magically are not the same? Or are they now projections. If they are projections, perhaps we could use sane notation instead, rather than keep putting kludges on top of kludges. Ok, that's a flame war ;) | |
| Jul 12, 2014 at 3:35 | comment | added | Zo the Relativist | @DonuArapura: I'd argue that anyone who uses the coordinate-free notation has never had to actually compute a tensor. The notation for contractions alone is just nightmarish in them. Abstract indices are absolutely the only way to go, and they are much more superficially similar to Einstein notation. | |
| Jul 12, 2014 at 2:10 | answer | added | Francois Ziegler | timeline score: 46 | |
| Jul 12, 2014 at 1:59 | comment | added | user21349 | @DonuArapura: Roger Penrose introduced abstract index notation, which combines the expressiveness of index notation with the coordinate independence of coordinate-free notation. | |
| Jul 11, 2014 at 21:29 | comment | added | user21349 | @AndrejBauer: There is nothing wrong with dy/dx; you just have to understand the implication that it's referring to the standard part. This was in fact understood pretty well in Leibniz's lifetime: arxiv.org/abs/1202.4153 . In your example of $\int x^2dx=x^3/3+C$, you can think of $x$ as the identity function rather than as a bound variable, and it makes perfect sense. There is nothing broken about the Leibniz notation. The Leibniz notation has many wonderful advantages, and that's why it caught on quickly and has been used universally ever since. | |
| Jul 11, 2014 at 20:06 | answer | added | Benjamin Steinberg | timeline score: 29 | |
| Jul 11, 2014 at 18:28 | comment | added | Donu Arapura | This is a bit off topic, but Einstein introduced the summation convention as a shorthand for doing long calculations with tensors. A lot of mathematicians working with the stuff nowadays use cleaner coordinate free notation. So maybe there is hope! | |
| Jul 11, 2014 at 18:07 | comment | added | Andrej Bauer | I am referring to $\frac{dy}{dx}$ and the fact that it's legal to write $\int x^2 dx = x^3/3 + C$ (which exposes the bound variable $x$), and the fact that ${{\Gamma_{ij}}^{kl}}_{mn}$ means something. | |
| Jul 11, 2014 at 17:45 | comment | added | goblin GONE | @AndrejBauer, what notation are you referring to? | |
| Jul 11, 2014 at 17:29 | comment | added | The Masked Avenger | Sorry, blurry vision had me thinking you were asking specifically about programmers. | |
| Jul 11, 2014 at 15:33 | answer | added | Donu Arapura | timeline score: 12 | |
| Jul 11, 2014 at 13:21 | answer | added | Joel David Hamkins | timeline score: 35 | |
| Jul 11, 2014 at 10:09 | comment | added | The Masked Avenger | Ken Iverson and Donald Knuth, partly by building the discipline and waiting for it to become part of mathematics. | |
| Jul 11, 2014 at 8:54 | comment | added | Andrej Bauer | Given that we still use 17th century broken notation in analysis, and people actually think the summation conventions are ok, I wouldn't harbor any hopes that things will get better. | |
| Jul 11, 2014 at 8:48 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jul 11, 2014 at 8:44 | history | edited | goblin GONE | CC BY-SA 3.0 |
added 8 characters in body
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| Jul 11, 2014 at 8:38 | history | asked | goblin GONE | CC BY-SA 3.0 |