Re: [math-fun] Who has written a clear summary of what research mathematicians do?
Scott Kim wrote--
I think it's an occupational hazard of being an expert in any field, not just math, that it can be hard to explain what you do to an outsider. Nonetheless I think it's important to do, and not just for outsiders, but also for people inside the field. At least it's important to me — the dearth of mathematicians talking about what mathematics is I find intolerable, and makes me distrustful of mathematics as a field. Ted Nelson's _Computer Lib_ (1974) for me was a taste of what the good thing can be:
An enthusiastic insider in a field who is also a skeptical outsider without missing a beat. There's the public-facing importance of that (especially with something commercial like computers), but also I like the way I oriented myself after reading that book. Stewart Brand, Martin Gardner, Aubrey de Grey, Vi Hart. https://youtu.be/v-pyuaThp-c "Doodling in Math Class: Connecting Dots" (talk about not missing beats) --Steve
Totally with you on Ted Nelson, Stewart Brand, Martin Gardner and Vi Hart, who I know/knew well. Hadn't heard of Aubrey de Grey, enjoyed hearing his provocative rant about de-inevitabilizing aging. Another hero in this clan, for me, is The Domain of Science's Map of Mathematics <https://www.youtube.com/watch?v=OmJ-4B-mS-Y>, which implicitly characterizes what math is by diagramming the field's evolution and structure. And 4 million YouTube views show there is a hunger for this. I'm a funny mixture of firebrand and overly polite, so citing these iconoclasts is inspiring. So I'll stop being too polite and be proud of taking a radical stance. My stance is that mathematics suffers from self-inflicted poor public relations, and that this is not all inevitable or desirable. I want to spread the news that: - Mathematics is more than (just) calculation. Yeah that's old hat to mathematicians, but it persists as public misunderstanding. - Mathematics is about understanding patterns in the digital universe (meaning the universe of things that can be wholly described in symbols). Eugenia Cheng is all over this idea; I've hardly heard it expressed by others. I think the digital universe is a precursor idea to defining mathematics, and encompasses a few things outside the bounds of normal mathematics, such as taxonomies, computer science, and symbolic systems. - Mathematics is the language / tool / body of knowledge we use when we need to be precise (when there are big consequences for being slightly wrong), deal with complexity (because patterns are hard to see without abstraction), or deal with digital systems (like DNA, physics, or computers). This is a definition that deals with the edge of what is or isn't mathematics; most definitions I've seen do not help determine this distinction. - Research mathematicians are advance scouts who proactively look for patterns before we need them — a wildly adventurous thing to do. Thus the field of mathematics is a wildly unpruned bush, a bit like science, but far less tethered to modeling reality (though that influence remains a factor). - Research mathematicians (strongly) favor abstraction and generality, but that ain't the only kind of math. There's a big spectrum from concrete math (recreational math tends this direction) to abstract math (e.g. category theory). - These big ideas can and should be clearly taught to kids by (for instance), having them analyze and create games and puzzles, which are small formal systems. Well, that's my particular angle. On Thu, Aug 15, 2019 at 8:45 PM Steve Witham <sw@tiac.net> wrote:
Scott Kim wrote--
I think it's an occupational hazard of being an expert in any field, not just math, that it can be hard to explain what you do to an outsider. Nonetheless I think it's important to do, and not just for outsiders, but also for people inside the field. At least it's important to me — the dearth of mathematicians talking about what mathematics is I find intolerable, and makes me distrustful of mathematics as a field. Ted Nelson's _Computer Lib_ (1974) for me was a taste of what the good thing can be:
An enthusiastic insider in a field who is also a skeptical outsider without missing a beat.
There's the public-facing importance of that (especially with something commercial like computers), but also I like the way I oriented myself after reading that book.
Stewart Brand, Martin Gardner, Aubrey de Grey,
Vi Hart. https://youtu.be/v-pyuaThp-c "Doodling in Math Class: Connecting Dots" (talk about not missing beats)
--Steve
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Hello Math-Fun, Fractions have always fascinated me and I was recently wondering: what about a finite subset of them, whose elements might be counted? So I started with this: « Fractions having no duplicate digit », with the examples 123/456, or 20983/1 -- but not 10657/2314 because of the duplicated "1". Two questions: a) how many such "no-dup fractions" are there in the subset? b) how could one start a seq for the OEIS with those? Question (a) is far too complicated for me because of the huge amount of such "no-dup fractions"; Question (b): Suppose we have them all, how could we now sort the "no-dup frations" from the smallest one (I guess the smallest one is 1/987654320) to the biggest one (I guess 987654320/1)? This problem arises when we bump into frations which are no-dup BUT equivalent: 1/2, 134/268, 15/30, 78/156,... In such a subset of "equivalent no-dup fractions" there is no smallest or biggest fraction, there is no order, they are all "the same". Except if we decide to take into account (for this subset only) the numerators -- and to sort the said subset with them. We would then start for instance the subset of "equivalent to 1/2 no-dup fractions" with: 1/2, 2/4, 3/6, 4/8, 5/10, 6/12, 7/14, 8/16, 9/18, 13/26, 14/28, 15/30, 16/32, 17/34, 18/36, 19/38, 23/46, 26/52, etc. This rule allows us to sort all those no-dup fractions with this simple (?) method: - find all a/b no-dup fractions - compute all a/b to the 10th decimal and sort those computations - if two ore more a/b computations have the same result, sort according to "a" (smallest "a" first, then second "a", etc.) Now that we have a complete list of no-dup fractions starting with the smallest one and ending with the biggest one (with sorted "plateaus" all over), the final touch will consists in building a sound OEIS seq "S". I propose to use two successive terms of S to encode the fraction a/b with a(n) = "a" and a(n+1) = "-b". This minus sign before "b" solves it all (and reminds us that there is a fraction bar after a(n) separating the numerator "a" from the denominator |b| of the encoded no-dup fraction. Is this an interesting idea? At least, how many no-dup fractions are possible (in base 10)? Best, É.
participants (3)
-
Scott Kim -
Steve Witham -
Éric Angelini