I guess I should mention that although I do not count myself a mathematician, I was ABD (all-but-dissertation) in a math PhD program at Duke. I guess I was studying algebraic geometry or something? I remember Lie algebras being important. I dunno, it’s been 24 years.
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The post in that Math Overflow link that talks about Bill Gates’s math contribution was made by me, back in 2010.
I find it hilarious that it’s referenced on an IF forum this year! It’s like two of my worlds colliding. 
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Go an MMATH several years back. Adore number theory. Enjoy trying (and failing) to solve unsolved number theory problems. 
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physicists just use [proofs]…
I think this is more characteristic of experimental physicists and of engineers than of theoretical physicists. In some areas of biology, there is now a theoretical side which develops mathematical models and an experimental-engineering side which uses these models.
And even engineering has its theoreticians. During my undergraduate days, I read quite a bit of work by mostly French and Dutch image processing engineers who worked in a sub-discipline called mathematical morphology – lots of lattice theory, topology, and real analysis, and yes lots of proof and abstraction.
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Only a mathematician in the broadest possible sense of the word (just finished a course that among other things was supposed to teach some maths), but encountered a bit of maths drama today. My “course to prepare for science/maths/technology degree” course’s maths content didn’t even reach algebra. The courses I want to do next vary in the amount of maths expected, but a worrying number of them appear to expect students to have at least seen differential equations before, and I last saw one of those back when the proof of the Poincaré conjecture was new!
The courses would all admit me anyway because I’m classed as a “mature student”, but I guess I’m going to be (re-)learning a lot of maths this summer 
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Sorry for nitpicking, but the abbreviation for mathematics is math, not maths. I think I remember an IF where that kind of mistake was used.
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Not in the UK… Here I only use maths. In spanish, it’s “las matemáticas”, which is plural. So “maths” is correct in both those languages.
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The correct abbreviation in the USA and Canada is math.
The correct abbreviation in the UK and Australia is maths.
Other regions may vary as to which, if either, is an acceptable abbreviation.
Using either in the other location is considered a significant abbreviation mistake* that still allows the intention of the word to be understood, and was the likely impetus of the (presumably US, Canadian or other area that expects “math”) IF you are referencing.
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- My university would have docked me a mark for using “math”, but that would be a spelling mark, not a comprehension mark. (There were two marks available for spelling, punctuation, grammar and other “it’s right or it’s wrong” issues relating to clarity of communication. There were a lot more for subjective clarity of communication, and losing one of those would be, for example, if “mathematics” had been used when specifying a specific field within mathematics would have better communicated the point being made (an assessment that requires knowledge of the essay subject rather than spelling rules). Obviously, a Canadian university asking for the same coursework would have docked the spelling mark for “maths” if its mark scheme had a spelling category.
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In Australia, when I was in High School back in the '60s and later studying Electronic Engineering at Technical College (now TAFE), it was always Maths. Unfortunately as time has gone by, and we have more and more American spelling creeping in to our language, (partly caused by the Internet and the Spelling Checkers included in various Apps.) to the point where everything has blurred and either spelling seems to be accepted. I would imagine that this would be reflected in other countries too as we are constantly being told that language is fluid. Personally, I don’t like it and trying to prevent it would be like King Canute trying to stop the tide.
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Sorry and thanks to all three of you for correcting my mistake. I learned something new. 
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You mean King Knútr?
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Some people say “maths” is more correct because “mathematics” is borrowing a Greek plural (ta mathēmatika, like ta physika “physics”), but English has never been consistent in how it adapts those. Egyptologists get up in arms about “hieroglyphics” even though that’s also borrowing a Greek plural ta hieroglyphika.
Language is weird!
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Beside the Greek plural roots the English language really likes plural. Think of glasses, pants, sports, scissors. In German these are all singular.
Also I think (hiero)glyphics is really wrong. Those are glyphs in contemporary English, or?
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My understanding is that the more-correct non-academic usage these days has “hieroglyphs” as the noun and “hieroglyphic” as the adjective (e.g., “the inscription was written in hieroglyphs” vs. “I pored over the hieroglyphic text”). But I’m not sure whether that reflects how actual experts use the terms, and people tend to be pretty loose about it regardless.
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Yeah, “hieroglyphic” as the adjective, “hieroglyph” for a single sign, “hieroglyphs” for multiple. Never “hieroglyphics”. I don’t think the term really deserves as much vitriol as it gets in the field, but that’s how it is.
It’s actually a calque into Greek: hieros “sacred” + glyphos “carving” is imitating Egyptian mādaw nāṯar “words/signs of the divine”. So it’s a good word to use for them, it’s a direct translation of what the ancient Egyptians actually called their writing. But as a result the term is also applied to any other writing systems with a similar aesthetic (like “Anatolian hieroglyphs” and “Mayan hieroglyphs”), whether or not there was anything sacred about them. Which seems like a much bigger misapplication of terminology than using “hieroglyphics” as a generic plural!
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North Americans have only the energy for one math, but everyone else can do two or more.
Or a North American might claim they only need one, and the rest have to deal with the exchange rate.
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Although I am used to the American nickname “math”, I think the British version “maths” actually makes more sense, especially in the case of pure mathematics. It is not unusual in mathematics to see areas of study where the number of experts can be counted on one’s fingers and toes, if not on fingers alone.
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I’m in that weird place of “Good at maths by layman’s standards” but “bad at maths by professional standards”. Found everything in the standard US K-12 curriculum circa 1990-2005 easy and enjoy a lot of mathy things not covered in the classroom, but it took me three tries to pass Calc 2 and two attempts at the upper level undergraduate maths required for my Computer Science degree.
I really like number theory and geometry.
Some mathy things I’ve been wondering about lately include:
What some Johnson Solid duals look like.
If we view thedeltoidal icositetrahedron and deltoidal hexacontahedron as transformations of the octahedron and icosahedron where each face is replaced by three kites, what the results of applying this transformation to the other convex deltahedra.
If you start with an equatorial band of 7 rhombi,add bands of seven rhombi each above and below, and repeat untill you have 49 faces in seven bandsof seven, is it possible for all seven layers to be rhombi or do some have to be kites, and if all rhombi are possible, what the minimum number of distinct rhombi faces is.
What the polar graph of r^2 + theta^2 = a constant looks like.
What a coloring of the xy-plane would look like if you mapped the -1:1 range of the sine function to the integer range 0-255 and colored each point as follows:
R= sin(x)
B = sin(y)
G = sin(r)
Where R, G, and B are the red, green, and blue color channel values and r is the distance from the origin.
if you took the section of the parabola y=x^2 from (-2,4) to (2,4), joined copies and their endpoints such that the joints where smooth and concavity was the same on both sides of the joints, would the figure eventually return to its starting point, how many lobes/petals/whatever the appropriate term would be would it have, and how closely would it approximate the most similar epicycloid?
What the graphs of latitude=longitude, absolute value of latitude=absolute value of longitude, and co-latitude=longitude would look like. Both in the constant radius from the origin case and the unbound, radius from zero to infinity case.
What spherical coordinate graphs such as Rho =phi, rho=sin(phi), rho=sin(theta)+sin(phi) would like…
What an animation of r=sin(t/60theta) where t is the frame # would look like.
Whether a generalization of the construction of a Taijitu/YinYang that goes as follows
- start with a circle of diameter n.
- divide the circle with a concave down semicircle of diameter 1 and a concave up semicircle of diameter n-1.
- divide the circle with a concave down semicircle of diameter 2 and concave up semicircle of diameter n-2.
…
n. divide the circle with a concave down semicircle of diameter n-1 and concave up semicircle of diameter 1.
Always results in dividing the circle into n regions of equal area. I’ve done some area calculations that seem to check out, but working for all n tested doesn’t constitute a proof.
N^/2 - ((n-1)^2/2) + 1/2 =
N^2/2 +(N^2+2n+1)/2) + 1/2 =
)n^2 - (N^2 + 2n + 1) + 1)/2 =
(n^2 - N^2 + 2n -1 + 1)/2 =
2n/2 =
n
Does seem to imply the claw-like shapes created in steps 2 and n are always the square root of the total area(I’m ignoring the factor of pi and the factor of 4 from squaring diameters instead of radius since it’s the raito of areas that’s important here, not the exact values of hte areas).
And sorry if any of this doesn’t make much sense. It’s nearly 2AM as I type this, I’m not always sure on the proper way to word things in maths, and I’m at the disadvantage that much of this is highly visual and I’m blind and unaware of any good options for generating visual aids to explainn my ideas, much less for making tactile representations to confirm/deny what I’m visualizing in my mind’s eye(I went blind in my mid-20s and retain a strong ability for visualization at 37, but at best I can predict what something might look like, at worst, I’m clueless.
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This is probably not exactly what you’re looking for, but my wife has made 3D printable models of all of the Catalan solids: Catalog of 3D-Printable Catalan Solids - mathgrrl
Caveat: the website is perhaps not so accessible.
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Starting from Phil’s wife’s website I surfed a bit and found several interesting things for us math-geeks:
- the book “Taking Sudoku seriously”, co-authored by her
- the term “recreational mathematics”
- the PROSE awards in the math category, viewable per year
Winners - PROSE Awards
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