⏚ Antoine Chambert-LoirNever too late to #mathober.
Day 1 - Spindle.
Be it for fun, or by rage,
Sophia will lead forever
The dance of the infidels.
Day 2 - Cubic.
Cubic forms are much rounder
than what their name tells you.
Still they hold 27 lines.
Day 4 - Dissection
Euclides knew how you can dissect a square into a triangle, but
you can rarely dissect a pyramid into a cube, as Dehn explained.
Anyway, Sydler tells you when you can.
Day 5 - Flat
Would you wish to descend along a flat mountain?
Nevertheless, Grothendieck descended objects from flat morphisms,
and even that was hard work.
Day 6 - Hyperbolic
My first journey in a hyperbolic world
was led by the painter M.C. Escher,
and driven by Caml.
Day 7 - Harmonic
The sound of a drum,
or the buzz of an electron,
o fearful symmetry.
Day 8 - Error
Mathematicians make so many errors
that they invented a whole field
to study them.
Day 9 - Identity
Mathematicians insist on the existence of identities,
they teach remarkable ones,
yet some mathematicians have to conceal theirs.
Day 10 - Similar
Mathematicians use all sorts of similarities,
from congruences of triangles to homotopy types,
and abuse of their self similarities.
Day 11 - Fundamental
Fundamental lemmas, groups,
fundamental theorem of algebra,
fundamenta fundamentatum et omnia fundamenta.
Day 12 - Category
Some people argue using Baire category,
some other use bare categories,
it's all a question of context.
Day 13 - Theory
Ring theory, Galois theory, Information theory…
Mathematicians have theories for everything,
even a theory of theories.
Day 14 - Paradox
Banach-Tarski, Russell, Simpson…
isn't it paradoxical
that mathematics is full of paradoxes?
Day 15 - Tiling
Beautifully regular or puzzlingly aperiodic,
Tilings make you feel
The Harmony of the world.
Day 16 - Capsule
I didn't know a capsule could be a mathematical object,
yet the picture made me think at the aspirine I needed to read the word
spheropolyhedron.
Day 17 - Vault
Some stairs in Musée du Louvre let you admire beautiful mathematical vaults.
That makes me muse about the architecture of mathematics:
Where would you say its keystones are?
Day 18 - Annulus
Can you imagine that the stability of the solar system would depend
On a problem that puzzled Henri Poincaré for a long time, until Birkhoff solved it?
— Do area preserving diffeomorphisms of the annulus have fixed points?
Day 19 - Inverse
With a little bit of reflection,
our inverse image in a mirror,
is an algebraic inversion.
So is the inverse of a number,
or even of a proposition.
But not of zero, that's an horror.
Day 20 - Moiré
These visual interference patterns
are beautiful on silk, but unwanted on print.
They also help you make precise measures.
Day 21 - Limaçon
Pascal's limaçon is not a slug,
but a particular case of roulette curve.
Dürer called it the spider curve…
Day 22 - Reciprocity
Not only a stunning mathematical result about prime numbers,
Gauss's Theorema Aureum
seems to lie at the crossroads of all of mathematics.
Day 23 - Braid
Artin's braids are just like hair braids, a weave of threads,
just more difficult to untangle,
if not impossible, as Dehornoy showed.
Day 24 - Antipodal
The Polish mathematician Karol Borsuk has shown that two antipodal places on earth
Share the same temperature and air pressure.
But there is much more to it, from combinatorics to geometry and functional analysis.
Day 25 - Packing
Apollonius and Kepler packed number theory, geometry and algebra
with beautiful problems
for the likes of Peter, Tom, and Marina…
Day 26 - Cell
Schubert cells, Whitehead cells, Fox-Artin's wild cells…
Mathematics is a living organism,
it even has amoebas…
Day 27 - Hull
Each time a convex hull
appears in a field of mathematics,
a star begins to shine in heaven.
Day 28 - Singularity
Whatever Hironaka allows you to do,
I pray you will never ever resolve
Your own singularity.
Day 29 - Catastrophe
Is it such a catastrophe
if Professor Thom's theory
lead to that nonsensicality?
Day 30 - Jitter
I view jitter bug
as the revenge of life
against the overall digitization.
Day 31 - Unity
To emphasize its unity,
Bourbaki wrote mathématique as a singular noun
— while letting spread some absurd idea of a hierarchy.
This is the end of this #mathober2022 journey.
I will aggregate this thread on my blog, sooner on later, here is the link already.
https://freedommathdance.blogspot.com/2022/11/mathober2022.html
Thank you so much to @fractalkitty to have come up with this idea!
Y'all, please have a look to her drawings and haikus :
https://fractalkitty.com/2022/10/01/mathober2022-sketches/
See you next year for #mathober2023 !
Fractal Kitty@antoinechambertloir thank you!!