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SunJester @sun-jester.bsky.social · 16/09/2026

This thursday it'll be 200 years after Riemann's birth. The Riemann integral is a way to define what the definite integral of a function is. The area under a curve can be approximated by many small vertical rectangles! #MathSky #200YearsRiemann #HistSky

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SunJester @sun-jester.bsky.social · 15/09/2026

This thursday it'll be 200 years after Riemann's birth. Riemannian geometry generalised the notions of curvature and distance that Gauss had developed for smooth surfaces to manifolds of arbitrary dimension. This is also the first mention of >4 dimensions* #MathSky #200YearsRiemann #HistSky

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SunJester @sun-jester.bsky.social · 14/09/2026

This thursday it'll be 200 years after Riemann's birth. Riemann surfaces are 1-dimensional connected complex manifolds, i.e. 2-dim connected real manifolds with holomorphic transition maps. He introduced these to study multivalued functions over C, such as sqrt #MathSky #200YearsRiemann #HistSky

The Riemann surface of the square root function

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SunJester @sun-jester.bsky.social · 25/08/2026

x^2 + y^2 = 1 defines a circle, but as n->oo the equation |x|^n + |y|^n = 1 looks more and more like a square This is because for |y| < 1 we have |y|^n -> 0, so that |x|^n has to approach 1, i.e. |x| -> 1, which gives the vertical sides (the horizontal sides are the same) #mathsky #mathematics

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SunJester @sun-jester.bsky.social · 22/08/2026

Evangelion (full title is Neon Genesis Evangelion) is an anime. The main antagonists are angels. One of them, called Ramiel, is just a floating octahedron (The gif below is from the remake movies, but whatever)

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SunJester @sun-jester.bsky.social · 14/08/2026

Wonder what the consensus is on Sapphire and Steel My personal views on the five serials: 1: pretty good, if a little clunky 2: genuinely good 3: also pretty good, some nice scary stuff 4: boring and bad 5: easily the best one 6: intriguing, too bad the series got cancelled #scifi #sciencefiction

Cover of Sapphire and Steel showing lead actors David McCallum and Joanna Lumley

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SunJester @sun-jester.bsky.social · 14/08/2026

Pretty funny sign I saw in Spain for the #eclipse I’d think that driving with eclipse glasses on is obviously a bad idea, but I guess not

Sign saying “no conducir con gafas de eclipse”, Spanish for “don’t drive with
eclipse glasses”

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SunJester @sun-jester.bsky.social · 13/08/2026

The #eclipse yesterday was really spectacular. It was my first ever total eclipse and it blew all my expectations out of the water The fact I was almost alone just made it even more spectacular Seriously, if you ever have the chance to see one, do it

The solar eclipse, seen from Alhama de Aragon in Spain, 12th of August 2026

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SunJester @sun-jester.bsky.social · 10/08/2026

Did James Joyce predict the 6-7 meme? New evidence supports this seemingly far-fetched theory #booksky #sixseven

Excerpt from Ulysses, the phrase “six or seven times” is highlighted

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SunJester @sun-jester.bsky.social · 07/08/2026

Just finished Ulysses … Wow, what a book Even with guides, I understood maybe 10% of it, but still. It’s an absolute breathtaking achievement. It took Joyce 7 years to write it and you can tell I’ve never read anything like it and likely never will again (1/2) #books #booksky #literature

The cover of the version of Ulysses I read. Go read Ulysses, it’s worth it

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SunJester @sun-jester.bsky.social · 31/07/2026

Still not really sure how to feel about this tbh… Like, on the one hand, it is really cool that another famous problem has been solved. On the other hand, as someone hoping to at least do a phd in math, I find this quite terrifying... (1/n) #mathsky #mathematics #math #maths

levent’s tweet announcing that the Jacobian conjecture is false

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SunJester @sun-jester.bsky.social · 23/06/2026

Recently learned of these pretty cool #geometry theorems: on the left we have proposition III.22 from Euclid's Elements and on the right we have Pitot's theorem, from the 180th century #math #mathsky #maths #mathematics

Euclid prop. III.22: A convex quadrilateral ABCD is inscribed inside a circle if and only if Â + B̂ = Ĉ + D̂.

Pitot's theorem: A convex quadrilateral ABCD is circumscribed around a circle if and only if |AB| + |CD| = |AD| + |BC|.

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SunJester @sun-jester.bsky.social · 03/06/2026

I'm honestly kinda proud of how this #cover turned out, mainly cause I didn't take that picture to be a cover #writingcommunity #art #photography btw, you get a cookie if you can guess what mountain that is in the background ;)

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SunJester @sun-jester.bsky.social · 31/05/2026

Today's #walk didn't go quite as planned...

A path I wanted to walk across was completely flooded...

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SunJester @sun-jester.bsky.social · 19/05/2026

It's amazing how basically nothing happens in Jeanne Dielman 23, quai du Commerce 1080 Bruxelles, yet it somehow isn't boring How did Chantal Akerman do that!? #filmsky #movies

Poster of Jeanne Dielman 23, quai du Commerce 1080 Bruxelles

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SunJester @sun-jester.bsky.social · 11/05/2026

I've moved my two short stories over to #royalroad, if I write some more they'll be added to that collection #writingcommunity #shortstory www.royalroad.com/fiction/1672...

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SunJester @sun-jester.bsky.social · 01/05/2026

~Inaccesible Treasure~ #poem #poetry #writingcommunity For more bad poems, check out www.wattpad.com/story/393302...

~Inaccesible Treasure~

I thought I was immune to greed,
like that temptation did not affect me.
Without any gems I would grow old,
I barely knew silver from gold.

Then I got a glimpse of a hold so fine,
like nothing before it had to be mine.
Kept coming back again and again,
I had never ever felt like then.

Sparkling like a thousand falling stars,
precious like a million golden bars.
Never had such things graced my sight,
I dreamt of it every night.

Years did pass, I got courage and went
for the shiny stones forced my hand.
Little did I know when I came close
it would be a thorny rose.

It was the inaccessible treasure.
Not meant for me or anyone.
Inaccessible treasure
Why must it be the one?

Why, oh why can’t it be mine?
What did I do wrong this time?
Please please please please give it to me,
Guess I’m not so free from greed.

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SunJester @sun-jester.bsky.social · 28/03/2026

Today is Alexander Grothendieck's birthday! He's probably the most important mathematician of the 20th century, but sadly enough almost completely unknown to the general public #math #maths #mathematics #mathsky #scisky #sciencesky #borntoday

Alexander Grothendieck (1928 - 2014) in 1970

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SunJester @sun-jester.bsky.social · 23/03/2026

Now those are some curly letters from the gallery of maps in #rome #typography #cartography

Text in the Vatican gallery of maps which is very curly

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SunJester @sun-jester.bsky.social · 23/03/2026

This is a dance off! If you see this, QRP with a dance or you will be eliminated!

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SunJester @sun-jester.bsky.social · 23/02/2026

Can we just take a few seconds to appreciate the pacing in Alien? Seriously, how is it nearly 2 hours long? I swear I've seen 10-minute youtube videos that felt longer than it #filmsky

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SunJester @sun-jester.bsky.social · 28/01/2026

Quick explanation of what it feels like to learn more advanced #mathematics. Specifically, how do you answer the question "How many intersections do two algebraic varieties have?" You could probably do this with any math subject tbh... #mathsky #maths #scisky

Meme of more and more technical ways to count the amount of intersections of two varieties.

1. "Just count the points"
2. "Don't forget this guy" Take exponents into account
3. "Or the length of this one" You have to the compute the length of some random module
4. "Or this" Chain complexes and derived functors

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SunJester @sun-jester.bsky.social · 06/10/2025

For some reason the additive formula for binomial coefficients is often proven using the formulas for the binomial coefficients, even though there is a way better combinatorial proof. Just remember that n choose k is how many ways there are to choose k balls out of n. #math #mathematics #mathsky

Combinatorial proof of the addition formula for binomial coefficients

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SunJester @sun-jester.bsky.social · 30/08/2025

#AugustOfGroups: every day of August I'll post all groups whose order is the number of that day. Today August 30th. There are four groups of order 30: Z/30Z, D15, (Z/5Z) × D3 and (Z/3Z) × D5. I'm a particular fan of the symmetry in those last two #math #maths #mathematics #mathsky

(Z/5Z) × D3 is the group of rotational symmetries of a pentagon times all symmetries of a triangle.

(Z/3Z) × D5 is the group of rotational symmetries of a triangle times all symmetries of a pentagon.

In other words: in the above picture you're allowed to transform one in any (symmetric) way you want, but can only rotate the other.

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SunJester @sun-jester.bsky.social · 18/08/2025

#AugustOfGroups: every day of August I'll post all groups whose order is the number of that day. Today August 18th. There are 5 groups of order 18: Z/18Z, (Z/3Z) × (Z/6Z), (Z/3Z) × S3, D9, (Z/3Z)³ ⋊ (Z/2Z) The latter has a nice matrix representation #math #maths #mathematics #mathsky

Z/3Z ⋊ Z/2Z where Z/2Z acts via inversion, is the only truly new group. IIt has this nice matrix representation.

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SunJester @sun-jester.bsky.social · 17/08/2025

Finally, the Pauli group is the group consisting of the Pauli matrices, multiplied by ±1 and ±i. As the name implies, this group is useful in quantum mechanics (6/6) #math #maths #mathematics #mathsky

The Pauli matrices sigma_x, sigma_y and sigma_z. These are used to describe spin in (non-relativistic) quantum mechanics.

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SunJester @sun-jester.bsky.social · 17/08/2025

Then there are two more interesting ones: (Z/4Z) ⋉ (Z/4Z) and (Z/4Z) ⋉ V4. Whereas in G × H (he product), the groups G and H don't really interact, in G ⋉ H (the semidirect product) they do (see image). Both of the top pairs only have a single non-trivial semidirect product. (3/6)

In the usual product group, G and H don't really interact. In the semidirect product, there is some homomorphism phi from H to Aut(G) which is used to make the groups 'link together' in a way.

Given two groups G, H there are usually many phi's to choose from, but for the two pairs at the top you can either take phi trivial (everything gets sent to the neutral element) or choose a single non-trivial one.

Excercise: what non-trivial automorphism phi is used?

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SunJester @sun-jester.bsky.social · 12/08/2025

The dicyclic group Dic3 consists of the three roots of unity in the complex plane together with the quaternion j, and then all possible products More generally, Dicn is the group generated by the nth roots of unity and the quaternion j. (3/3) #math #maths #mathematics #mathsky

The three cube roots of unity (blue) on the complex plane (grey) together with the quaternion j. Note that the full group would require 4 dimensions to draw

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SunJester @sun-jester.bsky.social · 12/08/2025

Given a permutation s of {1, 2, ..., n}, we have an inversion if i < j, but s(j) < s(i). If the amount of inversions of s is even, it's called an 'even permutation'. An is the group of even permutations. Beyond that: A4 is also the group of rotational symmetries of a reguler tetrahedron (2/3)

A regular tetrahedron can be rotated along several axes, like the two shown here. One passes through the midpoints of two edges, the other through a vertex and the midpoint of the opposing side

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SunJester @sun-jester.bsky.social · 09/08/2025

#AugustOfGroups: every day of August I'll post all groups whose order is the number of that day. Today August 9th. There are 2 of order 9: Z/9Z and (Z/3Z)² (Z/3Z)² is the rotational symmetries of a pair of equilateral triangles (each turns on its own) #math #maths #mathematics #mathsky

(Z/3Z)² is the group of rotational symmetries of a pair of equilateral triangles. (1,0) corresponds to rotating the yellow one 120° to the right, (2,0) rotates the yellow one 120° to the left. (0,1) rotates the right 120° to the right and (0,2) to the left.

For example: (1,2) means 'rotate the yellow triangle 120° to the right and the green one 120° to the left'

Z/9Z is the group of rotational symmetries of a regular nonagon

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SunJester @sun-jester.bsky.social · 08/08/2025

The first two are nothing new. (Z/2Z)³ is the symmetry of three pairs of points, D4 is the group of symmetries of a square. Q is the group of the quaternions i,j and k (hence the name). The last one has geomertic interpretations, but these are quite hard (2/2) #math #maths #mathematics #mathsky

Quaternion group is the symmetry group of this highly compliacted object (see https://archive.bridgesmathart.org/2014/bridges2014-143.pdf)

The defining relationship for the quaternion group Q.

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SunJester @sun-jester.bsky.social · 08/08/2025

#AugustOfGroups: every day of August I'll post all groups whose order is the number of that day. Today August 8th, the first actually interesting day. There are 5 groups of order 8: Z/8Z, the group (Z/2Z) × (Z/4Z), (Z/2Z)³, the dihedral group D4 and the quaternion group Q. (1/2)

(Z/2Z)³ is the symmetry group of these six points: (1,0,0) swaps the two blue ones, (0,1,0) the red ones and (0,0,1) the orange ones.

D4 is the symmetry group of a square. Note that there are permutations of the green, blue, yellow and purple point that do NOT appear. This shows that D4 and S4 are distinct!

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SunJester @sun-jester.bsky.social · 06/08/2025

S3 is the symmetry group of permutations of three elements. D3 is the symmetry group of an equilateral triangle. Amazingly enough, these two are the same! Symbolically, S3 ≅ D3 (2/2) #math #maths #mathematics #mathsky

Cayley table of S3 and D3. Note that we could give r^2, rm and r^2m distinct names if we wanted to, but that would only make things more complex.

This group is completely defined by asserting that r^3 = e, m^2 =e and mr = r^2m. All other identities follow (this is an example of a 'group presentation')

The group of symmetries of an equilateral triangle (the colors are only there so you can see the difference). r corresponds to a 120° degree rotation to the right, m to a reflection across the vertical line through the center.

Note that every single permutation of the blue, green and yellow dots appears, this is a visual proof that S3 ≅ D3.

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SunJester @sun-jester.bsky.social · 06/08/2025

#AugustOfGroups: every day of August I'll post all groups whose order is the number of that day. Today August 6th. There are two groups of order 6: Z/6Z and S3 the symmetric group of 3 elements (our first non-abelian group!) #math #maths #mathematics #mathsky (1/2)

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SunJester @sun-jester.bsky.social · 05/08/2025

#AugustOfGroups: every day of August I'll post all groups whose order is the number of that day. Today August 5th. There is again only 1 group of order 5: Z/5Z, the group of rotational symmetries of a pentagon (By now the pattern in Z/nZ is clear) #math #maths #mathematics #mathsky

Z/5Z gives the group of rotational symmetries of a regular pentagon, 1 rotates to the right by 72°, 2 to the right by 144°, 3 to the left by 144° and 4 to the left by 72°

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SunJester @sun-jester.bsky.social · 04/08/2025

Second: the Klein four-group V, our first non-cyclic group! V is also (Z/2Z)² and is the group of symmetries of a (non-square) rectangle. (2/2) #math #maths #mathematics #mathsky

The Klein four group is the symetry group of a rectangle, a is a reflection across the vertical, b across the horizontal and c is a 180° rotation.

Now a^2 = b^2 = c^2 = e and the product of any two is the third.

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SunJester @sun-jester.bsky.social · 04/08/2025

#AugustOfGroups: every day of August I'll post all groups whose order is the number of that day. Today August 4th, the first interesting day. There are two groups of order four: first Z/4Z (the integers modulo 4). This is the group of rotational symmetries of a square (1/2)

Z/4Z is the group of rotational symmetries of a square, 1 is a 90° rotation to the right, 2 is a 180° rotation and 3 is a 90° rotation to the left, so

1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 0
2 + 2 = 0, 2 + 3 = 1
3 + 3 = 2

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SunJester @sun-jester.bsky.social · 03/08/2025

#AugustOfGroups 3: every day of August I'll post all groups with order the number of that day there is only one group of order 3 (I swear it gets more interesting later on): Z/3Z, the integers modulo 3 Visually: the group of rotational symmetries of a triangle #math #maths #mathematics #mathsky

Z/3Z as group of rotational symmetries of an equilateral triangle: 1 corresponds to turning 120° to the right, 2 corresponds to a 120° turn to the left.
Rotating 120° to the right twice is the same as rotating 120° to the left, rotating 120° to the right thrice is the same as doing nothing. In other words: 1 + 1 = 2, 1 + 1 + 1 = 0

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SunJester @sun-jester.bsky.social · 02/08/2025

The Cayley table of the trivial group is a bit silly, but here it is anyway

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SunJester @sun-jester.bsky.social · 02/08/2025

#AugustOfGroups: every day of August I'll post all groups whose order is the number of that day. August 2nd. there is only one group of order 2: Z/2Z, the integers modulo 2 #math #maths #mathematics #mathsky

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SunJester @sun-jester.bsky.social · 24/07/2025

The determinant is often seen as a rather strange thing to define, the formula coming seemingly out of nowhere. In fact, it can be derived by simply asserting it has the following three properties: #math #mathematics #mathsky #matrices #determinant

Property 1: swapping two columns of a matrix switches the sign of the determinant.

Property 2: the determinant, when seen as a function on the columns, is multilinear.

Property 3: the determinant of the identity matrix is 1. This is just a normalisation.

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SunJester @sun-jester.bsky.social · 30/06/2025

~Poem #26 ~ All Bells Can Ding. Even Flying Ghosts Hear. I Jest, Knowledge Leaves More No’s. Only People Question Rights, Sometimes. Time Used Voraciously, Wastefully. Xericicity Yields Zealotry. #poem #poetry #writingcommunity #writing For more poems, please check out A Bridge Between Two Cs

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SunJester @sun-jester.bsky.social · 19/06/2025

I thought it'd be nice to have a #poem, where the roles of the title and the actual texts have switched #writing #WritingCommunity #poetry If you like it, you can read some more of my poems in my collection [A Bridge Between Two Cs](www.wattpad.com/story/393302...)

Poem titled ~To prepare the reader. Let them know what they’re in for, before the poem starts~

What's a Title For?

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SunJester @sun-jester.bsky.social · 14/06/2025

Cauchy's theorem is easily one of my favourite results from #math (why do you think it's my banner image?), it's almost unbelievable: The integral of a derivable function over a closed curve in the complex plane is always* zero! *under some (weak) conditions #mathsky #mathematics

Cauchy's theorem, drawn in sand of the Sahara

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SunJester @sun-jester.bsky.social · 12/06/2025

A simple #animation I made in #geogebra to illustrate the trigonometric functions. Sine is blue, cosine red, tangent orange and cotangent green #math #mathsky #mathematics

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SunJester @sun-jester.bsky.social · 07/06/2025

It is one of my favourite results from #mathematics and used in so many situations it's absurd: The Cauchy–Schwarz inequality, (also discovered by Bunyakovsky) its beauty and versatility is matched by hardly anything you’ll ever ever see. #math #MathSky

The Cauchy-Schwarz inequality, the dot product of two vectors is never greater than the product of the norms of the vectors

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SunJester @sun-jester.bsky.social · 05/06/2025

Another silly #poem, this ones pretty much a retelling of something that my cats actually did. Couldn't decide which title to give it, so like a true artist I gave it two: The Chase; or, The Folly of Cats #poetry #writing #WritingCommunity

~The Chase; or, The Folly of Cats~

I’ve got two little cats, cats, cats,
they really are my pets, pets, pets.

They run and play and meow and purr, -urr, -urr, -urr
They’re brother and sister, -er, -er, -er
One’s black and white, the other white and black, black black

One time there was a mouse, mouse, mouse.
They chased it around the house, house, house.
They were running, running all around,
in no time that mouse’ll be found, found, found.

but when the mouse stood still, still, still.
That went beyond their skill, skill, skill.
They didn’t know what to do, do, do, do, do, do, do, do
and so it flew the coop, coop, coop,
going where to, to, to?

They never caught it,
never did see it again, ‘gain, ‘gain…

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SunJester @sun-jester.bsky.social · 04/06/2025

It's the one where Benjamin Horne gets out of his confederate phase and James gets away from Evelyn and Malcolm. It ends with this mask

Twin Peaks mask from s2e15 left by Windom Earle

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