Latest Twitter Threads by @TamasGorbe on Thread Reader App

Oct 19, 2022 • 4 tweets • 1 min read

Gabriel's Horn is a solid you get by rotating the hyperbola y=1/x (with x>1) about the x-axis.

Having finite volume (π) and infinite(!) surface area, it leads to the apparent paradox:

"You can fill it with paint, but you cannot coat it."

The moral of this example is that infinity is a tricky concept and we need to be very careful with trusting our intuition when it comes to ∞.

May 31, 2021 • 33 tweets • 11 min read

NEW PAPER
Free to read rdcu.be/clsVe

Earlier this year a friend* and I've solved a long-standing problem which, in part, meant finding the eigenvectors of this matrix. In this thread, I'll review our result and bits of 170 years of history

*J.F. van Diejen, Talca

1/n

The title of our paper is "Elliptic Kac–Sylvester Matrix from Difference Lamé Equation" and it was recently published in the mathematical physics journal Annales Henri Poincaré.

Article page: doi.org/10.1007/s00023…

2/n

Nov 17, 2020 • 4 tweets • 1 min read

"Here's a photo of my boy, Peter. He doesn't yet know what the continuum is, but he doesn't know what fascism is either." - George Szekeres' message to Paul Erdős. Peter Szekeres was born in Shanghai, where his parents George Szekeres and Esther Klein escaped from Nazi persecution in 1938.

Oct 13, 2020 • 5 tweets • 2 min read

As a run-up to the "Introduction to Integrability" series (see my pinned tweet), I decided to share some interesting bits from the history of integrable systems.

Let's start at the beginning, shall we? So Newton...

#1 It all started with Newton solving the gravitational 2-body problem and deriving Kepler's laws of planetary motion as a result. I would argue that this was possible, because the Kepler problem is (super)integrable. [1/2]

Oct 12, 2020 • 11 tweets • 2 min read

I'm happy to announce "Introduction to Integrability", a series of 5 online lectures covering the basics of my research area, Integrable Systems.

The first lecture is on Thursday 22 October 3:30pm (BST).

You can register here:
icms.org.uk/V_INTERGRABILI…

The series is funded by the London Mathematical Society. It's also supported by ICMS as part of the ICMS Online Mathematical Sciences Seminars.

Sep 2, 2020 • 5 tweets • 1 min read

I thought of an integer between 1 and 100.

How many yes-no questions do you need me to answer so you find this number if you don't want to rely on luck? What if you have to send me the full list of your questions first? How many questions will you need then?

Aug 2, 2020 • 5 tweets • 1 min read

I don’t know who needs to hear this, but Physics ≠ Mathematics. Not gonna lie, the intensity of reactions/emotions this simple statement evoked surprises me.

Jul 22, 2020 • 4 tweets • 1 min read

Are you still a spy if you get registered as a spy? I'm really surprised by the result so far!

Jul 19, 2020 • 8 tweets • 1 min read

Pause the video and vote below

Where is the dot?

Jul 10, 2020 • 6 tweets • 1 min read

Integral representation of n factorial (Euler, 1729)

“Read Euler, read Euler, he is the master of us all.” – Laplace

Jul 2, 2020 • 4 tweets • 1 min read

For nearly 200 years, all publications about the French mathematician Legendre used the portrait on the left to depict him.

There's one small snag though, it's not him, but a contemporary politician named Legendre. The mistake was only discovered in 2005.

The only known portrait of Legendre, the mathematician is the caricature on the right from 1820.

Jun 19, 2020 • 4 tweets • 2 min read

This is the longest straight line on water on the Earth.

The path is 32,090km (20,000mi) long and following a great circle it connects Pakistan to Africa&Madagascar to Tierra del Fuego to Russia.

arxiv.org/abs/1804.07389

This is what it looks like on the (Mercator) map.

Jun 17, 2020 • 6 tweets • 1 min read

I was just asked by my university to justify why I need to buy maths books for my work using my own research grant. Absolute madness! The plot thickens!

Jun 13, 2020 • 8 tweets • 2 min read

James Clerk Maxwell was born #OTD in 1831

"His name stands magnificently over the portal of classical physics, and we can say this of him: by his birth, Maxwell belongs to Edinburgh, by his personality he belongs to Cambridge, by his work he belongs to the whole World." - Planck

Freeman Dyson: "It is difficult to read Maxwell's address without being infuriated by his excessive modesty, which led him to refer to his epoch-making discovery of nine years earlier as only 'Another theory of electricity which I prefer.'..." 1/2

May 11, 2020 • 4 tweets • 1 min read

Here you are in 2020 watching a 1952 interview with Russell, born in 1872, who talks about how his grandfather visited Napoleon on Elba in 1814.

Puts human history in a different perspective.

Full version

May 7, 2020 • 4 tweets • 1 min read

The United States of Voronoi (USV)

State borders redrawn such that wherever you live the closest state capital is your state's capital

Source: jasondavies.com/maps/voronoi/u…

Apr 29, 2020 • 4 tweets • 1 min read

Thomson Problem [Mostly Unsolved]

Where to put N electrons on a sphere to minimize energy? The exact solution is only known for N=1,2,3,4,5,6,12

N=5 is solved by the vertices of a triangular dipyramid

In other words, which configuration of points minimizes the sum of reciprocals of distances?

Apr 29, 2020 • 4 tweets • 1 min read

Don't we all...?

As one of my professors used to say, “I can teach my horse to calculate derivatives, but even I can’t integrate”.

Apr 28, 2020 • 10 tweets • 3 min read

Harmonic numbers
Hₖ = 1 + 1/2 + ... + 1/k
are never integers (except for H₁=1 of course).

Here is a proof from THE BOOK. (1/4)

In fact, I'll show you the proof of a stronger statement:

The reciprocals of two or more consecutive positive integers never add up to an integer.

In other words, the difference of distinct harmonic numbers is not an integer. (2/4)

Apr 24, 2020 • 4 tweets • 1 min read