Gaurish Korpal

Gaurish Korpal

Musings

Grothendieck Erdos Sophie Nueman Turing

I wrote about 180 blog posts from October 2014 to December 2018 at Gaurish4Math (Caution: This WordPress website is not mobile friendly and is supported via advertisements. Consider using ad-blocker like uBlock Origin)

Some old posts have been copied here. I might also write some new posts here once in a while, but they need not be about mathematics.

2025

I use Arch btw

18 minute read

Published:

I was introduced to Linux via Canonical’s advertisement program that it ran with PCWorld magazine, in which the accompanying CD had latest Ubuntu version and other software updates. This led to Linux explorations (including weirdos like BOSS Linux, Puppy Linux, Peppermint,…) in VirtualBox running on Windows XP. However, being unable to keep up with Microsoft Windows’ increasing system requirements, I ended up using Lubuntu once Windows XP reached end of life. Since then, over the last 20 years, I have had the pleasure of using the three major Linux distro families: APT (Debian/Ubuntu/Linux_Mint/Tuxedo_OS/Kali_Linux), DNF (Fedora/RHEL/CentOS), and ZYpp (SLE/openSUSE). You can read my long rants about various Linux distros in one of my old blog post. Long term Linux users might enjoy a comparison of Arch with other distros, why most of them are not endorsed by GNU, and the GNU/Linux naming controversy.

2022

2021

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

Higher Arithmetic Computations

15 minute read

Published:

In this post, I discuss the options available for doing computational experiments in advanced number theory.

2020

Drawing graphs and diagrams using pdfLaTeX

10 minute read

Published:

Here is a collection of options available for embedding vector graphics in LaTeX when using pdfLaTeX. We can always use simple mathematical programs like GeoGebra for 2D and 3D graphs and drawing programs like Google Drawing for diagrams. These graphs and diagrams can be exported as png or jpg (raster graphics) and then inserted in pdf using graphicx package.

Building a cheap Linux PC with cloud backup support

14 minute read

Published:

I would like to share my expereince of building a cheap PC capable of running Linux. With the “work-from-home” restriction imposed to counter COVID crisis, my chromebook became even more useless. It could neither run the desktop version of Zoom nor work with a drawing tablet. I believe these problems can be solved by enabling the Developer Mode and installing Ubuntu alongside ChromeOS, but I highly doubt that audio and other drivers will work in Ubuntu. However, since mobility is not desired anymore, I decided to build desktop PC with minimum possible budget (which turned out to be USD 650, same as the cost of the basic Pixelbook Go or an entry level ThinkPad with core i5 10th gen). Moreover, desktop CPUs are much more powerful than laptop CPUs, for instance the Intel Core i3-9100 gives slightly better performance than Intel Core i5-10210U.

LaTeX on Chromebook

14 minute read

Published:

The laptop that I got when I joined college 5 years ago was now old enough to be replaced. Mostly because I picked the wrong specs when there was a choice (like chose Realtek over Intel NIC, 1x8GB over 2x4GB RAM, and 48Wh over 62Wh battery) and my lack of maintenance (never cleaned dust from inside or the rust from the ports). So I wanted something portable that can allow me to browse internet, write homework assignments in LaTeX (not Overleaf) and backup my data to the cloud. Moreover, I find Windows very irritating to use and prefer Ubuntu. However, due to budget constraints, I couldn’t just buy the USD 1000 Linux friendly laptops like Dell XPS or Lenovo ThinkPad .

2019

Space filling curve

4 minute read

Published:

In this post I would like to share my old writeup about there existence of a continuous surjective map from $\mathbb{R}$ to $\mathbb{R}^2$. In other words, we will prove that that Hilbert’s Curve is a continuous surjective map. The proof presented here was explained by Dr. Manas Ranjan Sahoo, 3 years ago on 15th April 2016.

2018

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

2016

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

2014

Spot The Flaw

less than 1 minute read

Published:

Many of you must have seen numerous examples of such situations where we get an absurd result and have to spot flaw in proof.

Hello World

less than 1 minute read

Published:

Here is my first post.