Category: Mathematics

How Infinite Series Reveal the Unity of Mathematics:Quanta Magazine

Sometimes the insight that one can get from mathematics can feel like magic. If you allow yourself to follow the logic, you can find constructs in different areas of mathematics that seem to be unrelated to each other that somehow fit with each other in a logical and intellectual way that feels as real as any physical experience – like something you can touch and feel. Perhaps one can find a way to really begin to appreciate how the truths of math and science are foundational to our lives these days. Sadly, there are easier paths to other kinds of “beliefs”, paths that seem to require less effort to follow, which in the end can turn out to be very destructive to our collective existence.

At the least, check out the two puzzles in the Quanta article that I am providing a link for here. Follow your intuition!

https://www.quantamagazine.org/how-infinite-series-reveal-the-unity-of-mathematics-20220124

Federico Ardila on Math, Music and the Space of Possibilities: Quanta Magazine

This is beautiful! Combinatorics, geometry, algebra, multidimensional spaces, robotics, music, education, social awareness – this podcast episode touches on all of this! This guy is a remarkable human being.

https://www.quantamagazine.org/federico-ardila-on-math-music-and-the-space-of-possibilities-20210329/

From Brain Pickings – The Snail with the Right Heart: A True Story

The Snail with the Right Heart: A True Story

I expect that the viewpoint of this particular article could bother some folks – depending on how one sees the world. I found it thought-provoking.

This posting led me to do some investigating of my own. I was taken up by the science involved, and the apparent universality of some mathematical concepts in nature. I learnt about the concept of Chirality – about how chirality appears in nature, and how chirality extends even down to the genetic and atomic level. In general terms, left-handedness and right-handedness in nature can sometimes even lead to widely different properties of the objects in question. I also looked into how the Golden Mean, or the Golden Ratio, manifests itself in the world – even in the shapes of snail shells!

Go ahead and look it all up. The natural world is fascinating.

Computer Scientists Achieve ‘Crown Jewel’ of Cryptography | Quanta Magazine

I have worked on projects involving cryptography in my past. I understand some of the basic concepts that provide the security in cryptographic systems enough to be dangerous when discussing the topic, but I never became an “expert” on the subject. I found it a difficult subject to tackle, requiring a greater level of dedication and/or level of smartness than I was capable of. Nevertheless, it is a fascinating topic. I wrote about the extent of my exposure to the topic here.

https://www.quantamagazine.org/computer-scientists-achieve-crown-jewel-of-cryptography-20201110/

The Simple Math Problem We Still Can’t Solve | Quanta Magazine

Some of the problems that mathematicians attempt to solve can be intellectually very challenging, and also stimulating – maybe even fun, but could leave you wondering what, if any, practical use they have in real life. I mean, why did anyone even bother to create this problem?

https://www.quantamagazine.org/why-mathematicians-still-cant-solve-the-collatz-conjecture-20200922/

How Is Math Beautiful? | Quanta Magazine

“As Jean-Pierre Serre reportedly quipped to his mathematician colleague Raoul Bott, “While the other sciences search for the rules that God has chosen for this Universe, we mathematicians search for the rules that even God has to obey.””

https://www.quantamagazine.org/how-is-math-beautiful-20200616/

A ‘Rebel’ Without a Ph.D.| Quanta Magazine

Freeman Dyson is one of the mathematicians about whom I know very little.  I have heard the name many times, but have never really bothered to follow up in the past.  The video in the article, and the article itself, were very informative.  A great mind!  He died in February at the age of 96.

via A Math Puzzle Worthy of Freeman Dyson | Quanta Magazine

Also: Remembering the Unstoppable Freeman Dyson