2022 - A Good Year for Mathematics

For this post, I refer readers to the summary by Konstantin Kakaes of Quanta Magazine: The Biggest Math Breakthroughs in 2022 | Quanta Magazine.

Also see this video version: https://youtu.be/Nmgl78a02ys

 

Multiple Dimensions of Time - Part 3

                                            

Credit: Pixabay/CC0 Public Domain

In two prior posts, I explored how different authors and physicists have considered the possibility of multiple dimensions of time. See: Multiple Dimensions of Time and Multiple Dimensions of Time - Part 2.

As unusual as this topic may seem, I'm reading more about how many scientists have considered multiple dimensions of time to be a possibility. Just recently, another article was published this past week in which authors Andrzej Dragan et al. develop an extension of special relativity in 1+3 dimensional spacetime to account for superluminal inertial observers and show that such an extension rules out the conventional dynamics of mechanical point-like particles and forces one to use field-theoretic framework.

Update 12/25/2022 - another article posted: https://mindmatters.ai/2022/12/did-physicists-open-a-portal-to-extra-time-dimension-as-claimed-2/

Gunther Kletetschka, physicist - proposes that time has three dimensions and space is only its consequence - this theory could forever change the way we understand the universe https://share.google/wMBNWsoH2nVpGBByO

A Million Dollar Prize for Solving a Math Problem

 

(Yitang Zhang, Photo credit: http://www.voachinese.com/media/video/i-america-math-zhang-yitang-20131204/1803128.html)

The Riemann hypothesis, first proposed by Bernhard Riemann in 1859, deals with the distribution of prime numbers. At the beginning of the 20th century, it was one of the top 23 problems identified by David Hilbert for the mathematical community to work on for the upcoming century. Math Vacation: David Hilbert Problems (jamesmacmath.blogspot.com) Riemann hypothesis - Wikipedia

The Riemann hypothesis and five others remain unsolved. The Clay Mathematics Institute has offered a US$1 million prize to anyone who can solve the Riemann hypothesis. Millennium Problems | Clay Mathematics Institute

The list of unsolved Hilbert problems may be closer to being shorten by University of California – Santa Barbara professor Yitang Zhang. https://www.scmp.com/news/china/science/article/3198779/has-chinese-born-professor-discovered-big-piece-150-year-old-maths-puzzle

If successful, this would be remarkable for a 67-year-old mathematician. However, it won’t be the first time for Zhang to solve a difficult problem later in life. Nine years ago, he shocked the world with his work of the twin-prime conjecture. While he didn’t prove the twin prime conjecture, he did prove there exists a limit below which (at the time it was 70 million) there must be an infinite number of primes separated by that a specific gap size, N. Since then, using Zhang’s techniques, the limit for that minimum gap size has been dropped from 70 million to a few hundred. If mathematicians could bring this limit down to 2, it would prove the twin prime conjecture.

August 20, 2023 Update: New York Post Article - Riemann hypothesis: Unsolved math problem worth $1 million (nypost.com).