Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
What’s Happening in the Mathematical Sciences, Volume 13
 
Softcover ISBN:  978-1-4704-7490-4
Product Code:  HAPPENING/13
List Price: $29.00
MAA Member Price: $26.10
AMS Member Price: $23.20
Sale Price: $17.40
Not yet published - Preorder Now!
Expected availability date: September 08, 2024
Click above image for expanded view
What’s Happening in the Mathematical Sciences, Volume 13
Softcover ISBN:  978-1-4704-7490-4
Product Code:  HAPPENING/13
List Price: $29.00
MAA Member Price: $26.10
AMS Member Price: $23.20
Sale Price: $17.40
Not yet published - Preorder Now!
Expected availability date: September 08, 2024
  • Book Details
     
     
    What's Happening in the Mathematical Sciences
    Volume: 132024; 126 pp
    MSC: Primary 00

    The What’s Happening in the Mathematical Sciences series presents a selection of recent discoveries and exciting fields of research in mathematics, explained in depth but in a slow-paced, reader-friendly way.

    In the first few months of 2023, artificial “brains” like ChatGPT and GPT-4 were constantly in the news, and they have already turned into big business. One chapter in this book, “Deep Learning: Part Math, Part Alchemy”, explains how math disentangles hype from reality and explains some of the remarkable advances of machine learning. Meanwhile, “Organizing the Chaos Inside the Brain” explores animal brains, and describes how biologists can apply chaos theory to simulate the wanderings of a fly from firing data on neurons within its brain.

    This issue of What's Happening also includes many treats for readers who like pure math—especially those who are interested in geometry. In recent months and years, there have been unexpected discoveries in tiling (“One Stone to Rule Them All”), sphere-packing in more than three dimensions (“A Fascination of Spheres”) and the reconstruction of three-dimensional scenes from two-dimensional images (“Multi-View Geometry: E Pluribus Unum”). The chapter “How to Draw an Alternate Universe” will, as promised, open a door to a completely different, non-Euclidean universe—or several of them. Shakespeare’s words, “something rich and strange”, only begin to describe them.

    In “How Mathematicians Unearthed the Stubborn Secrets of Fano Varieties”, readers will learn about one of the building blocks of algebraic geometry, the branch of geometry that deals with surfaces defined by polynomial equations. The chapter “Missing One Digit” addresses a seemingly elementary problem in number theory: how many prime numbers do not have a “7” in them? The answer is easy to guess—but hard to prove. “Fluid Flow: Two Paths to a Singularity” discusses another guess that is hard to prove: can fluids in an enclosed region develop “singularities” akin to a breaking wave? Computer evidence is mounting that they can—including some evidence from machine learning algorithms. (Which brings us full circle back to the “Deep Learning” chapter.)

    Dana Mackenzie has written for the What's Happening series since Volume 6, published in 2006. In this volume he is joined by Leila Sloman, whose name will be familiar to many readers from her work for Quanta Magazine.

    Readership

    Anyone interested in cutting-edge advancements in mathematics.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 132024; 126 pp
MSC: Primary 00

The What’s Happening in the Mathematical Sciences series presents a selection of recent discoveries and exciting fields of research in mathematics, explained in depth but in a slow-paced, reader-friendly way.

In the first few months of 2023, artificial “brains” like ChatGPT and GPT-4 were constantly in the news, and they have already turned into big business. One chapter in this book, “Deep Learning: Part Math, Part Alchemy”, explains how math disentangles hype from reality and explains some of the remarkable advances of machine learning. Meanwhile, “Organizing the Chaos Inside the Brain” explores animal brains, and describes how biologists can apply chaos theory to simulate the wanderings of a fly from firing data on neurons within its brain.

This issue of What's Happening also includes many treats for readers who like pure math—especially those who are interested in geometry. In recent months and years, there have been unexpected discoveries in tiling (“One Stone to Rule Them All”), sphere-packing in more than three dimensions (“A Fascination of Spheres”) and the reconstruction of three-dimensional scenes from two-dimensional images (“Multi-View Geometry: E Pluribus Unum”). The chapter “How to Draw an Alternate Universe” will, as promised, open a door to a completely different, non-Euclidean universe—or several of them. Shakespeare’s words, “something rich and strange”, only begin to describe them.

In “How Mathematicians Unearthed the Stubborn Secrets of Fano Varieties”, readers will learn about one of the building blocks of algebraic geometry, the branch of geometry that deals with surfaces defined by polynomial equations. The chapter “Missing One Digit” addresses a seemingly elementary problem in number theory: how many prime numbers do not have a “7” in them? The answer is easy to guess—but hard to prove. “Fluid Flow: Two Paths to a Singularity” discusses another guess that is hard to prove: can fluids in an enclosed region develop “singularities” akin to a breaking wave? Computer evidence is mounting that they can—including some evidence from machine learning algorithms. (Which brings us full circle back to the “Deep Learning” chapter.)

Dana Mackenzie has written for the What's Happening series since Volume 6, published in 2006. In this volume he is joined by Leila Sloman, whose name will be familiar to many readers from her work for Quanta Magazine.

Readership

Anyone interested in cutting-edge advancements in mathematics.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.