What is the Unexpected Discovery in Basic Math?

In summary, the conversation touched on a link to an interesting article that discussed a discovery in basic math involving neutrinos and electrons interacting in an atom. However, the article did not mention the new formula being used. A blog by Terry Tao provided a good description of the result and his paper on the topic is also available. The conversation expressed fascination with the discovery and praised Tao's ability to explain complex concepts at an elementary level.
Mathematics news on Phys.org
  • #2
Fascinating. Now if only the article had mentioned what the new formula was!

The part about the neutrinos and electrons interacting in an atom is new to me though. Thanks for that reason as well!

-Dan
 
  • #4
topsquark said:
Fascinating. Now if only the article had mentioned what the new formula was!

The part about the neutrinos and electrons interacting in an atom is new to me though. Thanks for that reason as well!

-Dan

Here is Tao's paper. Short and sweet! I, too, thought this was fascinating! There is room for a masterful mathematician like Tao to write a paper at quite an elementary level.
 

FAQ: What is the Unexpected Discovery in Basic Math?

What are eigenvalues and eigenvectors?

Eigenvalues and eigenvectors are mathematical concepts used to describe the behavior of linear transformations. Eigenvalues represent the scalar values that a linear transformation scales its corresponding eigenvector by. Eigenvectors, on the other hand, are the non-zero vectors that remain in the same direction after a linear transformation is applied.

How are eigenvalues and eigenvectors calculated?

Eigenvalues and eigenvectors can be calculated by solving the characteristic equation of a linear transformation. This involves finding the values of lambda that satisfy the equation (A - λI)v = 0, where A is the transformation matrix and I is the identity matrix.

What is the significance of eigenvalues and eigenvectors?

Eigenvalues and eigenvectors are important because they provide a way to understand the behavior of linear transformations. They can be used to determine the stability of a system, identify key features of a dataset, and simplify complex calculations.

Can eigenvalues and eigenvectors be complex numbers?

Yes, eigenvalues and eigenvectors can be complex numbers. This is because the characteristic equation can have complex solutions, and the corresponding eigenvectors can also have complex components.

How are eigenvalues and eigenvectors used in data analysis?

Eigenvalues and eigenvectors are commonly used in data analysis for dimensionality reduction and feature extraction. They can also be used in machine learning algorithms, such as principal component analysis, to identify important patterns and relationships in a dataset.

Similar threads

B Looking for examples of unexpected applications of math concepts
Replies
15
Views
1K
I I found an interesting math result, but now I see a contradiction
Replies
3
Views
950
B Anonymous 4Chan User Proves a 25yr old Math Problem
Replies
31
Views
4K
What's the formula? - eigenvectors from eigenvalues
Replies
3
Views
1K
Operator T, ##T^2=I##, -1 not an eigenvalue of T, prove ##T=I##.
Replies
2
Views
691
What would be the impact of the discovery of the Graviton in the world?
Replies
6
Views
2K
What makes unexpected discoveries in science so exciting?
Replies
1
Views
360
B Mathematics in STEM fields: GATEKEEPER OR GATEWAY?
Replies
13
Views
3K
MHB Null and non null eigenvalues (Oinker's question at Yahoo Answers)
Replies
1
Views
2K
MHB Amanda's question at Yahoo Answers (Eigenvalues and eigenvectors)
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top