"...learn kind of basic things in mathematics, in modeling, mathematics that can be connected with reality....although you should learn philosophy ...this is done by learning things that have a long shelf life"

"... if you were starting your AI career today, what skills and research directions would you focus on? ---  I get a lot this question a lot from young students or parents of future students. I think you should learn things that have a long shelf life and you should learn things that help you learn to learn because technology is you know evolving so quickly that you want kind of the ability to learn really quickly. "

After 12 years at Meta, Turing Award winner Yann LeCun is betting his legacy on a radically different vision of AI. In this conversation, he explains why Silicon Valley's obsession with scaling language models is a dead end, and why his new company AMI is building world models that predict in abstract representation space rather than generating pixels.

Here is the podcast: https://www.youtube.com/watch?v=7u-DXVADyhc

#mathematics #coding #ai #artificialintelligence #YannLeCun #STEM

National Mathematics Day - Birthday of a great mathematician

A person of great Inspiration!

"Every positive integer was one of his personal friends" - British Mathematician John Littlewood.

During my high school days, I watched the movie "The Man Who Knew Infinity". It was the first time I was introduced to an eminent mathematician through a gripping biopic. I was inspired by Srinivasa Ramanujan and began reading about him, which led me to decide to major in math.

A quote by him always lingers - "An equation means nothing to me unless it expresses a thought of God"

A fascinating scene was the popular Ramanujan anecdote about taxi cab number 1729 - "the smallest number expressible as the sum of two cubes in two different ways (1³ + 12³ and 9³ + 10³)". One more scene that intrigues us is the fierce academic challenge between the totally sceptical Major Percy Alexander MacMahon and the supremely confident Ramanujan on partitions [p(200)], which Prof. Hardy relishes from the sidelines.

The poetic justice moment occurs during the committee's discussion to decide on the FRS for Ramanujan. When the fictional Prof Howard (who enacts the Prof Arthur Berry episode in an earlier scene from real biography) opposes FRS for him by saying, "enough is enough with this...this Ramujin", Major MacMahon quickly intervenes and says, "I think he has the finest mind I've seen in my lifetime", and then corrects Prof Howard, "And his name is Ramanujan."

However, the goosebump scene is when Prof Hardy opens the door for Ramanujan, and he is welcomed by all the senior academicians with a ritualistic tapping on the desk - when he is finally elected as a Fellow of the Royal Society (FRS) and a Fellow of Trinity College, signifying that the once-sceptical academic community has fully accepted him as an equal.

A well-made movie worth watching on the birthday of the mathematical genius Shri Srinivasa Ramanujan, December 22, which we celebrate in India as National Mathematics Day in his honour. With a lot of respect and reverence, remembering the genius who lived only for 32 years, but gifted humanity with bundles of mathematical works that still help us in various realms - from ATMs and RADARS to Blockchain encryption layers and Quantum gravity models.

#mathematics #nationalmathematicsday #srinivasaramanujan #infinity #themanwhoknewinfinity #ghhardy #ramanujan

 Researchers at the Institute for Advanced Study, Emory University and the Weizmann Institute of Science recently set out to model how humans represent meaningful narratives and store them in their memory, using mathematical objects known as "random trees." Their paper, published in Physical Review Letters, introduces a new framework for the study of human memory processes, which is rooted in mathematics, computer science and physics.

https://medicalxpress.com/news/2025-07-mathematical-reveals-humans-narrative-memories.html

#mathematics #cognitivepsychology #mathematicalmodel

Mathematics round the world

 Mathematics plays a crucial role in education all around the world, not just for solving equations but also for fostering logical reasoning, critical thinking, and organized problem-solving abilities. The topic of whether artificial intelligence (AI) should be taught with the same focus and framework as mathematics emerges as AI becomes more and more integrated into our daily lives.

In light of the fact that both AI and math teach us how to think more effectively, they should be taught similarly. Prompt engineering, like mathematics, should be at the center of education because it enables people to use AI for good in addition to understanding it.

https://www.analyticsinsight.net/artificial-intelligence/should-ai-be-taught-like-maths-why-prompt-engineering-might-be-the-next-literacy

#mathematics #AI #Artificialintelligence

Mangala Narlikar - an inspiration for women in STEM

 A mathematician who balanced family and figures, children and complex analysis, household and number theory. 

https://www.msn.com/en-in/autos/news/mangala-narlikar-changed-how-girls-in-india-learn-math-she-took-the-fear-out-of-it/ar-AA1ILULM

#mathematics  #math

Hidden Figures

 Recently I watched an exciting movie "Hidden Figures" which was about three of the great female mathematicians, Dorothy Vaughan, Katherine Goble Johnson and Mary Jackson. It was a very inspiring movie which told about the life and struggles of the three mathematicians, and their work contribution in NASA.

Katherine Goble Johnson (August 26, 1918 - February 24, 2020) was an African-American mathematician who was well known for solving the complex manual calculations such as orbital mechanics which led to the first and following US crewed spacecraft. The space agency noted her "historical role as one of the first African-American women to work as a NASA scientist.

Mary Jackson (April 9, 1921 - February 11, 2005) was a mathematician and an aerospace engineer at NASA. In 1958, after much struggle to enroll for engineering classes, she successfully became NASA's first African female engineer.

Dorothy Vaughan, (September 20, 1910 - November 10, 2008) was a mathematician and a human computer who worked in the Langley Research Centre. Later in 1949, she became acting supervisor of the West Area Computers, the first African-American woman to receive a promotion and supervise a group of staff at the center.

The movie is based on the biographical book, "Hidden Figures: The American Dream and the Untold Story of the Black Women Who Helped Win the Space Race" written by Margot Lee Shetterly, which tells the story of these determined mathematicians, who challenged biases and discrimination, worked tirelessly and achieved in their areas of expertise. Such an inspiration.

AWM Sadosky Research Prize in Analysis

 Every year, the Association for Women in Mathematics (AWM) recognizes exceptional research done by USA-based early-career women mathematicians with the Sadosky Research Prize in Analysis.

The recipient of 2026 AWM Sadosky Research Prize in Analysis is Dr. Hong Wang, Associate Professor of Mathematics at New York University's Courant Institute of Mathematical Sciences, and permanent professor of mathematics at Institut des Hautes Études Scientifiques (IHES).

Her contributions on solution for central problems in harmonic analysis and Courier restriction problem, the Kakeya Conjecture, and geometric measure theory is ground breaking. 

Great inspiration for women in math 👏. 

#AWM #Womeninmath #research #mathematics #womeninstem #HarmonicAnalysis #KakeyaConjecture

AWM Microsoft Research Prize in Algebra and Number Theory

 Dr Sarah Peluse, Associate Professor at Stanford University, will be the recipient of the 2026 Association for Women in Mathematics (AWM) Microsoft Research Prize in Algebra and Number Theory. 

🎁 This prize serves as a wonderful recognition of Prof. Peluse's impactful work in number theory, combinatorics, ergodic theory, and representation theory, which finds far-reaching applications in industry areas such as cybersecurity, cryptography, telecom, analytics, and energy grids.☎️

⭐️ Truly an inspiration for women in Math ⭐️

#AWM #WomenInMath #Research #mathematics #WomenInSTEM #SarahPeluse #StanfordUniversity #NumberTheory

SIx Seven

Numbers are always fascinating. Occasionally, numbers can also become a part of crazy phenomena like "Six Seven". The Gen Alpha frenzy for the "67" fad is reaching a crescendo in the USA. According to this WSJ report (pay-walled), schoolchildren are screaming "Six Sevennnnn" with the see-saw gesture whenever this number appears in a math problem or solution during a maths class, much to the irritation of the math teachers. The "Six Seven" trend started suddenly with Instagram Reels and TikTok videos and became viral with the rap singer Skrilla's song "Doot Doot (6 7)" and the basketball star LaMelo Ball (height 6'7"!!). Such no-meaning viral phenomena are called brainrot memes! 

It is a paywalled story. I have given the link below.

https://www.wsj.com/lifestyle/six-seven-meme-teens-math-teachers-42764bcb

#mathematics #sixseven #meme #GenAlpha #mathteaching #brainrot

Interactive Online textbook on Linear Algebra

The Delft Institute of Applied Mathematics (DIAM), in close collaboration with the Programme of Innovation in Mathematics Education (PRIME), has launched a new interactive online textbook on linear algebra, designed specifically for engineering students at the bachelor level.

According to the institute communication release, "The book introduces the fundamentals of linear algebra from a geometrical perspective, starting with vectors, lines, and planes, before moving on to core topics such as systems of linear equations, matrix arithmetic, eigenvalues and eigenvectors, and orthogonality. More advanced subjects, including symmetric matrices and discrete dynamical systems, are explored in later chapters.

Students can explore concepts hands-on through applets, while a wide range of embedded exercises with personalised feedback ensures active engagement and deeper understanding. The book has already been integrated into several interfaculty linear algebra courses at TU Delft."

Here is the link to the book:

https://interactivetextbooks.tudelft.nl/linear-algebra/index.html

Here is the repository of all the interactive open books from TU Delft.

https://books.open.tudelft.nl/home/catalog/category/interactive-textbooks

hashtag#mathematics #linearalgebra #TUDelft #MathematicsEducation #AppliedMathematics Delft University of Technology TU Delft | PRIME

Mathematical Reliability in Aviation Safety

✳️ The "Course Gallery" is a hands-on project exhibition at our college, where various departments showcase thematic display items created by students. This year, we had this during the first week of October. ✳️

🛩 Our team thematically explained the statistical reliability testing process by exhibiting a model Airplane Disaster safety system. 🛩

✈️ The tragic incident of the recent Ahmedabad plane crash prompted us to reflect on the importance of aviation safety. At that time, numerous discussions about various passenger protection innovations emerged in the media in the context of air crashes. What is crucial in deciding about a particular safety system is the statistically significant success rates achieved in multiple iterations during the testing phase, where mathematics plays a critical role.🚒

💡 We came across an innovative idea proposed by Ukrainian engineer Vladimir Tatarenko in 2016. His idea is as follows: Under normal conditions, the cabin remains attached to the plane. When an emergency occurs, the emergency switch is pressed. The motor activates and releases the cabin lock. Simultaneously, the parachute opens, and the cabin lands slowly and safely on the ground.🪂

📚 Our team believed that a practical demonstration model on this concept would be an effective way to explain the role of statistics in such critical areas. The details are provided in the image below. 🛠

The inventor conducted a survey, which showed that people are ready to pay extra for this safety idea. 

☢️ But there are challenges too: (1) The detachment mechanism could compromise the aircraft's structural integrity. (2) The falling cabin could pose a danger to people and property on the ground, and its landing could be affected.🚫

However, this innovation can serve as a stepping stone for creating better solutions to prevent loss of life during plane crashes. 

#mathematics #statistics #riskassessment #airplanesafety #aviationsafety #appliedmathematics #mathprojects

Application of Linear Algebra in Industrial Automation

Abstract: Linear algebra is a major topic in mathematics that deals with vectors, matrices, and linear functions, among other concepts. Industrial automation refers to the use of machines, robotics, and control systems to perform tasks that would otherwise be done by humans, thereby improving quality, productivity, and safety in industrial applications and developments. This article explores the significant reliance of industrial automation on linear algebra as its foundational basis. This article primarily focuses on explaining two crucial topics: robotics and artificial intelligence, as well as the application of linear algebra in these fields.

Introduction

Linear Algebra is an inevitable part of mathematics that deals with matrices, vectors, tensors, vector spaces, linear functions, and mappings, to name a few. This works like algebra, but instead of numbers, vectors are used. This is one of the important topics that forms the foundation of many other fields, including physics, chemistry, industrial automation, psychology, and engineering. Linear Algebra is used in many different fields due to its versatile concepts, such as matrices and vectors, which aid in simplifying and understanding complex problems.

The areas in Industrial Automation where linear algebra is applied are, 

• Robotics

• Artificial Intelligence

Robotics

Robotics is a field of engineering and computer science that deals with the design, manufacture, and operation of robots by applying concepts from computer science, mechanical engineering, and other related domains. Many industries, such as the automobile industry, use small robots to perform repetitive tasks. This field aims to create machines that can assist humans in various tasks. 

Vectors are quantities that contain both magnitude and direction. They are used to represent the movements made by the robots in 2D and 3D space. 

Few Applications of Linear Algebra in Robotics

The inverse of a matrix is used to solve a system of linear equations. This concept is applied in robotics to perform fundamental tasks, such as control, motion planning, and kinematics.

Singular Value Decomposition is an exciting concept in linear algebra. It is a technique used to break down complex matrices into smaller component matrices. In Robotics, this technique is used in motion planning to find the best configuration for the robot. This technique is used to evaluate the feasible trajectories by analyzing the workspace of the robot. SVD is also used in the analysis of applications in robotics.

Transformation is another exciting topic. It is a function from one vector space to another that does not alter the linear structure of either vector space. Matrices are used in transformations. This enables robots or machines to calculate their position and altitude in a 3D vector space.

Artificial Intelligence

Artificial Intelligence is a type of concept in Industrial automation that requires human intelligence. These tasks include reasoning, problem-solving, and language understanding. Artificial intelligence enables machines to analyze data, make informed decisions, and enhance their performance.

Application of Linear Algebra in Artificial Intelligence

Vectors are used to represent data points and attributes with magnitude and direction. It is used as a fundamental tool for capturing and manipulating information about data points, enabling the representation of numerical features in machine learning models.

Matrices are rectangular arrays of numbers that form a relation between vectors. Matrices are used to represent complex structures and capture intricate relationships within data sets.

In data representation, linear algebra serves as a tool for representing and manipulating data. Linear algebra enables the representation of text data as vectors and image data as matrices.

The data representations permit AI algorithms to process information effectively and make sense of textual and visual data. Linear algebra facilitates the handling of diverse and unstructured data types, including text, speech, and image data.

Optimization utilizes linear algebraic tools to solve optimization problems through systems of linear equations. Many AI algorithms rely on this concept to find solutions. Least squares regression and gradient descent are techniques that heavily depend upon linear algebra. Recent advancements in optimization have focused on addressing challenges like non-convexity and large-scale optimization problems. Stochastic gradient descent with acceleration in an algorithm that has been developed to train deep neural networks more efficiently. Concepts of optimization in linear algebra, such as interior point methods and conjugate gradient methods, have been extended to handle complex AI models with millions of parameters.

Neural Networks are a vast topic in AI and machine learning. It can be said to be the heart of AI. Linear Algebra serves as the foundation for neural networks. Neural networks have many layers, which can be represented in a matrix transformation. Matrix multiplication, elementary row operations, and activation functions are utilized in the forward and backward propagation steps during the training of neural networks. Image classification, natural language processing, and speech recognition are a few areas in which neural networks have proven highly successful.

Conclusion

From designing efficient robotic movements and improving image processing in quality control to optimizing resource allocation and enhancing machine learning models, linear algebra enables automation systems to function with precision and efficiency. As industries continue to embrace automation and AI-driven solutions, the application of linear algebra will remain indispensable in driving innovation, improving productivity, and ensuring seamless operations in modern manufacturing and industrial processes.

References

https://www.techtarget.com/whatis/defenition/robotics

https://www.cs.miami.edu/home/visser/csc398-files/linearalgebra-notes.pdf

https://www.linkedin.com/pulse/linear-algebra-fuels-artificial-intelligence-kayode-odeyemi

https://www.mirlabs.org/isda23/ISDA23_SS14.pdf

https://www.kiet.edu/blog/computer-science-information-technology/transforming-ai-and-%20machine-learning-the-crucial-role-of-linear-algebra/

https://medium.com/@rajat01221/mathematics-of-neural-networks-from-linear-algebra-to-%20backpropagation7bb72b73f49c

https://studywolf.wordpress.com/2017/06/09/deriving-a-robots-transform-matrices/

https://turcomat.org/index.php/turkbilmat/article/download/11829/8642/20975#:~:text=Algorithm%20of%20New%20Conjugate%20Gradient,0%2C1%2C2%2C%E2%80%A6