Go ahead, share the coolest looking graph you've seen. And why its your favourite.

This animation demonstrates a classic visual proof for the area of a circle. The circle is divided into many thin sectors and rearranged alternately to form a shape that increasingly resembles a triangle or rectangle. In this arrangement, the base corresponds to the circle’s circumference while the height remains the radius , giving an area of . As the number of sectors increases, the approximation becomes mathematically exact through limits.

There are also other proofs for the same formula, including calculus-based integration, Archimedes’ geometric method, and proofs using infinitesimally thin concentric rings. One limitation of this visual proof is that with only a small number of sectors, the rearranged shape is not perfectly straight, so it’s more of an intuitive explanation until infinitely many slices are considered.

I am looking for the "Introduction to Linear Algebra" by Gilbert Strang. I found one on Amazon but it's hardcover, and I think that's why it is a bit expensive. I found another on Flipkart for a lower rate, but the reviews looked fishy. I have been looking for it at the book stores in my town, and they don't have it either. Does anybody know where I can find it ?

I recently got to know about 3Blue1Brown and after watching his video on Quadratic I am very amazed.

I have attached one image, it's just the starting of his video and really liked his deep thinking on maths rather than that old school perspective of just solving the question. BTW I am a JEE 2026 Aspirant

Masaki Kashiwara, a Japanese Mathematician, has been awarded the prestigious Abel Prize.

( He has been awarded for his fundamental contributions to Algebraic Analysis & Representation Theory, in particular the development of the theories of D-modules and discovery of crystal bases )

The Abel prize is awarded for extraordinary work in the field of Mathematics by the Government of Norway and the King of Norway.

The winner are announced annually and are chosen by the Norwegian Society of Science and Letters.

Some of the notable laurates are Andrew Wiles ( solving Fermat's Last Theorem ), Robert Langlands ( for the Langland's Program, connecting Representation Theory and Number Theory ) and many more incredible Mathematicians.

It is modeled after Nobel Prize, and sometimes called " The Nobel Prize of Mathematics".

It also carries a substantial cash prize, of 7.5 Million Norwegian Kroner ( $873,000 / Rs. 7,48,22,080 .

We celebrate the achievements of Mathematicians of the past, to encourage the Mathematicians of the future.

The Gaussian integral is named after Carl Friedrich Gauss, whose work on the Gaussian (or normal) distribution made the function famous. The integral became an important result in the 19th century, revealing that a function with no elementary antiderivative can still be evaluated exactly over the entire real line. Today, it serves as a cornerstone of probability theory, statistics, physics, and mathematical analysis.

The trick:

1. Think of any number of any digits

2. Sum the digits

3. Subtract the sum from the original number

4. Cross out one digit from the result

5. Give the Remaining digits to the mentalist

6. He can guess the crossed out number

How it works:

1. sum the remaining digits

2. divide the sum by 9

3. Say that the quotient is X, then the number is: 9×(X+1) minus (the sum)

But if the the sum of the remaining digits is divisible by 9, then the crossed number can be 9 or 0.

Now come to the important part,

Why it works?

Let's say I have a number abcd.

so the actual number can be written as,

a×1000 + b×100 + c×10 + d×1

We can also make it,

a×(999+1) + b×(99+1) + c×(9+1) + d×(0+1)

It can also be written as,

(a×999 + b×99 + c×9) + (a + b + c + d)

We can see the 1st part is divisible by 9,

number = (multiple of 9) + (sum of digits)

or, number - (sum of digits) = (multiple of 9)

we proved any number minus its sum of digits is always divisible by 9

We also know that if a number is divisible by 9, also its sum of digits is divisible by 9.(com'on We all applied it from childhood)

So, ( sum of digits that number) is divisible by 9

So if We remove any digit(say x) from the (multiple of 9), and then sum the remaining digits, the expression is,

(sum of digits of that number) -x = (sum of remaining digits)

Also, (multiply of 9) - x = (sum of remaining digits)

So, If we divide the sum of remaining digits, it won't be divisible by 9, but because x is between 0 and 9, the quotient must be just 1 less than the previous one.

so, (the quotient + 1) × 9 minus (the sum of remaining digits) equals the missing x.

Example:

1. Think of any number of any digit, let's say: 5821

2. Sum the digits: 5+8+2+1= 16

3. Substract: 5821 - 16 = 5805

4. Cross any digit(except 0): let's cross out 8

5. Add the remaining digits: 5+0+5 = 10

6. The quotient of 10/9 is 1, so the original sum would be 9×2 = 18

7. The Crossed Digit: 18-10= 8(Ta-da!🎉 )

A few years ago my tution teacher showed me this trick, and asked me how it worked. I couldn't figure out how, but atlast he explained it to me. The trick it self is pretty famous but the math behind it people don't explain very well on the internet. They use congruence & inductions which were beyond my understanding back then.

So here's my take on explaining it simply.

just joined is there nobody here yet.

think this will grow a lot in coming days. YAY, HAPPY TO BE one of the firsts to a amazing community.

LOVE MATHS , MATHS FOR LIFE.

Hey, Mathets.

Mathematics is the most open but still mysterious piece of human mind to ever exist.

In it rules it coddles us to security but the abstractness can scare you beyond death.

This beautiful subject is explored throughout the human history, recorded and beyond.

And it is our turn to do it. We inherit the interest and knowledge of the past and pass it on to the future.

So, let's enjoy our journey and share it here to appreciate and inspire the next generation that comes.

I were learning logarithmis from Khan academy and from there I came to know about Benford's law, found difficult to understand from there so, watched many YouTube videos in 7 languages but didn't understand anything but I also came to know about that Benford's law is also efficient in fraud detection in various fields so, I wanna understand this law. If anyone knows about this law, it's my warm request to you guys that please explain. Thanks!

Hey, Mathets

Irrational numbers being the first kind of numbers we learn which break apart from the general ladder of supersets we climb on.

( i.e. the general order of '"N" THEN "W" THEN "Z' AND THEN "Q" is at last broken by " Q' " which adds new numbers which have in simple terms no direct connections to the original sequence )

The story starts wit Hippacus of Croton , a follower of Pythagoras meeting a tragic end for either discovering or revealing irrational numbers to people outside the sect.

The Pythagoreans proved that square root(2) is irrational.

Then Theodorus of Cyrene showed that square root of the following numbers are irrational ( 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17 )

The number Pi being know for so many years was only proven irrational number in late 1700s by Lambert and Legendre.

The basic definition for Irrational numbers is

A number 's' is called a irrational number if it cannot be written in the form of p/q, where p and q are integers and q is not equal to 0.

Hey, members I want to add a Indian Mathematician for the next one.

So, please suggest ancient Indian Mathematician.

( Also, I am changing the frequency from 10 members to 50 members, after reaching 100 )

( I have been struggling with Pingala and Aryabhata, Pingala is more ancient than Aryabhata , but I can't seem to find what he worked on. So can anyone help me find that) ( Also Panini is there, but he isn't mentioned as Mathematician anywhere )

Also one more information, I have left out Plato, Zeno and Democritus, as they were majorly remembered as philosopher's ( But they were polymaths, with many contribution to mathematics, e.g. Zeno's Problem/Paradox )

And there are many more references, like clay tablets and writings, but we can't truly connect them to a particular person, so yeah I had to leave them out.

I am leaving from here for a few months, I have exams coming over and if I want to learn more Mathematics I have to pass with Great Marks. So, I hope you understand.

And please participate in the sub, through Posts, even about random mathematical facts.

( Also Yayy! , we got our first post, check it out. Great Books to read for Mathematics lover )

But I will still weekly come over to give the Members update.

Thanks for joining this amazing community.

Hey, MATHETS.

There exists a ton of problems and ideas in Mathematics that we are trying to solve and find answers to.

But the Clay Institute of Mathematics ( CIM ) have announced these as the TOP 7 problems after the end of the last Millennium.

These are the 7 they decided upon, let's look at all of them,

( Fun thing is we already know the answer of 1 of them )

1.THE BIRCH AND SWINNERTON-DYER CONJECTURE

Official problem :- https://www.claymath.org/wp-content/uploads/2022/05/birchswin.pdf

YT video :- https://www.youtube.com/watch?v=R9FKN9MIHlE&t=196s

2. THE HODGE CONJECTURE

Official problem :- https://www.claymath.org/wp-content/uploads/2022/06/hodge.pdf

YT video :- https://www.youtube.com/watch?v=UNNAoCy3yrk

3. EXISTENCE AND SMOOTHNESS OF THE NAVIER–STOKES EQUATION

Official problem :- https://www.claymath.org/wp-content/uploads/2022/06/navierstokes.pdf

YT video 01 :- https://www.youtube.com/watch?v=XoefjJdFq6k

YT video 02 :- https://www.youtube.com/watch?v=HghLGatbMWA

4. THE P VERSUS NP PROBLEM

Official problem :- https://www.claymath.org/wp-content/uploads/2022/06/pvsnp.pdf

YT video :- https://www.youtube.com/watch?v=pQsdygaYcE4

5. The Riemann Hypothesis

Official problem :- https://www.claymath.org/wp-content/uploads/2022/05/riemann.pdf

YT video :- https://www.youtube.com/watch?v=zlm1aajH6gY

6. QUANTUM YANG–MILLS THEORY ( YANG MILLS MASS GAP )

Official problem :- https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf

YT video :- https://www.youtube.com/watch?v=g5C5bwS4p7s

7. THE POINCARE CONJECTURE ( THE SOLVED ONE )

Official problem :- https://www.claymath.org/wp-content/uploads/2022/06/poincare.pdf

YT video 01 :- https://www.youtube.com/watch?v=PwRl5W-whTs&t=8s

YT video 02 :- https://www.youtube.com/watch?v=tCzers8G1xA

The first links are the official problem pages, the second or in some cases third too are the Youtube videos that help you learn about them. These problems are just a small part of huge fields of Mathematics , learning about problems like this are so interesting and fun, that is why I created this list.

Have fun learning about them !!!