Zhang is the typical demonstration of pure perseverance of traditional Chinese mathematicians: knock harder and harder until the truth is finally cracked.

His work is based on the prior half-way proof by 3 other mathematicians “GPY”:

Gap between Primes:

Let p1 and p2 be two adjacent primes separated by gaps of 2N:

p1 – p2 = 2 (twin primes)
eg. (3, 5), (5, 7)… (11, 13) and the highest twin primes found so far (the pair below: +1 and -1)

p1 – p2 = 4 (cousin primes)
eg. (7, 11)

p1 – p2 = 6 (sexy primes)
eg. (23, 29)
…
p1 – p2 = 2N

Euclid proved 2,500 years ago there are infinite many primes, but until today nobody knows are these primes bounded by a gap (2N) ?

Zhang, while working as a sandwich delivery man in a Subway shop…

Carl Friedrich Gauss is named the “Prince of Math” for his great contributions in almost every branch of Math.

As a child of a bricklayer father, Gauss used to follow his father to construction site to help counting the bricks. He learned how to stack the bricks in a pile of ten, add them up to obtain the total. If a pile has only 3, for example, he would top up 7 to make it 10 in a pile. Then 15 piles of 10 bricks would give a total of 150 bricks.

One day in school, his teacher wanted to occupy the 9-year-old children from talking in class, made them add the sum:
1 + 2 + 3+ ….+ 98 + 99 + 100 = ?

Gauss was the first child to submit the sum within few seconds = 5,050.

He used his brick piling technique: add

1 + 100…

To prove the FLT, Prof Andrews Wiles used all the math tools developed from the past centuries till today. One of the key tool is the Galois Group,  invented by a 19-year-old French boy in 19th century, Evariste Galois. His story is a tragedy – thanks to the 2 ‘incompetent’ examiners of the Ecole Polytechnique (a.k.a. “X”), the Math genius failed in the Concours (Entrance Exams) not only once, but twice in consecutive years.
Rejected by universities and the ugly French politics and academic world, Galois suffered set back one after another, finally ended his life in a ‘meaningless’ duel at 20.

He wrote down his Math findings the eve before he died – “Je n’ai pas le temps” (I have no more time) – begged his friend to send them to two foreigners (Gauss and Jacobi) for review of its importance. “Group Theory”…

The story of Ramanujian:

http://en.m.wikipedia.org/wiki/Srinivasa_Ramanujan

http://mathworld.wolfram.com/Hardy-RamanujanNumber.html

We have seen how two 19th century greatest mathematicians Cauchy and Gauss who were not helpful to two young unknown mathematicians Galois and Abel, now let’s see an opposite example — the discovery of an unknown math genius Ramanujian by the greatest Pure Mathematician in 20th century Prof G.H. Hardy.

References:
1.
http://tomcircle.wordpress.com/2013/11/27/163-and-ramanujan-constant/

2.
http://tomcircle.wordpress.com/2013/07/04/ramanujian/

In the previous story (#9) we mentioned Ramanujan having the luck of being spotted by Prof G.H. Hardy as the treasure of mathematics, another Chinese Hua Luogeng 华罗庚, 20 years younger than Ramanujan,  was also coached by Prof Hardy, although Prof Hardy did not realize Hua’s potential later to the modern mathematics in China.

Hua dropped out of secondary school due to poverty, he worked in his father’s little grocery shop as the shop assistant. His talent was spotted by the French-educated mathematician Prof Xiong Qinlai ( 熊庆来) in Tsinghua University 清华大学 from a paper the young boy published – on Quantic Equation Solvability error made by a Math Professor Su. Hua was admitted to Tsinghua University as assistant math lecturer on exception. Later he was sent to Cambridge on 庚子赔款 Boxer Indemnity scholarship.

When Prof Hardy met Hua, he let Hua choose between:
1) Work on a PhD…

This video explains how to perform stick multiplication and shows how it relates to the method of partial products.

http://en.m.wikipedia.org/wiki/Augustin-Louis_Cauchy

We mentioned Augustin Louis Cauchy in the tragic stories of Galois and Abel. Had Cauchy been more generous and kind enough to submit the two young mathematicians’ papers to the French Academy of Sciences, their fates would have been different and they would not have died so young.

Cauchy was excellent in language. He was the 2nd most prolific writer (of Math papers) after Euler in history. When he was a math prodigy, his neighbor — the great French mathematician and scientist Pierre-Simon Laplace — advised Cauchy’s father to focus the boy on language before touching mathematics. (Teachers / Parents take note of the importance of language in Math education.)

Cauchy’s language education made him very rigorous in micro-details. This was the man who developed the most rigorous epsilon-delta Advanced Calculus (called Analysis) after Newton / Lebniz had invented the non-rigorous Calculus (why?).

Rigorous epsilon-delta…

We all know how terrible homework is and how long it takes and how you could be doing SOOO many other things that are not homework. Like nothing productive. That kind of stuff. And once we actually get started, it’s so difficult to keep on track. Sometimes we hit a brick wall and so we just stop and do something else. And then there are those moments where you have so much work to do that you take a nap. Or the infamous “due tomorrow do tomorrow” mentality. When teachers assign a certain portion of reading you think, “Sweet! No homework!” just because you don’t get credit for actually reading it. This affects almost every single person and extends beyond schooling and even into your real life work. What should you do? Well I can’t tell you, but I can confide in the type of mentality I have and what…

Free, engaging educational games for students in K-8 to practice skills in math, language arts, geography, and other subjects

Features multiplayer mode so students can practice while competing against classmates in real time

via tumblr published on March 02, 2014 at 05:30PM

I hope that most of you have either asked yourselves this question explicitly, or at least felt a vague sense of unease about how the definitions I gave in lectures, namely

$latex displaystyle cos x = 1 – frac{x^2}{2!}+frac{x^4}{4!}-dots$

and

$latex displaystyle sin x = x – frac{x^3}{3!}+frac{x^5}{5!}-dots,$

relate to things like the opposite, adjacent and hypotenuse. Using the power-series definitions, we proved several facts about trigonometric functions, such as the addition formulae, their derivatives, and the fact that they are periodic. But we didn’t quite get to the stage of proving that if $latex x^2+y^2=1$ and $latex theta$ is the angle that the line from $latex (0,0)$ to $latex (x,y)$ makes with the line from $latex (0,0)$ to $latex (1,0)$, then $latex x=costheta$ and $latex y=sintheta$. So how does one establish that? How does one even define the angle? In this post, I will give one possible answer to…

I remember my secondary teacher told me that 1 cannot be divided by 0.

Why 0 cannot be divisor?

“Because it is just not permitted in arithmetic”, he said.

Well. It is not permitted because it is not permitted. A kid shouldn’t ask much…

Throughout my N years of learning and teaching, I know that 0 cannot be a divisor because if it does, something will go wrong in mathematics. But how things can go wrong other than the calculator showing some error messages?

Here is a simple example.

Let say

  1 / 0 = SOMETHING,

is valid.

If so, I can multiply both left hand and right hand sides by 0.  And, it becomes

1 = SOMETHING * 0.
1 = 0.

Oops, something is wrong with the arithmetic. That’s why we can’t have 0 as the divisor.

Well. Perhaps you are not yet convinced and ask “how about…

Galois and Abel had many things in common: both worked on the Quintic equation (of degree 5). Abel first proved there was NO radical solution; Galois, who was 9 years younger, went one step further to explain WHY no solution (with Group theory).

Both were young Math genius not recognized by the world of mathematics. Their fates were ruined by the same French mathematician Cauchy, who hid their Math papers from the recognition of the French Academy of Science.

Both died young: Abel at 26,  Galois 20.
Abel was poor and weak in health. His dream job of professorship came 2 days (too late) after his death.

Ironically, today the top Math award in monetary term (US$ 1 million) for the world’s top mathematician is named after this extremely poor mathematician – the Abel Prize.

http://scienceworld.wolfram.com/biography/Abel.html

(Go to YouTube “Niels Henrik Abel” to read the English sub-title)

If you want to feel comfortable with math, you have to understand that the world exists through a series of complex patterns. Admittedly, we can’t say this for sure. The universe is so infinitely large (and by the time you finish reading this blog post it will have already grown by an immeasurable amount), and our grasp on math is so tentative as humans that it’s impossible to notice or even understand the pattern at work on a large scale. However, the belief in patterns can be thought of more as a philosophy rather than an explanation for the world.

One of the most fundamental patterns in Algebra and number theory is the Fibonacci sequence. Now, this can get pretty dense, so bear with me.

The Fibonacci sequence was first introduced in 1202 by an (you guessed it) Italian mathematician Leonardo Fibonacci. Though, as we’ll soon see…

Follow up with the story #1 on FLT (Fermat’s Last Theorem),  it was finally cracked 358 years later in 1994 by a British mathematician Professor Andrew Wiles in Cambridge.
The proof of FLT is itself another exciting story, a 7-year lonely task on the attic top of his Cambridge house, nobody in the world knew anything about it, until the very day when Prof Wiles gave a seemingly unrelated lecture which ended with his announcement: FLT is finally proved. The whole world was shocked!

http://en.m.wikipedia.org/wiki/Wiles%27_proof_of_Fermat%27s_Last_Theorem

Part 1/5 Andrew Wiles and FLT Proof:

(Part 2 – 5 to follow from YouTube)

Speech at IMO by Andrew Wiles:

While reading “Our Daily Bread” during my daily Bible reading time, it strikes me an idea to create a series of “Our Daily Story” for our Math studying time.
The former makes the Bible alive, connected to our daily life in the context of scriptures; the later will make Math alive, motivate the interest and curiosity of the students to the otherwise cold (and scary, boring) subject, connecting Math to their familiar world.

It is encouraged by Math educationists that a10-minute math story time before class will enthuse the students, to want to know more about the Math topic relating to the mathematician in the story.

My first story will start from The Fermat’s Last Theorem (or FLT), simply because I admire the amateur mathematicians who, for all better choices to spend their spare times, are attracted by the beauty of Math and to become great mathematician…

To prove the FLT, Prof Andrews Wiles used all the math tools developed from the past centuries till today. One of the key tool is the Galois Group,  invented by a 19-year-old French boy in 19th century, Evariste Galois. His story is a tragedy – thanks to the 2 ‘incompetent’ examiners of the Ecole Polytechnique (a.k.a. “X”), the Math genius failed in the Concours (Entrance Exams) not only once, but twice in consecutive years.
Rejected by universities and the ugly French politics and academic world, Galois suffered set back one after another, finally ended his life in a ‘meaningless’ duel at 20.

He wrote down his Math findings the eve before he died – “Je n’ai pas le temps” (I have no more time) – begged his friend to send them to two foreigners (Gauss and Jacobi) for review of its importance. “Group Theory”…

http://chinesepuzzles.org/nine-linked-rings/

Math Theory: Galois Field GF(2)
http://tomcircle.wordpress.com/2013/04/02/field-dedekind-web/

Computer games – some people like them and some people hate them (usually parents).  However at Gastrells Primary School the students  make computer games.  These computer games  have a difference, the student design them to teach Maths.  The first project they undertook was the development of their own coordinate game. This was so successful that the students have volunteered to teach the whole class how to develop coordinate games.  Furthermore, the school has gained some great homegrown resources.

So far on this blog we’ve given some introductory notes on a few kinds of algebraic structures in mathematics (most notably groups and rings, but also monoids). Fields are the next natural step in the progression.

If the reader is comfortable with rings, then a field is extremely simple to describe: they’re just commutative rings with 0 and 1, where every nonzero element has a multiplicative inverse. We’ll give a list of all of the properties that go into this “simple” definition in a moment, but an even more simple way to describe a field is as a place where “arithmetic makes sense.” That is, you get operations for $latex +,-, cdot , /$ which satisfy the expected properties of addition, subtraction, multiplication, and division. So whatever the objects in your field are (and sometimes they are quite weird objects), they behave like usual numbers in a very…

In a Ferris wheel, the circle is used as the main shape of the ride and makes the ride continuous. A circle is special and useful in this situation in the aspect that all the carts are equally distant from the center point and the wheel rotates 360 degrees. The second picture shows a slide from one of the rides in Star City that when it was built, people calculated the right slope in order to give excitement to the riders but not that much for safety. The concept of slope was used then.

Trigonometric Functions are used to “solve” or think of a solution to everyday life problems even though we don’t see them all. For example, the picture above shows a sketch that we can solve by using trigonometry. There are many other examples like:

a. Hula Hoop-concept of tangents is used. Every time it rotates one side…