Maths whizz solves a master's riddle

[n2doc]

Terence Tao successfully attacks the Erdős discrepancy problem by building on an online collaboration.

Chris Cesare

A mathematical puzzle that resisted solution for 80 years — including computerized attempts to crack it — seems to have yielded to a single mathematician.

Terence Tao, a mathematician at the University of California, Los Angeles, and a winner of the Fields Medal in 2006, submitted a paper1 to the arXiv preprint server on 17 September that claims to prove a number theory conjecture posed by mathematician Paul Erdős in the 1930s.

“Terry Tao just dropped a bomb,” tweeted Derrick Stolee, a mathematician at Iowa State University in Ames, the day the paper detailing the solution appeared online.

Like many puzzles in number theory, the Erdős discrepancy problem is simple to state but devilishly difficult to prove. Erdős, who died in 1996, speculated that any infinite string of the numbers 1 and −1 could add up to an arbitrarily large (positive or negative) value by counting only the numbers at a fixed interval for a finite number of steps.

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http://www.nature.com/news/maths-whizz-solves-a-master-s-riddle-1.18441

[cantbeserious]

1. Feats Of Imagination And Mind Amaze Me

eom

[Warren DeMontague]

2. This is America! Speak Englishes!

just kiddin'.

Good for him.

[gvstn]

3. I'm not good at math.

But I must say thinking about these types of "problems" creates new pathways in the brain. Every time someone says when will I ever use this math later in life, I think it doesn't matter, you have already opened new doors in your brain to think in different ways. Well worth the struggle. It will last a lifetime even if you can't remember how to actually apply/use Algebra in a particular incidence.

[Duppers]

4. Yes, new pathways indeed.

However, I must disagree that anyone working and solving number theory problems would never be at a loss to apply algebraic solution in any particular incidence
...unless they were to develop dementia in old age.

[Fortinbras Armstrong]

5. In the family room of my house, there was a really ugly square recessed light fixture in the ceiling

So I replaced it with a circular ceiling light. In order to cover the fourteen inch hole in the ceiling, I needed to know what the diameter of the new light had to be. So, I dusted off the Pythagorean Theorem to figure out that I needed a 20 inch light fixture.

Sometimes, high school algebra or geometry can come in handy.

[lastlib]

6. Sometimes I even find a use for the calculus and Trigonometry

I took in HS and college. Even if I can't remember an exact equation, I at least know how to approach it mathematically and get to the right equation.

[Thor_MN]

8. Wouldn't just measuring diagonally also solve the light problem?

I assume you were up there and measured the sides of the hole, but if you had put the tape measure diagonally across opposite corners, you could have measured directly.

Good use of math, especially if you didn't use a calculator, but there was an easier way.

[Fortinbras Armstrong]

9. What I actually measured was the side of the fixture.

Which I could easily do after I had taken it out. And yes, I did use a calculator: I remember the Pythagorean Theorem, but I do not remember how to calculate square roots using pencil and paper. (And even when I had to do it on paper, what I would do is estimate what the square root was, square it, sharpen my estimation using the result and repeat that process until I had reached the desired precision.)

[eppur_se_muova]

7. "Man's mind, once stretched by a new idea, never regains its original dimensions."

Man's mind, once stretched by a new idea, never regains its original dimensions.
Oliver Wendell Holmes
US author & physician (1809 - 1894)

http://www.quotationspage.com/quote/26186.html