2 HS students from NOLA shake up the world of math in a huge way... (1 Viewer)

[buzd]

I had to take abstract math for comp sci. To this day I don't know what I learned and I finished near the top of those classes. I later learned about Ramanujan and his equations, just looking at them gave me a headache

We had one class where the tests would be a single problem, it was open book, and it took 2 90 minute class periods to complete. I enjoyed it, but it wasn't easy.

 

[Nisey55]

Amen Bro. I starting struggling at calc 2. I'm not bragging, but i',m pretty good in math. Trig is a breeze.
These young girls are heroes in my humble opinion

Calc 2 and above is Eienstien and above in inteligence level. I've never claimed will I be there. I will claim Math
is the true test of a persons IQ

Well shoot, according to your claim I'm an idiot. I always considered myself to be intelligent but my math skills (other than common sense math) are pretty lacking.
There's alot more to IQ than mathematics.

 

[DCSaints_Fan]

Pfft. Calc 2 isn't even the beginning. Things get really weird when you start getting into satellite math and Fourier transforms and such.

/math degree

I started down the path of math. My high school actually offered post calculus courses Multivariable Calclus and Linear Algebra(also known as matrix algebra). You learn pretty cool stuff there - calculus in three dimensions is pretty interesting and connects quite neatly with physics, esp. electricity and magnetism. In college as a freshman I took Differential Equations, Complex Analysis then as a sophomore Number Theory/Intro to Proofs and Modern Algebra. I also had a fair amount of discrete math with my comp sci major. Mostly alot of stuff with sets and logic.

But I found it started getting dry and technical. I took Advanced Calculus and Linear Algebra but they just seemed like rehashes of the same thing. I've heard this complain about Real Analysis, upper division undergrad/lower division grad course, its a real slug and almost no one likes it but I never got there. I also never got to the more exotic topics like advanced geometry (e.g. non-Euclidean). If you want to understand general relativity, this is required.

But to this day the math problems you see in competitive math still astound me how people ar eable to solve them, and relatively quickly (e.g. on average within 30 minutes). I took the Putnam once as a freshman but didn't score (most people actually dont). One guy who went ot my high school was a total math whiz though and was on IMO and actually won the Putnam one year. But it looks like he never went down the academic path - I don't even think he got a masters much less a PhD. And he could have named his grad school being a Putnam fellow.

About a year back I got sucked into to watching Michael Penn solve some of the these competition math problems.

 

[LAhotsauce]

Pythagoras came up with the theorm 2000 years ago. Since then it has been proven correct by using abstraction. These 2 young women were able to prove it using trigonometry. Something no one has been able to do in 2000 years.

Pythagoras might have turned it into a "theorem", but it was already in practical use long before somebody named Pythagoras was on earth.

Matter of fact I believe there are some old papyrus that shows ancient egyptians creating problems with it as a teaching tool.

 

[staphory]

Pythagoras came up with the theorm 2000 years ago. Since then it has been proven correct by using abstraction. These 2 young women were able to prove it using trigonometry. Something no one has been able to do in 2000 years.

I don’t do well with math. It’s all Greek to me.

 

[Sun Wukong]

So they haven't actually written a paper or submitted any of this for peer review.

Feels like the cart is being put way before the horse here.

 

[tjharris]

I don’t do well with math. It’s all Greek to me.

 

[kansast]

Can someone briefly explain what it is these girls did to “turn heads” in the math world ? Compared to my simple google search that showed apparently several ways of proving this ? Not trying to down play it any. Just haven’t read anywhere where they try to explain what they did

 

[faceman]

Well shoot, according to your claim I'm an idiot. I always considered myself to be intelligent but my math skills (other than common sense math) are pretty lacking.
There's alot more to IQ than mathematics.

No are not a idiot. I was only speaking of standardized tests.

I remember damn near revolting when UNO wouldn't let me take calculus (took it in high school; 31 math ACT)... These days I don't even remember my days in college algebra.

My ATC was jumbled. I scored a 34 in math and a 13 in English. I did not care about having to diagram a sentence
in later life

I know now I was young and dumb. I wish I paid more attention in grammar class.

 

[faceman]

Pfft. Calc 2 isn't even the beginning. Things get really weird when you start getting into satellite math and Fourier transforms and such.

/math degree

You are above me sir. I say this with the most humble respect.

 

[faceman]

Can someone briefly explain what it is these girls did to “turn heads” in the math world ? Compared to my simple google search that showed apparently several ways of proving this ? Not trying to down play it any. Just haven’t read anywhere where they try to explain what they did

They used the scientific method. Without it One cannot disprove the existence of God or even Santa Clause

 

[NewOrleansFan]

Can someone briefly explain what it is these girls did to “turn heads” in the math world ? Compared to my simple google search that showed apparently several ways of proving this ? Not trying to down play it any. Just haven’t read anywhere where they try to explain what they did

To prove the Pythagorean theorem, one needs to use trigonometry. However, Pythagorean theorem is the base foundation of trigonometry. So if someone uses trig to prove the Pythagorean theorem, they must’ve already accepted that the theorem is true before proving it. The proof then becomes circular logic.

The two girls countered in their work that the claim above isn’t true. They were able to use the Law of Sines to prove the Pythagorean theorem, which did not rely on circular trigonometry.

 

[DCSaints_Fan]

So they haven't actually written a paper or submitted any of this for peer review.

Feels like the cart is being put way before the horse here.

I wouldn't say that quite yet. The math world can be pretty brutal.

Andrew Wiles presented his proof of Fermat's last theorem at a conference before writing a paper. And he didn't even advertise that it was the proof of Fermat's last theorem, it was only the relatively small group of people in the math world who understood what was going on that was able to deduce that he did prove it.

Wiles's proof of Fermat's Last Theorem - Wikipedia

en.wikipedia.org

 

[FullMonte]

To prove the Pythagorean theorem, one needs to use trigonometry. However, Pythagorean theorem is the base foundation of trigonometry. So if someone uses trig to prove the Pythagorean theorem, they must’ve already accepted that the theorem is true before proving it. The proof then becomes circular logic.

The two girls countered in their work that the claim above isn’t true. They were able to use the Law of Sines to prove the Pythagorean theorem, which did not rely on circular trigonometry.

I'm impressed with what is being reported, and I'm looking forward to reading their paper whenever it is published. But, I've also seen the Pythagorean theorem proved with geometry.

In short. Take a right triangle with sides a,b, and c. Make four copies, rotating each 90 degrees, and placing it so that the points are touching, and sides a of the copy and b of the previous triangle are in line with each other. This creates a square with sides of length a+b. Inside of this square is a smaller square with sides of length c (rotated a bit). The area of the large square is (a+b)^2. The area of each triangle is 1/2(ab). The area of the smaller square is c^2. The area of the large square is also equal to the sum of the areas of the four triangles and the smaller square, 4[ 1/2(ab)] + c^2 (which reduces to 2ab + c^2). This leaves us with (a+b)^2 = 2ab + c^2. Multiply out the left side, and we get a^2 + 2ab + b^2 = 2ab + c^2. Subtract 2ab from both sides, and you are left with a^2 + b^2 = c^2.

 

[Sailorsaint]

I'm impressed with what is being reported, and I'm looking forward to reading their paper whenever it is published. But, I've also seen the Pythagorean theorem proved with geometry.

In short. Take a right triangle with sides a,b, and c. Make four copies, rotating each 90 degrees, and placing it so that the points are touching, and sides a of the copy and b of the previous triangle are in line with each other. This creates a square with sides of length a+b. Inside of this square is a smaller square with sides of length c (rotated a bit). The area of the large square is (a+b)^2. The area of each triangle is 1/2(ab). The area of the smaller square is c^2. The area of the large square is also equal to the sum of the areas of the four triangles and the smaller square, 4[ 1/2(ab)] + c^2 (which reduces to 2ab + c^2). This leaves us with (a+b)^2 = 2ab + c^2. Multiply out the left side, and we get a^2 + 2ab + b^2 = 2ab + c^2. Subtract 2ab from both sides, and you are left with a^2 + b^2 = c^2.

That's what you consider, "In Short"?