TIL Gauss personal diaries indicate that he had made several important math discoveries years/dec...

The dude was a genius. He told his children he didn't want them going into science/math since he didn't want them to bring down the family reputation he created.

He also is known for that famous anecdote where he was being a lil shit in third grade, and his teacher instructed him to leave the class until he added up the numbers from one to 100. Shortly after being sent out, he returned with the correct sum after developing a formula for adding subsequent numbers (n/2)*(n+1)

Edit: parenthesis for clarification, spelling.

He told his children he didn't want them going into science/math since he didn't want them to bring down the family reputation he created.

Unlike many anecdotes about him, this one is actually 100% verifiable, too. His grandson told a professor this in a letter, and the letter is available online.

EDIT: This is silly of me. I really should have just posted the letter.

Page 1:

Page 2: http://www.gausschildren.org/genwiki/index.php?title=File:1898-12-21-p2.jpg

Page 3: http://www.gausschildren.org/genwiki/index.php?title=File:1898-12-21-p3.jpg

Page 4: http://www.gausschildren.org/genwiki/index.php?title=File:1898-12-21-p4.jpg

Page 5: http://www.gausschildren.org/genwiki/index.php?title=File:1898-12-21-p5.jpg

Page 6: http://www.gausschildren.org/genwiki/images/c/c6/1898-12-21-p6.jpg

Haven't you ever tried to construct a polygon with a compass and straight edge only to get to the end and realize that the number of sides was not a product of distinct Fermat primes and a power of 2?

something like 100 % i guess

om 1795 to 1798. While at university, Gauss independently rediscovered several important theorems. His breakthrough occurred in 1796 when he showed that a regular polygon can be constructed by compass and straightedge if and only if the number of sides is the product of distinct Fermat primes and a power of 2. This was a major discovery in an important field of mathematics; construction problems had occupied mathematicians since the days of the Ancient Greeks, and the discovery ultimately led Gauss to choose mathematics instead of philology as a career.

but WHY is this important? this always happens to me when i go spelunking into mathematics and science articles on Wikipedia.

With n=100, n/2*(n+1) = 5050

Gauss noticed that if he was to split the numbers into two groups (1 to 50 and 51 to 100), he could add them together vertically to get a sum of 101.

1+ 2 + 3 + 4 + 5 + … + 48 + 49 + 50

100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

...

48 + 53 = 101

49 + 52 = 101

50 + 51 = 101

Gauss realized then that his final total would be 50(101) = 5050.

Sauce: http://mathcentral.uregina.ca/qq/database/qq.02.06/jo1.html

Edit to include more detail

happens every day, still don't know why tho.

Or he cared so much about his children's emotional health that he wanted them to make their own way independently and not have to bare the burden of continuing another's legacy. TomAto, tomAHto.

People tend to view great scientists like Darwin or Newton as lone geniuses making great discoveries in some kind of vacuum. While their works are revolutionary, they weren't alone and were working from prior research and theories that proceeded them.

For example, Alfred Russel Wallace was also developing his own theory of evolution via natural selection at the same time as Darwin, even corresponding and publishing papers together. And Wallace was a staunch defender of On the Origin of Species after its publication.

There is a difference though, if he said "find the right path for your skills, don't just go into math and science because I did"

Vs

"Don't do math or science, y'all can't touch this."

Eric Temple Bell was a mathematician who wrote hagiographies, and was a huge bullshitter. He was not really a historian and is not to be trusted. The statement from the thread title is pretty typical of the kind of nonsense he was apt to say. His famous book is basically just a collection of sensationalized accounts and all the folklore he had ever heard about famous mathematicians from the past repeated as fact. If I recall, he literally didn't even record his sources; we just have to take his word for it.

Don't worry, it's completely natural for boys your age.

There's a much simpler way to derive his result. Just double the series by adding the 0th element to the nth, the 1st to the n-1 etc. You're left with n values, each equal to n+1. Divide by 2 to account for the duplication to get the final result. No need for awkward calculus or car metaphors.

Isn't this perverse? Someone who believes in family legacy but doesn't believe in their ability to educate their children must be harboring some perversities.

n/2*(n+1)

n(n+1)/2

Not every mathematical result is important. At least not in the way most people would use "important". Some math is indeed important in the sense that you require it to do some types of science or if you want to build stuff.

Geometry is indeed important and is the basis for a good portion of math you learn in school. But when one develops/studies a theory, you being to ask questions to yourself. In Euclid's geometry everything could be done with a straight edge (with no markings) and a compass. You can double lengths, bisect angles and create all sorts of stuff, but an interesting problem is what CAN you create? You can make triangles, squares and pentagons fairly easily but what about other polygons?

Gauss showed you can make a regular 17-gon but the septagon eluded us for a long time. Why? Cause it turns out its impossible. A young mathematician named Galois showed exactly which regular polygons you can make. The solution, usually given in the fourth year of a bachelors in math, is quite elegant if I do say so myself.

I dont even know of any other math that uses this result let alone any actual applications of it. But it's like a fun puzzle.

tl;dr not important but an elegant solution to an "interesting" problem.

Darwin also held off publishing his work on evolution for 20 years. Imagine he died in those 20 years. How would the world be different? Would evolution be discovered later? Nobody knows...

He's gauss he can say what he want

Huh. What are the chances all of the numbers from 1-100 would add up to 5050?

1/1. Would read again.

It's important for mathematics... it doesn't really have much to do with the price of beans.

It's not even a coincidence either that we have so many examples of contemporaries in a field discovering the same things at similar times.

Humans are largely a product of their environment, and if any idea hits you because you've been marinating your brain in the atmosphere of your field, there's a good chance it'll happen to someone else too. Put the same information in, get the same information out.

Of course this isn't always the case, but it explains enough for me.

but then how can he sound smart

Gauss worked it out using the pairing method.

I have a feeling DisproveRainbowDash had the other result pointed out to him in a lesson and has backward engineered its "obviousness"

It's not super hard to figure out on one's own.

pfff. Because first thing everyone thinks of summing a series is the parallels to distance calculations /s

I dunno but my friend sally got 14 beans for .25 cents each, and my friend billy got 23 beans for $5.00. What's the average they spent per bean?

Let n = 100%.

n = 100%.

If someone went back in time and made him published his math theory's I'd still be here on Reddit wasting my time.

Sorry but I have some news

But I'm a girl..

I don't know but your friend Billy got ripped off.

Alfred Russel Wallace independently came up with a theory of evolution and selection pressure at the same time as Darwin, but with much more extensive physical evidence that he had collected himself.

Yelling is a natural reaction when taking calculus

Above genius IQ here. I loathe it when plebeians inflate their common tongue to appear more intelligent.

Thank you, that formatting was giving me an eye twitch.

Did you just come up with a cool new formula to do that?!

When I was 11 I made a formula to find the sum of angles in a 2d polygon it was (n-2)*180 with n being number of sides, I was so exited but it turns out there already was a formula and my parents laughed at me when I told them :(

Read again. Sally paid .25 cents per bean.

We would be on Reddit 3 by now and wasting time at an exponential rate

being important in mathematics is different from being important to regular people.

consider the map coloring problem. nobody really gives a crap about coloring maps with the least number of colors possible. but the proof for it is an important math proof.

another example is the couch problem. it basically boils down to prove that a certain method is the best way to transport a couch around a corner. there's also the question of what shape of couch is best for getting around corners, if your goal is to have as much surface area on the couch as possible. there have been mathematicians that have worked out this problem in 2d. but there's no rigorous mathematical proof for either of these problems in 3d. it's a totally pointless mathematical question but it's proof is still undiscovered after decades.

how does this relate the polygon construction problem? well the ancient greeks were trying to figure out the highest sided polygon that you could construct (using compass and straight edge). that's how long that problem went unanswered. literally millennia and he solved it. that's why it's important.

edit: there's not even a rigorous proof for the 2d couch problem. there's a pretty good conjecture for the current believed best couch. but there's no rigorous proof that it is in fact the optimal couch.

His famous book is basically just a collection of sensationalized accounts and all the folklore he had ever heard about famous mathematicians from the past repeated as fact.

A historian in the tradition of Herodotus.

No you're thinking of weeping

For every idea that has ever cross your mind, thousands have thought about it, hundred writes it down somewhere, but only less than 10 study it.

-some redditors.

consider the map coloring problem. nobody really gives a crap about coloring maps with the least number of colors possible. but the proof for it is an important math proof.

U wot m8? Let me quote from my favorite book, The Nature of Computation:

Colorful Graphs At most scientific conferences, the vast majority of talks are boring. This makes it especially frustrating when two of the few talks you actually want to see take place at the same time in different rooms. Suppose, in a rare act of candor, each conference participant supplies the organizers with the list of talks they want to hear. Suppose further that there is a plentiful supply of lecture rooms, but only k time slots. Can we schedule the talks in such a way that makes everyone happy? That is, can we assign a time slot to each talk, so that no two talks take place simultaneously if someone wants to see them both? We can formalize this as follows. Let G be a graph whose vertices are the talks, and let two talks be adjacent (i.e., joined by an edge) if there is someone who wants to attend both of them. We want to assign one of the k time slots to each vertex in such a way that adjacent vertices have different time slots. Let's represent each time slot by a color. A k-coloring is an assignment of one of k different colors to each vertex, and a coloring is proper if no two adjacent vertices have the same color. Thus we wish to solve the following kind of problem:

Graph k-Coloring Input: A graph G Question: Is there a proper k-coloring of G?

Despite its colorful terminology, Graph k-Coloring is a serious problem with a wide range of applications. It arises naturally whenever one is trying to allocate resources in the presence of conflicts, as in our scheduling example. For instance, suppose we are trying to assign frequencies to avoid interference. This problem is equivalent to Graph k-Coloring where each vertex is a device, k is the number of frequencies and there is an edge between two devices if they are close enough to interfere with each other.

Map Coloring is merely the special case of Graph Coloring where the Graph is planar (can be drawn in 2d without any edges crossing). So if you can somehow guarantee that your allocation problem leads to planar graphs and you have at least 4 "colors" available, math tells you that there's a solution without any conflicts. That sounds useful to me.

You welcome're

I was the hero for this question in high school. It was science bowl, senior year, and our first time we had made the national tournament. I was on a team with some hella smart guys, so I had only answered a couple of questions the whole game (if you got it wrong your team couldn't answer any more, so I was normally pretty timid not to answer, because I didn't want to hurt our smart guys). So we are in the last round of the round-robin, and we needed to win this game to make it into the playoff bracket. You got 4 points for getting the question right and 10 points for the bonus, and we were down by 12 going into the last question.

The question was "What is the sum of all integers from 1-20?" The other team quickly buzzed in 420 (heh) and were wrong. So I was waiting for my team to buzz in and they didn't! So with like one second left I sheepishly answered 210 and we got the question right (and the bonus) to make it to the playoffs. We end up placing 3rd and got to meet the department of energy head or something and cool shit like that. And now they're like all at MIT - but they didn't know the sum of the numbers from 1-20. Hahaaaaaaa.

I wish you had. Yes. Seriously. I mean that.

This world needs kids who love science and reason more than ever right now. A teacher or parent who knows that their kid is talented enough to reinvent the wheel using their limited knowledge would hopefully stimulate that.

Think of the sort of person you could be today if your educators had capitalized on your appreciation of math. Think of the achievements you maybe could have made.

Living your entire life going 'well fuck, at least I didn't make a fool out of myself for doing something my peers probably couldn't do nor be arsed to even try or consider' is an absolute shame imho.

well he is dead now so i dont think he will be saying very much

I can get a 1lbs bag of beans for a dollar. They're both getting ripped off. Tell them to shop at reputable grocery stores in the future.

And here I just thought he made my monitor go wacky.

TFW your dad throws shade at your math abilities from the get go

You have it completely wrong. Leibniz published his work on calculus in 1696, but maintained that he had been working on it since 1675. Newton had been using calculus in his work since 1666 and published a full explanation of his notation in 1693. Newton both invented and published calculus well before Leibniz. The question is whether Leibniz used Newton's work as inspiration for his own discovery of calculus. Newton thought he had, and Leibniz maintained that he came up with it independently of Newton.

Also the f'(x) notation for a derivative was used by Lagrange, not Newton. Newton used the dot notation (a dot over the x to indicate the derivative).

are you doing CALCULUS here?! This sounds like CALCULUS! (im taking calculus right now)

Not smashed enough to forget the next day aka not drunk at all

Isn't it obvious? Pizza delivery dude. This revolutionizes pizza delivery algorithms! Hotter, fresher pies, to more customers, in less time.

This was the foundation for what we consider modern pizza: stuffed crust, breadsticks, even jalapeño poppers which had been envisioned as a deliverable good since the latter days of the Roman empire became provably profitable with Gauss's pizza delivery route construction theorem.

This in turn led to the Ninja Turtles, Terminator, Snoop Dogg, and the replaying of Star Wars in the late 90s. And of course 9/11 and the advent of drone delivery.

Yes Leibniz actually discovered calculus just before Newton but Newton beat him to the printing press. That's why you have two common notations for the derivative of a function f(x) given by f'(x) and df/dx. Newton used the prime notation f'(x) whilst Leibniz used df/dx.

After reading about his proof about constructible polygons, I am incredibly confused. Apparently a heptadecagon (17 sides) is a product of a power of 2 and a Fermat Prime? How can 17 possibly be a product of a power of 2? I get that 1 is technically a power of 2, but if that's how the term "power of 2" is being used in this case, why even bother with that part of the definition, since literally every integer under that definition would be a product of a power of 2.

A regular n-gon is constructible if and only if the n is the product of distinct Fermant primes and a power of 2.

It must be a product of both to be constructible, is what this means. So you have to be able to write the number n like n = F_1 F_2 ... F_j *2k where F_i is a Fermat prime.

17 is a Fermat prime, and 1 = 20 is a power of 2.

So, since n = 17 = 17*1 = 17*20 , we have written n = 17 as a product of distinct Fermat primes and a power of 2. Therefore, the regular 17-gon is constructible by compass and straightedge.

A regular 7-gon is not constructible - 7 is prime, and therefore not a product of primes, so it will be constructible if and only if it is a Fermat prime. But it isn't: the first few Fermat primes are 3,5,17,257.

I created a formula to get the original equation from its derivative only to find out a week later about integrals. Thank God I told no one about it.

Geometry is indeed important and is the basis for a good portion of math you learn in school. But when one develops/studies a theory, you being to ask questions to yourself. In Euclid's geometry everything could be done with a straight edge (with no markings) and a compass.

What about trisecting it? Checkmate atheists

The same chances that n=102 adds up to 5253.

GODDAMMIT, WADE!!!!You're an idiot.

From what I've seen, Wallace had better evidence but Darwin was a better communicator.

Whomst've'st

He did believe in the ability to educate his children. All his children were educated. He specifically said that he believed none of his children would surpass his accomplishments, therefore they shouldn't go into math for fear of ruining the family name. His grandson also noted that none of Gauss's children (so the grandson's aunts, uncles, and father) inherited Gauss's natural power. Apparently one guy came close (being able to perform really complicated calculations without pen and paper, which is something Gauss could also do).

How much do beans go for nowadays anyways?

Alright, I'm a little slow: Can I fit these 300 melons in my trunk now or what?

I improved on Newton's notation by denoting the antiderivative 'f(x)

Someone give me an Erdos number

Helpfully, there's a couple of numberphile videos on the subject.

And

Make me.

Yes.

https://en.wikipedia.org/wiki/List_of_things_named_after_Carl_Friedrich_Gauss

2pooky4mesk8r

Why are you yelling. Anything to do with changing values usually involves calculus.

No, Gauss proved that can't happen.

Gauss he can!

Sounds like he needed to visit /sub/getmotivated

This guy sounds amazing but all i can see is grandpa Munster in the thumbnail.

No he paid around 21 cents each, whereas sally paid 25 cents each.

Newton was publishing his work involving calculus since 1666, well before Leibniz published his work in 1675. Newton simply didn't give much of an explanation of calculus in any of his publications (I guess he assumed it was trivial and could be left as an exercise for the reader), until after Leibniz published his work on calculus.

Here you go: ∞

Fukin fite me bro ive had this dicussion one too many times ill fuking smash ur gobber m8

Newton did the same with calculus. When Leibniz discovered it, he claimed he knew that shit- showed his notebook as proof (or something like that). When asked why he didn't let the world know earlier his reply was, " shit! The world wouldn't have understood it."

Alright, let's do it with this demonstration 90° angle . . .

About tree-fiddy

This is a great novel about Gauss and Alexander von Humboldt. Really portraits their characters quite well.

This guy smokes.

Erm, the same chances that the naturals from 1 to 1000 would sum to 500,500.

Regarding the summing all numbers up to some bigger number though- that ones pretty believable. It's not super hard to figure out on one's own. It's very much like a problem involving the distance traveled by a single accelerating body.

It's the average of the starting number and the ending number, plus the difference between the starting number and the ending number. You can get this by imagining a car accelerating at 1m/s. The distance (read: the sum of its velocity at each second) will be the average velocity traveled at the time you measure plus the initial velocity times the time taken. Since it's a constant acceleration, we know that it's just the average of the starting and the ending velocity. This means that the sum of all the numbers in a given range will be the distance traveled by a car initially going the starting value and accelerating at a rate of one meter per second for the difference between the starting value and the ending value in seconds. This means that the distance (the sum) is eaqual to the (initial value* time)+((the initial value + the final value)/2)

A genius ten year old could definitely come up with this, minus the whole car bit.

It's the average of the starting number and the ending number, plus the difference between the starting number and the ending number.

(0 + 100) / 2 + |(100 - 0)| = 150