At the age of seven, Johann Carl Friedrich Gauss corrected his father's salary calculation errors. Later, within ten years he wrote seventy critical scientific articles. Today there are almost no scientists who stick to it
My wife's exam periods during her studies were a fertile ground for new worlds that I came into contact with for the first time. The fact that I was dozing off while explaining the way psychology sees the activity of the human brain did not prevent her from continuing to detail in my ears the results of Freud's research. Aka, I came to life when the question is about the nature of the minds of geniuses, and one detail from quite a few studies caught my attention, which is the term "brain convolutions", and in intra-territorial language - the gray-white folds that look as if they were created by a failed origami artist. The interesting claim raised a well-founded hypothesis that the number of twists is the main factor in a person's genius. The mind of the German mathematician I chose to talk about this time is preserved in a jar to this day and was found to have the largest number of convolutions known in scientific literature. So yes, I could give my opinion on the obvious and obvious conclusion from these words, if I were not currently looking at the picture of another German whose nationality is wildly entertaining above his head and he, how to say it - belongs to the seed of a nation in which I am also a permanent member. But now we are dealing with what is known by most - "the prince of mathematicians" and his wonderful story throughout his life - Gauss.
Johann Carl Friedrich Gauss (Johann Carl Friedrich Gauss) was born in Germany in 1777 and already in his childhood it was evident that he was different from everyone else around him. Many stories have been related to the child prodigy about his many mathematical abilities that began, according to him, even before he could speak. The biographer Eric Temple Bell did a good job of telling about this in his famous book Men of Mathematics. It is claimed that already at the age of 3 his mathematical genius was evident when his father was busy preparing a pay sheet for several employees and after a long time of calculations little Gauss discovered a calculation error in an instant. Another thing is his amazing ability to learn foreign languages, it is said that at the age of 4, Gauss already knew 3 languages on Borean. Another story, the most well-known, took place within the walls of the school where he attended at the age of 7. The students in the class caused a commotion and were given as punishment to calculate the sum of the numbers from 1 to 100. At the time, such a calculation would take many minutes for an average adult, while Gauss succeeded Solve this after a few seconds and without noticing he "invented" a new branch of mathematics. Some of these things seem, how can we say it, inhuman and it seems that some of them are indeed fiction, but after reading the following biography, even the biggest skeptic of all will wonder whether these are indeed just stories or whether they are true.
Gauss began studying at the age of 11 in a gymnasium and at the age of 15 he was already awarded a scholarship to study at the academy on behalf of a local duke where he independently discovered "Bode's law" (regarding the movement of stars), the binomial theory, the arithmetic-geometric mean and important theories regarding prime numbers, these are the numbers that are divisible only by themselves and the digit 1. At the age of 18, he started his career at the University of Göttingen where he met his only friend Farkash Boleyai, whose son, one of the founders of non-Euclidean geometry, would also become one of the greatest mathematicians of all time.
Gauss graduated when he left behind one of the greatest achievements since the days of Greek mathematics which involved building complicated geometric shapes using a caliper. Later on, when he was only 24 years old, he authored a revolutionary book about number theory and in the same year also got a taste of the world of astronomy when he joined forces with a famous figure in this world named Zach in studies concerning star orbits. Gauss's ability is also reflected here when he knew how to describe the trajectories using the new theory he developed known as the "method of least squares" (the central theory that is the basis for probability studies and statistics on their branches).
At the age of 32, Gauss was appointed head of the observatory at the university where he studied, and there he wrote his second book, Eb Hachars, which dealt with celestial bodies (stars and their motion) in which he contributed greatly to the development of the differential equations, elliptical orbits of stars and a general description of finding the position of a star according to its orbit. Gauss continued for a long time in this role but at the same time he conducted many studies on diverse topics such as series of numbers, the hypergeometric function (which is also related to probability theory), integration (which deals with finding areas), generalized probability, partial differential equations (what we all learned in high school as a "derivative" but with a few more variables) and the field he loved most of all - the study of the earth and the forces acting on it, mainly on the topic of gravity. In 1818, he was asked to conduct a large-scale study on this last topic while gathering huge amounts of data during the day and doing all the complicated calculations in his head at lightning speed (remember there were no calculators or Excel tables then). During this research, he invented the device known as the "heliotrope" which is used to measure land using sunlight. This research and Gauss's other interests have yielded more than 70! Critical scientific papers in just 10 years. Just for the sake of illustration, a doctoral dissertation today takes an average of 3-4 years, while Gauss wrote 70 papers of a similar level (more or less) in the time it takes an ordinary (and usually smart) person to write 3 of the same type.
During the 80s of the same century, especially in 1816 when he was 39 years old, he began to investigate the Torah known today as non-Euclidean geometry while managing to prove the non-parallelism of parallel lines. This theory was known in the world of mathematics back in the days of the Greeks and was put together by Euclid. In order to write his book "The Elements" Euclid laid down assumptions as axioms, the fifth of which was the claim (in a simple description) that parallel lines will never meet. From this explanation it can be thought that this is "another mathematical claim", but the face of things is completely the opposite and it is therefore one of the foundations on which mathematics has been based for generations. Even Gauss himself knew this and despite an exchange of letters with fellow mathematicians he refused to publish such a revolutionary theory which, if found to be wrong, would have put the "prince of mathematicians" in a ridiculous light despite his achievements. As stated at the beginning of the article, this revolutionary theory will be carried out and perfected later by Gauss's genius student - Bernard Riemann, Janos Bolyai (Bolyai, son of Perkash Bolyai) and a Russian mathematician named Lobachevsky. Very amusing (and somewhat arrogant) were Gauss's words to a fellow mathematician when he heard about Lubachevsky's research: "I was 54 years ahead of him", meaning that he supposedly conceived the idea of non-Euclidean geometry already at the age of 15.
Gauss found great interest in the field of differential geometry and joining hands with the great physicist Weber produced a large number of books and articles about the earth and the forces that exist in it, especially the magnetic one. While basing themselves on the writings of the giants of mathematics Poisson (Poisson), Dirichlet (Dirichlet) and Laplace (Laplace), Phylles herself made a discovery of a global magnitude (literally) when the two were able to prove that there can only be two magnetic poles on Earth and Gauss even pointed out precisely the location of the magnetic field above the South Pole. This teamwork also led to the invention of the first "e-mail", a kind of primitive device for sending messages over a distance of about one and a half kilometers. In 1837 Weber was forced to leave Göttingen as a result of a political scandal in which he was involved and this caused a significant slowdown in Gauss's research and efforts, but what he tirelessly continued was an extensive correspondence with fellow mathematicians in which he always remembered to sting them that all the results of their many years of research had been discovered by himself a long time before, and he did not feel the need to present them publicly; If he were alive today, he would be able to summarize it in two words - "Well, really..." But despite this, it is surprising to discover that among all the others, Gauss actually appreciated an elite Jewish mathematician named Ferdinand Eisenstein, who, like Everest visible (Evariste Galois), died before reaching the age of 30 and we will tell his story another time.
In Gauss' last years, he served as an accompanying professor to two mathematics doctoral students, naturally also included in the pantheon of the greatest, named Maurice Cantor and Dedekind. The two wrote a fascinating description of Gauss' behavior when he gave free rein to his thoughts - Usually he would sit quietly and look down while folding his hands. He would speak freely, clearly and simply, but when he wanted to explain a new theory to us he would raise his head and with his beautiful blue eyes he would look penetratingly at the one who sat next to him throughout the conversation. If there were mathematical proofs According to him, he would get up from his chair and start scribbling formulas on the blackboard in amazing handwriting. When he was required for numerical examples, on which he placed special emphasis, he would write them on small pieces of paper."
In 1855 his health began to slowly deteriorate until he died in his sleep on a winter's morning.
41 תגובות
The article states "And if Gauss managed to solve it after a few seconds and without noticing, he "invented" a new branch of mathematics." Many articles also state that Gauss, without noticing, "invented" the method for summing an arithmetic column.
If we look at the owners of the additions in tractate Minachot page XNUMX page XNUMX, in the speech beginning "that they are one thousand eight hundred and thirty", we will see, in detail, the method supposedly "invented" by Gauss. The owners of the additions lived in the twelfth and thirteenth centuries AD. I mean, this method exists, black on white, at least five hundred years before Gauss
what is my name?
In the article there is a misunderstanding of the relationship between the geometric teachings.
If a straight line is given and a separate point is given that is not included in the straight line, is there a parallel to the straight line that passes through it?
Only one of three options is possible:
1. There is a parallel line(s) that passes through the given point.
2. The line does not have any parallel passing through the given point.
3. The data is not enough to answer the question.
According to the rules of geometry developed until the discussion of this question, there is no way to prove which of the three answers is correct.
Euclidean geometry chose answer number 1 as a starting point. This is called an axiom. An arbitrary assumption for which no proof was presented. (and later: there is only one straight line parallel to the point)
There is another non-Euclidean geometry that chose answer 1 as an axiom (and further: there is an infinite beam of straight lines that pass through the given point and all of them are parallel to the given straight line)
And there is another non-Euclidean geometry that chose answer 2 as an axiom.
And what about answer 3? As far as I know - this is because it has not been investigated.
(According to what is said in the article - it is evident that there is no understanding of the subject here)
Excellent, interesting and fascinating article! Even me, who is only 13 years old, you managed to captivate. Thank you very much, Liran.
I'm in the fourth grade, 9 and a half years old, I learned things you only learn in high school lol
I learned a lot from Gauss the calculus champion
I read on Wikipedia that the story of the punishment from which the invoice series originated is fiction... but a great story anyway.
And of course a very interesting article!
Nice but I'm only 9 years old lol I want a shape day how do you say let's say a shape that has 7 sides 8 and 9
First of all, I will start by stating that there is no doubt that the subject you chose to deal with is interesting in itself and, as was said in the comments before me, it is always nice to know who the people are behind the sentences and formulas you memorized in high school. I am not a mathematician, but a simple human being with an affection for the subject, yet the criticism directed by Gadi "took the words out of my mouth". I believe that it is possible to write an article in mathematics and explain it in an abundant way even to a person with no connection to the subject at all if you take into account two significant factors. One is that with a little creativity you can simplify complicated areas into easy to understand examples and the other is to give a little more credit to the reader. If you start from the premise that attaching a formula in order to clarify a claim in an article dealing with mathematics (how absurd) is a big deal on the reader, you are a little underestimating his intelligence, which I'm sure you didn't intend to do. If I am able to explain to my sister who calls math calculus and just started learning about non-integer numbers a proof of a formula I learned in XNUMXth grade then I have also shown her that she is able to understand things that older than her do not always understand and also (I hope) instilled in her the love, curiosity and beauty of the profession. The feeling is that the article "throws away" facts (which are also disputed) and does not tell a story. I recommend you read books such as "A Brief History of Time" and "Perma's Last Theorem" to get inspiration on how to properly popularize these fields.
Ehud and Adam Adom:
The truth is that the direct proof of the matter is much simpler.
Before I describe it, I will mention that in my opinion this is really a small example about Gauss and I also found this formula on my own while I was in elementary school.
Simple - the sum of the first and last is the same as the sum of the second and penultimate and so on. All these sums are N+1
If the number is even, there are N divided by two pairs, so the sum is N divided by two times (N plus one).
It is easy to see that the formula remains true for odd N because the middle number (the one that remains unpaired) is exactly (N plus one) divided by two.
It seems much simpler to me - among other things because it doesn't require knowing anything about areas (what's more, calculating the area is not a real proof, but I don't have the strength to explain in depth what the unfounded assumption this method of proof is based on)
I learned much more from the comments than from the article itself... 🙂
Thank you all.
Ehud, nice example, thank you
Sounds like an urban legend very loosely based on Ramanujan's life.
I wonder what we would have done at that time if we had been excited about the field of mathematics
And we had all the free time that was without TV / Internet etc.
I once read about a math notebook that contained amazing formulas and exercises
Which some Indian genius wrote after living for years alone in the forest with a single math book in his hand
An urban legend? … Do not know
Liran,
My intention was to make a clear separation between paragraphs that address the general audience and paragraphs that go deeper into the material. For example, it is possible to hide them, so that when a user enters the page, he will see the article as you wrote it, and in certain places where you want to expand, it will be possible to click on the word or sign you choose and the expanded paragraph will be displayed. That way no one will be alarmed and those who want to expand their knowledge will be able to do so on the same page.
Great, thanks Liran.
By the way, I was very interested in the line that says "The interesting claim raised a well-founded hypothesis that the number of twists is the main factor in a person's genius"
I have never heard of such a claim, and would love to read more about it. Is there a link I can use, or better yet - a reference to a scientific article?
Thanks
kid:
Regarding the first words - I understand what bothered you.
My words were mainly that I was offended on behalf of the writer and in retrospect - what seemed offensive to me was the style more than the content.
I must say that I do not excel in gentle language either, but I try to whip only those who seem to me to be acting dishonestly or out of disdain for others and not those who have simply made a mistake or expressed themselves imperfectly.
Regarding the riddles - let's start with this:
A faun is given, some of whose wigs are black and some are white (this means complete wigs, each of which is white or black).
It is a given that there are more black wigs than white, but no two black wigs share a profession.
It has been proven that in such a pawn it is not possible to block a ball (for the avoidance of doubt, the expression "ball blocked by a pawn" refers to a ball that touches all of the pawn's whiskers. A maximal ball that can be "inflated" in a pawn always exists, of course).
Here's another one:
Given N numbers less than a thousand whose least common multiple of any two of them is greater than a thousand.
It was proved that the sum of their inverses is less than 1.5
And for dessert:
A quarter plane (say - the one above the X axis and to the right of the Y axis) is organized as an infinite matrix (to the right and upwards).
Begin to write the elements of the matrix starting with the element in the left column in the bottom row with natural numbers while observing the following rule: it is allowed to fill an element only after the entire row to its left and the entire column below it have been filled and then the smallest natural element that has not yet appeared must be placed in it - neither in its row on the left nor in the column below .
Find (and prove) an efficient algorithm that will allow you to quickly answer the question of what is the number that sits in column I and row J
Note:
I'm giving you the puzzles just for fun.
I ask you not to post the solution here because I use these kinds of puzzles to put some of the pretenders to be smarter in their place and I don't want to waste "ammunition".
If you would like to talk about these or other puzzles, you are welcome to ask Avi Blizovsky for my email and show him this response as an expression of my agreement that he will indeed do so.
Maybe because in them I know the subject...
(Gladly, give one, or even several).
kid:
In my opinion, a proper response from someone who likes math and didn't follow the comments could have been something along the lines of "Well, give one example".
I read a lot on this site and on other sites and I must say that Liran's articles stand out for their eloquence and clarity. It is not clear to me how things catch your eye in them.
Michael, no one makes an effort. There are things that just jump out at the eyes (and the last comment does not deserve a response, except for the diagnosis that not everyone follows your comments or all the comments on the site at all).
The #1 mathematician in the world is Dr. Alex Spivak from Tel Aviv University, thanks to whom I passed linear algebra.
what a king!
Learn:
I think this is a wonderful article that is part of a wonderful series.
I am also a mathematician, but the limitations of writing an article for the general public are clear to me.
Moreover, I even enjoy hearing the personal stories of the mathematicians and I definitely think it's a great way to love mathematics over the humanities.
Many people tend to see a mathematician as a cold and alienated genius and presenting him as a person is, in my opinion, a very important act.
It is not at all surprising that entire books in this style (such as "Secrets of Cryptography", "The Last Theorem of Fermat" and others) are very successful.
In any written text you can find here and there mistakes or ways to improve and the fact that people try so hard to do it here just amazes me.
And to all the math enthusiasts who responded to this article:
During my comments on this website, I have already scattered quite a number of mathematical puzzles here.
For some reason you did not find it appropriate to deal with any of them.
Therefore, the question arises, what really motivates you?
Have you decided to prefer the profession of proofreading articles over the profession you say you love?
Thank you very much for the interesting article.
In my opinion, it would have been desirable to bring links for deepening for those interested: what things are supposed to do mathematically.
I have to admit that I am a little saddened by the attitude that in order to write an interesting article about mathematics, it must not contain mathematics. So the article said that Gauss was a mathematical genius, good and beautiful; He could equally say that he was a genius in endrinology and had impressive breakthroughs in Castronisophinia and the theory of the Khmermars. The main thing is that the reader should not be frightened by numbers.
Eyal - As I emphasized, I do not want to introduce any equation or theoretical information, if only because of the bad name given to mathematics in our country. You have to understand that numbers discourage many people, even if it is the method that Gauss used for the number scheme which is extremely easy, but if I were to include it - the average reader would think to himself - "Oh, one more time equations and explanations". I have been interested in mathematics since high school and read a lot about it. More than once I tried to explain all kinds of fascinating things that Gauss and his ilk did to other people, just like that to show them what genius is, but they just can't understand even things that seem completely trivial to me, and these guys learn one by one. If I write down certain things, I first think about how it will be interpreted by the average reader and not the scholar, of course I can incorporate Gauss's proof regarding the minimum distance of the residuals in the regression, but how useful will it be to the average person? Why should a pensioner who just sits down in front of the computer and wants to enjoy popular science understand what regression or divergence is? There is no doubt that these are revolutions in the world of mathematics, but again - the question is who you turn to. Take a small example, in his book on Hadova for students, Ben Zion Koon gives the life story of Leibniz and Newton in 5 lines, do you think this is enough to understand the contribution of the two to the world? Certainly not, but he briefly noted that his goal was to prove theorems and not to describe the lifestyle of those who proved them. The fact that he omitted a large part of the biography of these two giants does not indicate that he does not know them or underestimates them, but that every matter has its time and place.
Ehud - I mentioned Eric Temple Bell's book in this article. It is indeed a good book, there are some exaggerations in it but really fascinating, it is for example a book that is suitable for every person and not only for mathematicians or those with a mathematical background.
I want to give you an example from the Jewish sources - if you ever read the Talmud, you could quickly understand that the vast majority of the stories there never happened even though the heroes in it were completely real. Maimonides divides the people who read the Talmud into three - there is a group he calls - "the poor who destroy the religion" and it includes people who think that the stories are completely true and Abraham really jumped into a burning oven and came out alive, everything is true. There is the second group that is a great evil for religion, and this is the group of wise people (in matters of science and not religion) who claim that the very fact that the story is historically incorrect and physically illogical - there is no point in reading it. And there is the third group, which is made up of the truly wise, who read the Talmudic story and understand that it is a parable that the Tanim and the Amorites brought to teach them important morals, but used images and folktales to bring the great ideas also to the people of the land who do not always manage to understand philosophy and high-level nonsense.
Eric Temple Bell records things, some of which probably did not happen, but the question is, how does this detract from your reading? If he had omitted these things and inserted proofs of Gauss's equations in their place, would this be what the average reader would assume? He actually came to describe to people how smart and more importantly - human these mathematicians were, they too had loves like Galois, they too could be depressed like Henrik but more, and that is what is important. I wrote that Gauss invented the arithmetic series because that's what I got from my teacher and what's written in the biographies I've read so far. If he finds that someone else discovered it a few years before him, will that take away from the genius? After all, his genius in the end is not summed up in what he did at the age of 7, but his articles that you and I and the other academics read and are enthusiastic about their sophistication and originality, this is what makes him special, and this is actually the purpose of the article, to make people enthusiastic about Gauss and his friends and want to know more about them, also Historically, but mainly from the mathematical point of view, people need to understand that mathematics can be a wonderful thing and it's a shame that we don't have such a bad name here. Of course I'm not arguing against you specifically, of course not, I'm aiming at the majority in Israel, and yes - the majority don't really like math and don't really understand math, so in order to reach them I don't want to use formulas even if they are the easiest to understand, I want to use only words , in a language that everyone can understand.
Yigal - Look, in relation to Yanosh Boleyai, the fact that he is the son of Farkash is certainly important since the latter was the only and best friend of Gauss. The connection between the two is described at length in other biographies I found, but adding information would cause the average reader to deviate from the main point and he is Gauss. I intend, if I may, to bring many more mini-biographies to this excellent site, mainly from the Middle Ages to the 19th century. I want people to read the articles and make connections between one another to get a perspective on the power relations between the mathematicians in terms of time, place and more, the goal is to show the mathematicians as people and not as calculators. The average reader can probably understand from my words that there was a lot of tension between Gauss and Boulayi Jr. since they both competed for the invention of the new geometry, and this, in my opinion, is what will interest the reader, the intrigues between them, the power struggles and not necessarily the fact that in spherical space parallel lines can meet at a certain point, this not the main thing.
Regarding editing the text, I review it at least 3 times and also send it to my wife for review. I try to do my best in editing the text, but I am not a linguistic consultant or a skilled editor to bring the product to XNUMX% form-wise. In any case, I try to correct the text each time according to what you say here, so your comments, positive and negative, are important to me.
As I have said before and here I will conclude - for me it is enough that a young man who reads these articles will be inspired by these giants and begin to study mathematics in depth, who knows - maybe the second manifestation is hiding for him somehow and we don't know. I try to do everything I can from my side. I'm not a mathematician but I have a pretty good mathematical background, and that's the way things are. Take the articles lightly and not with rigorous evidence as is required when it comes to mathematical proof, that is not the goal here.
My friend, I will soon upload the third article. This time I will deal with one of the Italian giants of mathematics. I would love to hear your responses to this article as well.
thank you and good night,
Liran Zeidman
Liran,
The topics you cover are interesting, but two small problems slightly detract from the potential of enjoying the articles:
1. Unnecessary interpretation of unimportant directions (...that he was the son of... who...) and irrelevant.
2. Editing of the text is missing (perhaps it is enough that you read the text you wrote again and look at it as a side reader).
Successfully
Well done for the initiative!!!
Since you are interested in the review, I will comment that I was also disturbed by certain inaccuracies.
By the way, I am puzzled by the fact that you claimed that the child Gauss invented a new field of mathematics by doing so
who quickly summed up all the numbers up to a hundred.
The sum formula has a simple and beautiful graphic explanation that can be explained even to an elementary school student.
Simply indicate the numbers by dots and write the dots in ascending order like this
At the top on the right side is a dot below which are two dots
And so on... if you start recording the points uniformly on the right, you get a triangle
whose base is the last number in the sum, n, and so is its height, the triangle is paid into the rectangle by
Adding another triangle, calculate the area of the rectangle and divide by two: n(n+1)/2
0
00
000
0000
Add another triangle
0 ****
00***
000**
0000*
Calculate the area and divide by two.
Note: It may be possible to put a link to additional sites for those with a special interest.
By the way, I assume you know, but there is a canonical book about the history
of mathematics: "Men of Mathematics" written by
ET Bell
Once again it was successful and congratulations on the initiative, the first two episodes were fascinating.
Hi Liran, an example or two of "nonsense" that is not related to mathematics:
"At the age of 18, he started his career at the University of Göttingen where he met his only friend Farkash Boleyai, whose son, one of the founders of non-Euclidean geometry, would also become one of the greatest mathematicians of all time."
There is a space before a comma here, and a missing space after "non-Euclidean" (perhaps not necessary, but definitely improves readability). Apart from that, there is an unsuccessful radicalization of Boulay (an important mathematician, but if he is one of the greatest of all time, there are hundreds of all time greats).
These are things that, in principle, should be handled by an editor, and in my opinion, they are not the main problem here. As mentioned, these style statements about the parallels do not seem to me to be lacking or strange, but simply wrong, misleading and confusing. I really appreciate your good intention and am sure that many of the readers will enjoy the article and be intrigued and I am happy about it; I just think you can do it even better.
Idea - maybe you can write an article that appeals both to the average person and to more learned people. These are also those who enter this site. how? For example, extensions of a different color can be planted so that those who are not knowledgeable or not interested, will skip them.
Hey learn,
I enjoyed reading and waiting for the continuation of the series.
As for the fundamentals of economics, apparently it really is mind boggling.
She should have explained that the rich are getting richer and the poor remain poor...
hi dot,
First of all thank you for the support.
I must correct - they do not confuse the mind. As I noted, I believe they are scholars and therefore look at this article in a different perspective than another person and therefore things seem strange or lacking to them.
About a year ago, my macroeconomics lecturer, who is a professor in our department, was invited to an interview with London and Kirschenbaum regarding the terrible situation that prevailed at that time in the world. She had about 5 minutes to explain to a sleepy audience with a high school education the main teachings of the father of modern economics, John Maynard Keynes. During the dialogue, she tried to explain a concept called "Keynesian multiplier" in economics, which is basically the foundation of all economic thought at the macro level and from the first term you study in the degree. As an economist, it was immediately clear to me what was meant, but my father, who was sitting next to me, required "childish" and imprecise explanations exactly as she gave because in order to understand this you have to make all kinds of certain assumptions and the multiplier formula should be in front of your eyes. If I were advocating the method of the writers who disagree with me, I could claim that her understanding of macroeconomics is lacking, but this would sound a bit problematic since she was a regular member of Paul Krugman's team, winner of the Nobel Prize in Economics this year.
Before I wrote down these articles, I talked with the editor and submitted that I do not intend to add any complicated formula or phrase to the mini-biographies that I will write down, since this website is directed, among other things, to a population that does not belong to the top of the Israeli academy, and this is a very welcome thing, yes there will be more such websites. Therefore, it is necessary to address the readers in such a way that they will get a "taste" and not an explanation, even if this taste is flawed by inaccuracy, because the basis of things is correct but the accuracy of things will only destroy instead of benefit, even if it is a relatively simple formula.
I hope that average people will read these articles and say to themselves - "Wow, what a genius this Gaussian is, and how did Galois become such a genius at an age when I would have been studying equations with one vanishing point? What interested them so much in mathematics that they devoted their whole lives to it?" How do their findings really affect us on a daily basis? "
If I can get one person to research the stuff about Borim, I've done my part. And who knows, maybe there are more geniuses with unrealized potential because they didn't have an interesting direction and needed a little push.
Liran I'm with you...
They just confuse the mind.
Another comment:
Gadi - Following on from the previous statements, I also wanted to ask for clarification regarding the term "Elig", is this a low level of Hebrew or syntax errors? If so, I would be happy to receive comments on this topic as well.
Maxim - if you give a lecture at the German Academy of Mathematics where Leibniz studied and point out that Newton is the one who invented calculus, what do you think the reactions will be?
Regarding India, many claims have also been made about the ability of the ancient Egyptians (Papyrus Ahmes) in finding algebraic equations of the form we know today, but a thorough examination will bring you to the conclusion that these are nonsense. The concept of equations like you learned in high school or academia was only brought to the learned community around the Middle Ages by mathematicians like François Vietta and his friends.
Spike - As I mentioned, I would love to hear comments and criticism, but it is difficult for me to gauge the nature of an abstract concept such as "I expected" because you did not specify what expectations you had from an article he wrote in a newspaper and not a purely scientific article.
My goal is not to teach mathematics and insist on a portrait of definitions and formulas, but to give a taste of this world to average people so that they will read more biographies and engage in mathematics itself if this is possible for them.
Hi Liran. I have no argument with the need to write in a way that is legible to the lay reader and I did not "complain" about it - what bothers me is writing wrong things, or writing meaningless things.
However, you raise a good point - what does the lay reader actually understand from reading an article in which he is mainly thrown a lot of blown-up names of fields in which Gauss dabbled? My feeling is that not much - just that Gauss was a smart guy who dabbled in a lot of things with big names. He hears that Gauss "proved the non-parallelism of parallel lines", and what does he understand by that? is nothing; It's just that Gauss proved the aforementioned lack of parallelism, which doesn't mean anything to him (except maybe "parallel lines aren't really parallel", which is a bit confusing - isn't it?)
If so, perhaps it is still worth making some effort to explain what Gauss did in simple words (of course, not by copying from lectures by mathematicians intended for mathematicians but by the hard work of correctly describing mathematical facts using easy-to-understand words and images), and since the canvas is wide, Focus on two or three key things (non-Euclidean geometry is a good example; and the sum of the arithmetic column that Gauss discovered independently can also be presented to the lay reader without much difficulty - even a child can understand the idea).
I agree with the first two and in addition I expected more Gauss was indeed one of the greatest geniuses ever and he deserves a slightly more serious summary!
Hello Capricorn.
As I mentioned in the response about Galua, I would be happy to receive any opinion, comment and criticism from the readers even if it is negative as understood from your words. Accordingly, I would like to respond briefly:
The purpose of these articles is to bring the world of mathematics to the group of people that is the majority, unfortunately, in our society where mathematics is considered difficult and boring. An approach to such a group places more emphasis on interesting and suggestive writing than mathematical/conceptual writing. As an economist, I am familiar with the method of least squares and the important principles of the partial differential theory, which is the basis of all serious economic theory, and certainly also the Gauss-Jordan method for finding determinants, and it is true - I too looked in awe at this mathematics that I learned from Merzi in the academy, but did Do you think the average reader would have continued reading my article if I had combined such words? Do you think that it is possible to explain what a differential or an integral is to the average person outside the walls of the academy? I have set myself a goal in these articles not to introduce foreign equations and terms that can quickly drive away the reader who is not well versed in mathematics.
The same for non-Euclidean geometry. I assume with a high degree of probability that most of the people reading this article have only encountered in their lives the case of parallel lines as proposed by Euclid. Also, you can assume that I know his fifth axiom as it is an important milestone in the world of mathematics, but do you think any of the readers were Do you understand the original definition? In addition to this, I could have copied the full content of Riemann's well-known lecture regarding the non-parallelism of lines and the sum of the angles in a triangle in spherical space, but what would a high school student or a pensioner seeking knowledge get out of it if they happened to come across this article?
My friend, according to your words I believe you are a scholar. Therefore, my request is one - remember the instructions for writing a seminar at the university: the examiner does not know the material and you have to explain everything (underlined twice) in a way that will be clear to the reasonable uneducated reader.
Gauss deserves many articles about him, his fields of activity are each a fascinating world in itself and I find it hard to believe that there is a person who is able to testify that he knows all of Gauss's writings so that he can write a complete biography. Although the website editor does not limit me in place, I always keep 2 WORD pages, again - in order not to bore the reader.
Hope I managed to clarify the controversial points,
Liran Zeidman
Agree with Gadi!
I also feel this while reading.
And there are inaccuracies, for example:
That Gauss "invented" a new branch, which one exactly? Invoice series?
It is also known that he is not the first to identify this pattern.
Today I read that even in India in the first millennium, the "formula" for finding the sum of an invoice series was known.
The intention behind the article is good, but the execution is bad. The article is simply lazy in parts, and confusing in other parts. For example, to say "proved the lack of parallelism of parallel lines" or to present the axiom of parallels as presented is simply wrong and misleading (what is true is that the axiom of parallels means, approximately, that given a line and a point outside it, one and only one parallel passing through the point can be transferred to the line - in geometry Non-Euclideanism is not the state of affairs). Also saying that partial differential equations is "like the derivative we learned in high school but with a few more variables" is wrong and confusing, etc., etc. Gauss deserves an article that does more than throw out a bunch of complicated names of fields he dealt with and doesn't even properly explain what those fields are.
It should be noted that along with Gauss and Riemann, it is doubtful whether Einstein would have completed the theory of general relativity in his lifetime.
Amazing article.
We agreed on a lot about it, but now you added more to us.