MHB Favorite Mathematician: Rene Descartes

[Farmtalk]

Does anyone here have a favorite mathematician?

Mine would be the Frenchmen, Rene' Descartes. I like him because not only was he mathematical but also very philosophical.

In math, you may have messed with Descartes' discoveries if you have ever messed with:

• Descartes rule of signs (Roots of polynomials)
• The Cartesian Coordinate System
• The tangent line problem

 

[alyafey22]

Mine are two :

1- Riemann , imagine mathematics without the idea of analytic continuation that he used to extend many functions like zeta.
2- Euler , his contribution can not be neglected . You will find his name almost any time we are talking about series ,integration and special functions.

I can say that these two guys complemented each other with there fantastic work . Euler was tackling various unsolved sophisticated problems and his idea of connecting zeta function to primes had opened a new field of interest in number theory. Riemann ,on the other hand , is a perfect analyst whose hypothesis remains undetermined. His contribution in complex analysis is enormous.

 

[MarkFL]

Farmtalk, Nice choice...I believe Descartes was one of the giants to who Newton was referring when he said something along the lines of "If I appear to see farther than others, it is because I stand on the shoulders of giants."

I've always been intrigued by the life and works of Karl Gauss. He was a child prodigy, and remained a prodigy throughout his life.

Zaid, also good choices! If I recall correctly, Gauss was very impressed with the young Riemann and his works. And of course Euler is certainly a giant and should be on anyone's top 5 list. :D

 

[alyafey22]

Euler claimed that he made some of his greatest mathematical discoveries while holding a baby in his arms with other children playing round his feet.

 

[alyafey22]

During the twenty-five years spent in Berlin, Euler wrote around 380 articles. He wrote books on the calculus of variations; on the calculation of planetary orbits; on artillery and ballistics (extending the book by Robins); on analysis; on shipbuilding and navigation; on the motion of the moon; lectures on the differential calculus; and a popular scientific publication Letters to a Princess of Germany (3 vols., 1768-72).

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(Euler was 59) he produced almost half his total works despite the total blindness.

 

[alyafey22]

For a brief history of Euler see the link.

 

[I like Serena]

I think mine is Leibniz.
It seems he's usually rated second behind Newton.
But I feel his notation and understanding with infinitesimals is much more intuitive than Newton's dot notation or Lagrange's prime notation.
Since at heart I'm an applied mathematician/physicist, as I see it, Leibniz's impact on applied calculus and analysis is incalculable. ;)

Second is Euler, specifically with his $e^{i\phi}$ that pops up in many applied mathematics branches.
And also with his $\phi(n)$ totient function in number theory.

 

[chisigma]

Mine are two :

1- Riemann , imagine mathematics without the idea of analytic continuation that he used to extend many functions like zeta.
2- Euler , his contribution can not be neglected . You will find his name almost any time we are talking about series ,integration and special functions.

I can say that these two guys complemented each other with there fantastic work . Euler was tackling various unsolved sophisticated problems and his idea of connecting zeta function to primes had opened a new field of interest in number theory. Riemann ,on the other hand , is a perfect analyst whose hypothesis remains undetermined. His contribution in complex analysis is enormous.

I'm strongly certain that if someone Would have proposed to Leonhard Euler to demonstrate the Riemann's Hypothesis, he have though that the problem was not to difficult and and assigned it to a disciple (Nod)...

Kind regards

$\chi$ $\sigma$

 

[I like Serena]

I'm strongly certain that if someone Would have proposed to Leonhard Euler to demonstrate the Riemann's Hypothesis, he have though that the problem was not to difficult and and assigned it to a disciple ...

Kind regards

$\chi$ $\sigma$

I just knew that if you would respond to this thread it would likely relate to the ζ(s) function!
It seems to me as if most of your contributions relate to this function.
You seem to be the ultimate authority as far as this function is concerned.
I'd like to suggest that you incorporate ζ into your signature. ;)

 

[Farmtalk]

As far as more modern mathematicians, I like George Polya. He wrote a book on the approach of mathematics known as "How to Solve It".

Though his approach to mathematics is likely what made him more important in mathematical history, he also had a lifetime of study in number theory and series.

 

[MarkFL]

For my contemporary choice, see my avatar...Dr. Ed Witten. (Yes)

From Wikipedia:

"He has made contributions in mathematics and helped bridge gaps between fundamental physics and other areas of mathematics. In 1990 he became the first physicist to be awarded a Fields Medal by the International Union of Mathematics. In 2004, Time magazine stated that Witten was widely thought to be the world's greatest living theoretical physicist."

 

[chisigma]

I just knew that if you would respond to this thread it would likely relate to the ζ(s) function!
It seems to me as if most of your contributions relate to this function.
You seem to be the ultimate authority as far as this function is concerned.
I'd like to suggest that you incorporate ζ into your signature. ;)

The two 'Goldenkeys' that allow You to access to the 'Holy Graal' of Mathematics were both discovered by Leonhard Euler...

$\displaystyle \zeta(1-s) = 2\ (2\ \pi)^{-s}\ \cos (\frac{\pi}{2}\ s)\ \Gamma(s)\ \zeta(s)$ (1)

$\displaystyle \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^{s}} = \prod_{\text{p prime}} \frac{1}{1-p^{-s}}$ (2)

In my opinion the Riemann Hypothesis is a 'simple' consequence of (1) and (2)... for Leonhard Euler no more than a 'homework' (Wink)... Kind regards $\chi$ $\sigma$

 

[I like Serena]

The two 'Goldenkeys' that allow You to access to the 'Holy Graal' of Mathematics were both discovered by Leonhard Euler...

$\displaystyle \zeta(1-s) = 2\ (2\ \pi)^{-s}\ \cos (\frac{\pi}{2}\ s)\ \Gamma(s)\ \zeta(s)$ (1)

$\displaystyle \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^{s}} = \prod_{\text{p prime}} \frac{1}{1-p^{-s}}$ (2)

In my opinion the Riemann Hypothesis is a 'simple' consequence of (1) and (2)... for Leonhard Euler no more than a 'homework' (Wink)... Kind regards $\chi$ $\sigma$

So how do you feel about xi?

 

[chisigma]

So how do you feel about xi?

All what I say is that, like Dante in 'Divine Comedy', the way to 'Holy Graal' is for me still very very long (Thinking)...

Kind regards

$\chi$ $\sigma$

 

[ModusPonens]

Mine is Gödel. He may not be the best mathematician, but he was the best logician ever. And he proved the most deep/interesting theorem in the history of mathematics: his first incompleteness theorem.

Anyone who has read "The man who loved only numbers" can't help but "fall in love" with such an amazing human being: Paul Erdös. If you haven't read the book yet, read it imediatly! From the review on amazon (I couldn't put it better, except to mention that this book is also about many of his mathematician friends):

A mathematical genius of the first order, Paul Erdos was totally obsessed with his subject – he thought and wrote mathematics for nineteen hours a day until he died. He traveled constantly, living out of a plastic bag and had no interest in food, sex, companionship, art – all that is usually indispensable to a human life. Paul Hoffman, in this marvellous biography, gives us a vivid and strangely moving portrait of this singular creature, one that brings out not only Erdos’s genius and his oddness, but his warmth and sense of fun, the joyfulness of his strange life.

For six decades Erdos had no job, no hobbies, no wife, no home; he never learned to cook, do laundry, drive a car and died a virgin. Instead he traveled the world with his mother in tow, arriving at the doorstep of esteemed mathematicians declaring ‘My brain is open’. He traveled until his death at 83, racing across four continents to prove as many theorems as possible, fuelled by a diet of espresso and amphetamines. With more than 1,500 papers written or co-written, a daily routine of 19 hours of mathematics a day, seven days a week, Paul Erdos was one of the most extraordinary thinkers of our times.

Here's a picture of Erdös passing the torch to Terry Tao

View attachment 724

I also like Grigori Perelman, both for his monumental feat and for his detachment from wroldly concerns. Very admirable man.

And, for last, I have to mention Gröthendieck. Although I barely know what he really did, it is said that his influence in mathematics was absolutely gigantic! There's a saying "There are two types of mathematicians: those who don't understand Gröthendieck and those who pretend to understand Gröthendieck"

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Great topic! Thanks to the OP. :)

 

[Plato2]

Does anyone here have a favorite mathematician?

Here is my entry: http://www.maa.org/devlin/devlin_5_99.html.

Now I confess that he is my mathematical "grandfather". I also spent my life rejecting his social views. Nevertheless, his impact on the teaching of mathematics cannot be under-stated.

 

[tkhunny]

Jules Henri Poincaré

One historian, I recall vaguely, characterized him as the last mathematician to know ALL of mathematics. It is not that there have not been greater mathematicians since, or that there were none greater before, but there is now so much mathematics, no one ever will be characterized in this way again.

 

[alyafey22]

The two 'Goldenkeys' that allow You to access to the 'Holy Graal' of Mathematics were both discovered by Leonhard Euler...

$\displaystyle \zeta(1-s) = 2\ (2\ \pi)^{-s}\ \cos (\frac{\pi}{2}\ s)\ \Gamma(s)\ \zeta(s)$ (1)

$\displaystyle \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^{s}} = \prod_{\text{p prime}} \frac{1}{1-p^{-s}}$ (2)

In my opinion the Riemann Hypothesis is a 'simple' consequence of (1) and (2)... for Leonhard Euler no more than a 'homework' (Wink)... Kind regards

$\chi$ $\sigma$

To prove the Riemann hypothesis , I believe , anyone needs no more than an equation that explicitly states how to find the non-trivial roots . Now , does such a formula even exist!

 

[alyafey22]

Ramanujan a genius whose work is enormous in many fields of mathematics .He worked on mathematics developing his own ideas without any help and without any real idea of the then current research topics other than that provided by Carr's book.

 

[pedja]

Srinivasa Aiyanger Ramanujan

 

[mathbalarka]

In my opinion the Riemann Hypothesis is a 'simple' consequence of (1) and (2)...

Absolutely not! In the proof hat 40% of the zeros lie on the 1/2-line (1) is no where to be seen and (2) isn't been directly applied. Yes, in a proof (1) and (2) will always be needed but it wouldn't be very obvious that they are being used; so your "simple" idea is wrong.

My favorites are three (in no particular order, just the numerals being used) :

1) Carl Gustav Jacob Jacobi
2) Felix Klein
3) John Von Neumann

 

[Fernando Revilla]

Luitzen Egbertus Jan Brouwer made me think more than any other one.

 

[kanderson]

My favourite is john forbes nash jr and john von neumann. They all had something to do with economics.

 

[Farmtalk]

Srinivasa Aiyanger Ramanujan

Is he the guy that came up with the prime numbers formula?

 

[Prometheus1]

Jean Dieudonné.

 

[ModusPonens]

Is Bourbaki a valid answer? :D

 

[mathmaniac1]

John Nash-for his fight against paranoid scrizophenia along with doing mathematical wonders
Andrey Wiles-Proof of Fermat's last theorem
Langrange-for his wonderful methods of solving cubics and quartics using a complex number.
Heron-for deriving the simplified Heron's formula.I tried deriving it on my own.Its very hard.
Euler-I think he was ahead of his time in mathematics

 

[mathbalarka]

Is he the guy that came up with the prime numbers formula?

He is the person gave 500v shock to every great mathematicians. Ramanujan is most famous for 1729 = 12^3 + 1^3 = 10^3 + 9^3 but that's definitely not everything. He has some marvelous contribution in the analytic branches in mathematics.

PS : Deriving prime number formulas are easy :p.

Andrey Wiles-Proof of Fermat's last theorem
Langrange-for his wonderful methods of solving cubics and quartics using a complex number.

If Andrew wiles, then why not Tanyama,Shimura,Diamond,Taylor and all the ones contributed in the modularity theorem?

And I don't recall complex numbers are used in Lagrange's resolvent. Perhaps you are talking about the roots of unity?

 

[mathmaniac1]

If Andrew wiles, then why not Tanyama,Shimura,Diamond,Taylor and all the ones contributed in the modularity theorem?

I don't have too much detail of Shimura(even though I know he contributed to the proof of FLT somehow)thats why he is not in my list.

And I don't recall complex numbers are used in Lagrange's resolvent. Perhaps you are talking about the roots of unity?

I don't like calling it like that.It is a wonder complex number to me

 

[Bruce Wayne1]

Sesame Street's resident mathematician: Count von Count. Ok ok ... I have to be honest and say I'm not sure I can pick a favorite, simply because math has had so many wonderful contributions over the centuries. I do, however, favor the mathematicians that spoke French (not necessarily themselves French).

My search for my favorite mathematician would no doubt begin with my favorite mathematical theorems/concepts/formulas. I am very fascinated by Chaos Theory, so that brings Henri Poincaré (who was French). Then there's the Riemann bringing Bernhard Riemann into the fray. René Descartes arguably advanced mathematics in such a way that it probably made up for the lost time in the Dark Ages. However, I hear he was a bit of a mean person and not too pleasant.

I also keep in mind those that contributed great to mathematics but had tragic stories, like Nikolai Lobachevsky.

 

[topsquark]

I don't have much to say on the subject but because it's me...

I'd like to nominate not a Mathematician, but a Physicist. Some of Hawking's landmark works in Physics are showing some cracks, and there are a number of Physicists (and certainly Mathematicians) that can do everything that he can do, but there's one thought that makes me propose him:

He used to do most or all of it in his head.

-Dan

 

[youth4ever]

I like very much Euler.
Imagine how limited mathematics would be without the Euler formula.

I remained impressed for the rest of my life when I saw how he solved the famous limit

$$Sum from 0 to Infinity 1/x^2$$

A Famous Infinite Series

 

[Deveno]

I have 2 (both algebraists, of course):

Evariste Galois. He was misunderstood in his own lifetime, never got the education nor the recognition he wanted, was in and out of jail, and died tragically young, allegedly over the honor of a young lady (the truth about the duel, and even who he dueled, may never be known).

He was passionate, pig-headed, arrogant, and foolish. He died at 20 having a scant 60 pages of work to his name, almost all of it published posthumously. Oh, and he revolutionized mathematics.

Emmy Noether. A victim of sexual discrimination for most of her life, whose penetrating insight into algebraic structures gave abstract algebra the form we know it as today. I believed she casually remarked at a dinner party once that topology could be viewed in a more cohesive light by categorizing spaces by their associated topological groups. Reputedly one of the best lecturers and teachers ever, who often let her students and collaborators take credit for her work. Her first few years as a professor were unpaid.

Like so many other German intellectuals of the 20-th century, Emmy Noether was persecuted for being Jewish, eventually stripped of her position, and forced to flee her country. Noetherian rings are named after her.

Taken together, these two mathematicians remind me that mathematicians are exquisitely HUMAN, and possesses individual quirks that give them character, not only just genius.

 

[mathbalarka]

Paul Erdos.

Apparently a story I recall posted here about him and his collaborator Graham explains how sane minded he was. The one and only who can match the works of Euler (who, in turn, matches the works of Ramanujan - though of course not the age which is challenged by Terry Tao lately) the establisher of something I call TheBook-ism, a kind of a religion I believe in. The Number Theorist Extraordinaire, analytic, algebraic, transcendental, diophantine and combinatorial all the same; and the man whom communists feared, being one and only of the Hungarians to be able to go anywhere out and in of Hungary he and do anything he wants. Locally mad, totally genius and who accused of the supreme fascist of stealing his socks.

 

[ModusPonens]

I have to review my previous list. Not the names, but the order. Grothendieck must come first. He is the mathematician who has fascinated me the most, both on a professional level, and on a human level. Here's a quote from the short biography published on a AMS magazine:

Schwartz [Grothendieck's PhD advisor] gave Grothendieck a paper to read that he had just written with Dieudonné, which ended with a list of fourteen unsolved problems. After a few months, Grothendieck had solved all of them. Try to visualize the situation: On one side, Schwartz, who had just received a Fields Medal and was at the top of his scientific career, and on the other side the unknown student from the provinces, who had a rather inadequate and unorthodox education.

If you're so inclined, find the biographical articles from the AMS. There are several. The best one is divided in two parts. It's like reading the biography of an extraterrestial superior mind.

 

[Prometheus1]

I've heard so many amazing stories about Grothendieck. What's amazing is that he was able to view mathematics from bird's-eye view. Even when I'm learning elementary results I learn by considering specific examples, and find generality bit of an effort. He seems to have been completely the other way round. Consider, for example, the story of the Grothendieck prime (57):

One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. “He doesn’t think concretely.” Consider by contrast the Indian mathematician Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. “He really never worked on examples,” Mumford observed. “I only understand things through examples and then gradually make them more abstract. I don’t think it helped Grothendieck in the least to look at an example. He really got control of the situation by thinking of it in absolutely the most abstract possible way. It’s just very strange. That’s the way his mind worked.