Who are the top five most influential mathematicians? I have five in mind that are important and are helpful when teaching math as related to MathCounts. Many students do not know of any mathematicians and I think it is important to teach some of the more important and influential mathematicians. It is also possible to study some of the lesser known but just as important mathematicians, but that would be for a more advanced class. I usually have the students learn some basic facts and the date of birth using the Peg System. Here are my top five. What do you think?
1. Carl Friedrich Gauss 1777-1855
Gauss is the undisputed champ in my book. His great genius was demonstrated at a young age. When he was in school, his teacher gave the class a task that he thought would take a long time to complete. His task was to sum the first 100 numbers. Gauss completed the task in a very short time. Much later, when the teacher checked the answers, Gauss had the correct answer. He summed the first hundred numbers not by addition, but by multiplication. He found that there are 50 pairs of 101. And 50 x 101 = 5050. He would always tell this story later in his life on how he was the first to complete the task.
He did not publish much and his motto of ” few, but ripe” reflected his style of not publishing his mathematics until it was polished to perfection. Many times, other mathematicians would publish their findings and Gauss would say that he already knew about it. His work in number theory has shaped the way it is presented today.
2. Archimedes cira 287-212 B.C.
Archimedes spent most of his productive years in Syracuse. Many engineering students know him for his mechanical contraptions such as the screw pump, a claw that could flip a ship, and the heat ray that would use mirrors to burn a hole in a ship and sink it. In mathematics, he gave very close approximations of pi. Archimedes was always more interested in the theoretical studies than the more practical applications of his inventions. He died when a Roman soldier killed him after Archimedes refused to move away from his geometry problem that he was working on in the sand with a stick.
3. Newton 1643-1727
Newton gave us Newton’s laws of motion and of universal gravitation. He, along with Leibniz, developed calculus. Many topics in physical science and math are related to Newton and all of his discoveries.
4. Bernhard Riemann 1826-1866
Riemann’s paper, published in 1859, titled ” On the Number of Prime Numbers Less Than a Given Quantity” has sparked much interest and research into the question of how the prime numbers are structured. This is the greatest unsolved mathematics problem and students are real interested to know what the problem is about. This is a very interesting topic for a club like MathCounts were number theory and prime numbers come up all the time. I recommend the book Prime Obsession by John Derbyshire for a interesting read with some good history and mathematics.
5. Paul Erdos 1913-1996
Erdos was an interesting mathematician. He was very social and always tried to work with others. He was the opposite of Gauss who liked to work alone. He called young students “epsilons”, which means a little. He would give challenges to students to prove small theorems and pay them if they could prove it. He liked to travel around the world to work with other mathematicians and would say ” another roof, another proof”. His whole life was mathematics. He did not know how to drive or even how to do his laundry. He hated to waste time on anything but mathematics. Others who have published with him are given an Erdos number. The lower the number, the more directly related to working with him you are. I wish I had met him.
I agree with you. Very few math students can name say a bout 20 mathematicians. The list as well as the short intro was brilliant. Like you I too wish I had met Erdos.
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Hello Manjil Saikia., and thanks for stopping by. I’m working on my list of mathematicians for next year and it’s a bigger list.
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june Reply:
May 19th, 2010 at 4:12 am
okay then, i thought this was a game site!
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nia Reply:
March 8th, 2011 at 3:54 am
wat a dummy u are hahahahahaha
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nia Reply:
March 8th, 2011 at 3:57 am
sike nahh…this my first time on this website im doing a school project this is cool learning about are history on famous poeple well gotta go talk to u some other time when i gotta do another project did not mean to be mean when i said wat a dumyy hahahaha i nwas just jocking,sorry i like to joke around hbu do u like to joke around lol? well byee
I disagree with this list partially. If the list was constructed purely on the basis of influence and necessarily greatness( as such a list would have to atleast contain the likes of a jacobi and a srinivasa ramanujan) then it was an egragious error to omit Leonard Euler . Further, I think Leonard Euler was a far greater mathematician than Gauss.
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Fabio (São Paulo, Brazil) Reply:
October 6th, 2010 at 7:57 pm
The reason Gauss is generally regarded to have been superior to Euler (and to the rest of mathematicians) is the fact that Gauss’ breakthroughs are more profound and rigorous than Euler’s. Read the article below for an interesting evaluation of Gauss’ legacy:
http://www.wlym.com/~animations/ceres/PDF/courageofgauss.pdf
The list below provides a ranked hierarchy which roughly represents the majority of opinions on the subject:
http://james.fabpedigree.com/mathmen.htm
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Kevin Smith Reply:
October 19th, 2010 at 5:14 am
Fabio,
Thanks for the nice article on Gauss. There is not much published on his life. I also enjoyed reading the Top Mathematicians List
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Dujon, you are partially right I agree about Ramanujan and Euler, not on Jacobi.
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Dujon Dunn,
Thanks for visiting and your point is well taken. I tend to think who is the most influential related to middle school mathematics. That’s why I put Erdos in the top five because he influenced many students to go into mathematics by encouraging them with number theory problems and would even pay them to solve a problem.
I think Ramanujan was a great mathematician with a vision unmatched till this day. I usually link him together with G.H. Hardy and the taxi number.
My 6-10 contains Euler, GH Hardy, and Ramanujan.
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Thanks for replying kevin, I see your point about influence as it pertains to middle school students Erdos and Newton are certainly influencial in that respect.
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Srinivas Ramanujan is great matematician of this century and many of mathematician in india also present who doesn’t get explosure……..
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to me,i think archimedes is the greatest of all mathematicians,he was born in the time where little was known but has proved that he is really archimedes.”give me a place to stand on and i will move the earth
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what do you think about khawrizmi”father of algebra”?
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june Reply:
May 19th, 2010 at 4:13 am
salam bhaia and hows life.
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nia Reply:
March 8th, 2011 at 3:58 am
lifes good hbuu…im living life to mthe fullest are ?? dont worry about people anymore just worry about your self
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the best mathematician in 2009 is prof.ayitey from ghana
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i believe , euler must be in the list too ………..:)
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Kevin Reply:
December 3rd, 2009 at 6:51 pm
Hello Aman,
Yes, Euler in on my list as number 6. Thanks for visiting.
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i think that newton is the greatest mathematician of all the times.
euler
gauss
wr hamilton
lagrange
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Kevin Smith Reply:
July 30th, 2010 at 6:11 am
Hi Antonio Carlos Motta,
I see you have w r Hamilton. I don’t know much about him. I see that he is Irish. I’ll do some research on him and put him on my big list. Thanks for stopping by.
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we all are on a fast lane of greatness, in which responsibility remains the price. Any way i am d nest
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2 ME I THINK D BEST SO FAR IS GREAT ADETULA.
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Kevin Reply:
July 30th, 2010 at 6:03 am
Hi Emmanuel
Not quite sure who Adetula is. Could you be more specific?
Thanks for visiting.
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[...] The top five most influential mathematicians [...]
why arent i on the list?
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i think what
NEWTON-for all works in pure mathematics and physics
EULER
RIEMANN
W R HAMILTON -BEGAN THE RELATIVITY with pure mathematics
ED WITTEN OR SIMON DONALDSON
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NEWTON
EULER
RIEMANN
W H HAMILTON originated the mathematicas of the special relativity
theory
ED WITTEN OR SIMON DONALDSON -STRING THEORY
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Kevin Smith Reply:
July 30th, 2010 at 6:28 am
Antonio Carlos,
Thanks for visiting. Nice list . You’re the second person who has W H Hamilton in their list. I will add him to my big list of mathematicians. I like that I can link him to some science content.
I know Einstein used Riemann’s geometry to explain special relativity. I tend to focus the content on middle school students and string theory is probably too complicated.
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too short list, where are Kolmogorov, Viner, fon Newman, Arnold?:)
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Kevin Smith Reply:
July 30th, 2010 at 6:32 am
Andrey,
Thanks for visiting. Yes, it’s a short list. I have a longer list of mathematicians that I use and I have von Newman on that list.
Of the other three on your list, which one do you think was the most influential in mathematics?
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i think that newton,gauss,riemann.hamilton and cantor.
newton.einstein,maxwell,dirac and witten
the greatest mathematicians comtemporary
donaldson,witten,wiles,atyah,serre,conway,connes,thompson,mumford,deligne
i prefer,hamilton,clifford,riemann and poincare
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Kevin Reply:
August 5th, 2010 at 12:06 pm
Antonio,
I see you have another different list. I’ve changed my mind a few times also. Thanks for visiting.
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1.leibniz
2.riemann
3.euler
4.gauss
5.poincare
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Kevin Smith Reply:
August 24th, 2010 at 3:02 am
meskh1,
Thanks for visiting. Riemann’s new geometries really paved the way for Einstein’s theories . Leibniz co-invented calculus: Is that why you have him as number 1?
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i think what the special relativity theory has a quaternions theory as
base to the mathematics str,and the general relativy theory has the
split-biquaternions
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Kevin Smith Reply:
August 26th, 2010 at 6:01 pm
That’s a good observation
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i thnk that does exist a mathematical structure as foundation to str,would be a spinoral geometry generated by the quaternions that
measure the motions of in the curvatures of spacetime
i think that the conjugation of space and time in spacetime continuos is purely geometical,que is originated by the breakdown of the opperator CPT,where the chiralities of the spins calculate the spacetime and has both lorentz transformations as supergroup,or the
complex poincare group as generators of the symmetries of the spacetime,and mesures the spacetome at each points of the curvatures. so the dilation of the time and the contraction of the space are derived of the trasformations of the spinors from left-handed to right-handed rotations and vice versa
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I agree with the original list, with the exception of the great Archimedes. He was not that influential simply because he was too far ahead of is time (which is ironic, indeed). I would replace Archimedes by Euclid and add Euler at an “honorary” sixth place.
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cool i agree to this list
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mathematicians what i most like::
newton
w,r hamilton
g cantor
b riemann
clifford
euler
simon donaldson- a greatests mathematician of the century xx and xxi
ed witten
poincare
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Kevin Smith Reply:
October 26th, 2010 at 5:32 am
Antonio,
That’s a nice list- I’ll read up on ed witten.
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ed wiiten created a mathematics at start from physical mathematics
structure as topological quantum fields theory-using delta and theta
functions and morse structures so as the spacetime 4-dimensional
manifolds with non smooth differentiable theories.the expectative
does appear physical dimension major than 4,with a chern-simons
manifolds curled up and chiralities.
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Kevin Smith Reply:
March 5th, 2011 at 6:28 am
Thanks Antonio, I appreciate his detailed background information.
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It is form me difficult tu accept that Newton was a better mathematician than Riemann and Euler. Also, I have infinite doubt that Erdos, more of a problem solver than a math generator, could even come close to Euler, Cauchy, Godel or Hilbert.
Euler was a great genius, I still contradict someone who said he was better than Gauss. Gauss gave at least four proves to fundamental theorem of algebra while Euler did not manage one.
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Kevin Smith Reply:
November 12th, 2010 at 1:17 am
Hi Nick,
That’s a good insight about Erdos, mostly being a problem solver. But I still think he influenced many more students to become involved in mathematics. I agree with you about Gauss as he is my number one.
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all white.bit biased
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I like albert einstien
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Kevin Smith Reply:
March 5th, 2011 at 6:30 am
My students enjoy learning about Einstein and also he was born on pi day–3 . 14
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It’s all relative, but when we talk about mathematicians let’s don’t confuse pure math with physics and we should not involve in the first five names of people who did not make revolution in math, but in physics.
What did Einstein do in math? Just about nothing. Can he compare in math to Euler or Cauchy, or many others? No way. Newton’s work in math is also not very profound and his name is very little linked to subjects in the today modern mathematical papers. This cannot be said about Riemann, Gauss, Euler, Galois, etc., for example.
About Ramanujan. He had an exceptional talent in theory of numbers. No doubt here, a genius, we owe him lots of respect.But, again, he did not leave behind him a revolution to influence what happens today.
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Kevin Smith Reply:
March 5th, 2011 at 6:33 am
Hi Nick, I agree with most of your comment. Ramanujan had the great gift of mathematics and could almost do it in his head. He came up with the “taxi” number when he was in the hospital and G.H. Hardy came to visit him when he wad ill.
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In response to Balzur Mahmud about the bias. We do not forget Al-Khwarizmi and Al-jabr wa’l muqabalah. When we talk about the first five is a very difficult challenge to pick the best in a very short list. Many great white mathematcians are out of it. ( Archimede, Euclid, Galois, Cauchy, and so many of our time, Terence Tao, Andrew Wiles, Alan Connes, etc.)
This is life all about. Difficult to please everybody.
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Rajat tripathi Reply:
March 25th, 2011 at 9:23 pm
i think THE name Srinivas Ramanujan should be there..
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newton invented the calculus-the your fluxion calculus-is the small infinitely today,concept used
at all mathematics.there has the origin the concept
of limit,differentiation and integration,so as the concept of as use the small infinitely as finite;and
newton influenced cantor and dedekind and conway..and newton is not very profound?
he “is” the greatest mathematician of all the times,and stiil gave origin to all the calculus made in physics
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Kevin Smith Reply:
March 5th, 2011 at 6:36 am
Hi antonio, many people would say Newton is the best- as you say.
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Liebnitz is also considered the inventor of calculus publishing his work prior to Newton. From Wikipedia:
“The claim that Leibniz invented the calculus independently of Newton rests on the fact that Leibniz published a description of his method some years before Newton printed anything on fluxions;
Always alluded to the discovery as being his own invention. Moreover, this statement went unchallenged some years;
Demonstrates in his private papers his development of the ideas of calculus in a manner independent of the path taken by Newton
According to Leibniz’s detractors, to rebut this case it is necessary to show that he (I) saw some of Newton’s papers on the subject in or before 1675 or at least 1677, and (II) obtained the fundamental ideas of the calculus from those papers. They see the fact that Leibniz’s claim went unchallenged for some years as immaterial”
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The idea with Newton the best mathematicain of all times is contradicted by all great mathematicians who generally see Gauss in that place. It is interesting to
interpret this:
“In their development of the calculus both Newton and Leibniz used “infinitesimals”, quantities that are infinitely small and yet nonzero. Of course, such infinitesimals do not really exist, but Newton and Leibniz found it convenient to use these quantities in their computations and their derivations of results. Although one could not argue with the success of calculus, this concept of infinitesimals bothered mathematicians. Lord Bishop Berkeley made serious criticisms of the calculus referring to infinitesimals as “the ghosts of departed quantities”.
Berkeley’s criticisms were well founded and important in that they focused the attention of mathematicians on a logical clarification of the calculus. It was to be over 100 years, however, before Calculus was to be made rigorous. Ultimately, Cauchy, Weierstrass, and Riemann reformulated Calculus in terms of limits rather than infinitesimals. Thus the need for these infinitely small (and nonexistent) quantities was removed, and replaced by a notion of quantities being “close” to others. The derivative and the integral were both reformulated in terms of limits. While it may seem like a lot of work to create rigorous justifications of computations that seemed to work fine in the first place, this is an important development. By putting Calculus on a logical footing, mathematicians were better able to understand and extend its results, as well as to come to terms with some of the more subtle aspects of the theory. “
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i think that the theorical physics produced by newton
already who really iinvented the calculus.compare the physics of newton and of leibinitz and already
shall know that invented the calculus and newton solved many problems in it epoch-in geometry and algebra,e appear that bernoulli knew very well the capacity of newton to solve problems of mathematics
and mathematical physics.
think newton,gauss,euler,riemann,hamilton,cantor..are the greatest mathematicians by the order
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i think that the quaternions are the foundations of the STR,because it is associated to the hyperbolic
rotation functions-that is the are hyperbolic quaternions-and the split octonions are foundations
to the elliptical rotations functions that base to
GTR,where the time is variable-and the appers a double time to explain the connection of space and time in spacetime continuos,that are CTCs lines but
that are generated by two opposite spacetime lines.as electrons and positrons travelling at same time in two opposite direction two that whether connect generating the “present” as one irrationa cut” that is imaginary segment that is the time curving the space in spacetime continuos.
i believe that hamilton,cayley and clifford are very special to the study of RELATIVITY THEORY
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think that geometry and physical structures are equivalents.the proprties of particles and geometry structures are exchanges.the quantum topology fields
are the same thing that the geometrical deformations.this is the “holes” in the spaces are
equivalents to the quantum
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Newton was one the most profound minds in the history of humanity. But, in math Newton is linked mostly to Calculus which was discovered also by Leibnitz existing motives that its principles were used by Pierre de Fermat and others.
Not to deny his genius, but his work is understood today by any good high school student.
Friedrich Gauss was much more profound and touched almost every area of math including Number Theory, Statistics, Analysis, Differential Geometry, Geodesy, leaving out his work in Geophysics. Electrostatics, Astronomy, and Optics,these area not being part of pure math.
The title says “top five most influential mathematicians”, the critical word being “influential”, and it is my understanding that these mathematicians left behind a treasure which today represent a source of new ideas and new math fields.
Here, one cannot leave out the names of Riemann, Euler, and Galois.
Everything what Riemann wrote was revolution. This tells much and if the greatest unsolved math problem will prove that Riemann was right when he stated that all non-trivial Zeta function’s zeroes lie on the critical line 1/2+it, then he will be as big as anybody in math!
“Riemann’s published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory. The theory of Riemann surfaces was elaborated by Felix Klein and particularly Adolf Hurwitz. This area of mathematics is part of the foundation of topology, and is still being applied in novel ways to mathematical physics.
Riemann made major contributions to real analysis. He defined the Riemann integral by means of Riemann sums, developed a theory of trigonometric series that are not Fourier series—a first step in generalized function theory—and studied the Riemann–Liouville differintegral.
He made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he introduced the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis.
He applied the Dirichlet principle from variational calculus to great effect; this was later seen to be a powerful heuristic rather than a rigorous method. Its justification took at least a generation. His work on monodromy and the hypergeometric function in the complex domain made a great impression, and established a basic way of working with functions by consideration only of their singularities.
Riemann’s idea was to introduce a collection of numbers at every point in space (i.e., a tensor) which would describe how much it was bent or curved. Riemann found that in four spatial dimensions, one needs a collection of ten numbers at each point to describe the properties of a manifold, no matter how distorted it is. This is the famous construction central to his geometry, known now as a Riemannian metric.”
Q.E.D.
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the greatest mathematician alive today for me is
simon donaldson
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i think that the FLUXION CALCULUS ELABORATED BY ISAAC NEWTON IS VERY DEEP.NEWTON IS BEYOND OF THE SYMPLES CALCULUS OF DIFFERENTIATION AND INTEGRATION,BUT HE DOES A DEEP STUDY OF SMAL INFINITELY,AND SEEKING THE TRANSCENDECE BETEEN WHAT
THAT IS CURVES AND FLATS.AND THAT IN THAT DIFFERENTIATIONS BETEEN CURVES AND FLAT THERE ARE
A TRANSCENDE BETWEEN THE CONTINUOS AND DISCRETES
SETS.THAT PERMIT A NUMBER OF TRANSCENDENTS OPERATIONS
TO TRANSFORM CURVES TO FLAT AND VICEVERSA,THESE TRANSFORMATIONS ARE SIMULTANEOULY CONTINUOS AND DISCRTES-HAVE THERE THE NONCOMMUTATIVE GEOMETRY-.STILL NEWTON SEES THE POTETIAL TO GENERATE THE MOTION IN INFINITE SERIES THROUGH OF MANIPULATIONS
CONTINUOS AND DISCRETES.THE CONCEPT OF LIMIT GENERATE
A LATERAL SYMMETRY,THAT IS ASSYMMETRY IN SYMMETRY MIRRORS.CONNECTING TWO OPERATIONS LEFT-RIGHT HANDED
TO AN ONLY ONE “POINT”-THAT IS STRING VIBRATING AND RESSONATING IN INFINITIES KNOTS IN A NUMBER OF MANIPULATIONS BEING finite…THIS IS newton
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Rocky Marciano Reply:
March 18th, 2011 at 7:40 pm
This is excessive pro-brittish propaganda. “Fluxions” is a term which today is completely out of use. At that time Newton named calculus as calculation of fluxions. As someone wrote Cauchy and Riemann defined better than Newton the basis of calculus.
While a genius, Newton lived 85 years. Riemann lived only 39 and produced much more math than Newton, quantity and quality .. something to think about. Today mathematicians are more inspired and linked to Riemann’s math then to that of Newton’s.
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is very strange,newton makes mathematics,physics,and
use time very much still with religions and otherthings.riemann only makes mathematics.are different epochs.newton was complete for it time.gave
structures for mathematics and physics.riemann,alredy
all knoelegment,while newton had that constroy all the things.
i are mot pro british.fluxions were inventions fantastics of genial mind of newton,as the mathematica physics.newton is universal and riemann is restrict,so as cantor and dedekind what were genious,but restrics.
gauss and riemann gave the same colaboration to theoretical physics than newton?
many thanks
antonio carlos pocobi motta
i am of ascendence italian
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is the same that compare the musical structures of
mozart and stravinsky.today,mozart is simples,but understand the musics in his time was much complex.
musical structure of stravinsky is extremely complex compared to mozart.but mozart had that synthetizer
all knowlegment of the epoch and create new language
to express new emotions and things,after amplied at the extreme by beethoven,or same mozart was lapse in the temporal sequence of the musical evolution.
the newtonian thought is greatest that the simples calculus.
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Pete Reply:
March 19th, 2011 at 2:26 am
It is too much hard to argue with someone who:
1. has difficulty to express himself in a clear and logical manner
2. has serious problems with the english grammar
3. is clearly convinced that he is right and everybody else is wrong
4. does not understand that the basic question here is who was more influential, and not who was the greatest scientist ever
5. thinks that Pele was greater than Maradona (this is probably the worst)
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mathematics is not product of english language.
who is pele?who is maradona?
i know mozart,stravinski.
i never needed learn english to understand mathematics.in my oppinion the greatest mathematics was newton,and the greatest physicist newton.
understood?
you send some problems of mathematics and and i send you others.maybe we shall know who is best mathematicians,okay,dr.pete?
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Bringing phyisical science and religion in this conversation is rather useless. The title say clearly “top five most infuential mathematicians” and it is clear that Carlos Motta brings pro-brittish feel since he also introduced Hamilton in the first five while he has no place there. Carlos Motta is the only one who makes this favor to Hamilton and have never seen his name in any other place among the first five. I sutdied his work, is good, but did not give me any trouble.
Newton was included in the best ten because of those who did this are british. Gauss, Riemann and Euler were not restrict. B.S. When talk about Gauss just remember Ceres.
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i am in the line of michael atyah;with newton.gauss,riemann.hamilton.thence could to put
euler,cantor..
what bernoulli said of newton after send some problems to great mathematicians of the epoch?
what fascinate me is the idea of the fluxions,not the calculus made until by the proper leibinitz. newton does theirs works with 26 years ago.after wrote about of themes non- scientifics,okay?
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Indian mathematicians have made many important contributions especially those of ancient India such as Aryabhatta, Brahmagupta and Bhaskara II. We in India are fully aware of them. However most people especially in the West don’t know or are reluctant to recognize their contributions. Mathematics in India has a long history starting from the Indus Valley Civilization – Bronze Age Civilization (3300 B.C)and we in India are extremely proud of our mathematics heritage. Since this was a list of famous mathematicians I just wanted to put this out there.
Also refer links
http://en.wikipedia.org/wiki/Indian_mathematics
http://www-history.mcs.st-and.ac.uk/HistTopics/Indian_mathematics.html
http://www.esamskriti.com/essay-chapters/A-brief-history-of-Indian-Mathematics-1.aspx
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Luciano Borromei Reply:
May 30th, 2011 at 12:22 am
It is very true, but what should be considered first is work that revolutized mathematics. A good and fair mathematician cannot deny Riemann for his work in theory of numbers and geometry, and Galois for his astounishing discoveries.
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What about Euclid???
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Kevin Smith Reply:
April 6th, 2011 at 5:11 am
Hey Bob
Thanks for the comment. I didn’t include him because I don’t think he influenced many middle school math students. Even though the Elements has been used as a text for over a thousand years.
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its very helpful to us thnks
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hey, i cant understood why u r giving information in only 2paras. they are a great mathematicians invented some things which we are still learning.so, please try to give us more information about them. but the matter is good.thanks for it.
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