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.

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vishal ku ranjan,

Thanks for visiting. I see you enjoy mathematics also.

manan sharma Reply:

January 16th, 2012 at 10:46 pm

they were so intilegent and great

hey where is abel?

Kevin Smith Reply:

November 14th, 2011 at 12:14 am

Thanks,

Niels Abel is on my next list.

Despite his genius, the placement of Newton ahead of Riemann is highly questionable. All Newton’s math work would have happened even if he did not touch those subjects. I am sure that most of Riemann’s work would not happen because all he did was revolution.

Kevin Smith Reply:

January 19th, 2012 at 10:25 am

Hi Ninck,

I see what you have to say, but considering the students are only 14 years old, I thought Newton was more influential to this age group as he is has more connections to science and mathematics which are easier to teach at this level. On a purely theoretical note, Riemann has the deeper and more interesting theorem about the nature of the primes and how the number system fits together.

Kevin

Paul Erdos is my hero!!

Kevin Smith Reply:

February 19th, 2012 at 10:56 pm

Rajan,

Thanks for visiting, I like your website with all the division problems.

The title is asking for the most infuential mathematicians. Most great mathematicians have been and are influential because their ideas could generate other great ideas. We must weigh the importance of each math work left behind by those greats.

For example Newton, great in phyisics but not equally great in the math revolution. Summary of Newton’s work from the math history http://www-history.mcs.st-and.ac.uk/Mathematicians/Newton.html:

“Isaac Newton was the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.”

But the integral calculus had been published seven years earlier by Leibnitz! Would be a great provocation to belive that without Newton there will be no calculus today! Proof is so simple knowing that Fermat made calculations similar to the simple ones we make today by using the derivatives. Quote from Wiki:

“In particular, he (n.a.Fermat) is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then unknown differential calculus, and his research into number theory”

In today’s modern math, Archimede also did not produce much, even if for his time was a giant-genius.

Some people made positive comments about Riemann and Galois. These two along with Gauss, Euler, and Cauchy, are the mathematicians who have made revolution in mathematics.

Dare to imagine Number Theory without Riemann! Or complex function analysis, foundation of geometry, etc.

From Wiki:

”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”

“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.”

“He was also the first to suggest using dimensions higher than merely three or four in order to describe physical reality[2]—an idea that was ultimately vindicated with Einstein’s contribution in the early 20th century.”

Imagine that he lived twenty more years! Dead at 40..what a world!

antoniocarlos motta Reply:

June 10th, 2013 at 1:24 pm

i have doubt that anyone would have invented the calculus as newton. today little know the calculus

as newton found it.bernoully knew the mathematical talent of newton. leibniz with surely had not all those mathematical knowledge as newton.

riemann was later very much.was fantastic.without doubt as was gauss.but not as newton.

Lrak Ssuag Reply:

December 13th, 2013 at 1:38 am

In today’s modern calculus the notations are those used by Leibnitz. One should look on Newton’s book, which was great for that time, but the apropach is rather simple, nothing extensive, like the ciontinuity of functions nor that he had an approach on limits, convergence, and integrals. Newton is mostly very popular because F=m*a which is not math. Leibnitz published his work on calculus 7(seven) years earlier than Newton. What does it tell you? I saw someone beating here the drum on fluxions. His math knowledge appeard limited not knowing that the term fluxions has meant nothing else but the derivative in Newton’s work. It was Hardy who wrote in one his literary works about Newton’s fluxions and mentioned in a patriotic way Newton being one of first three acording to other mathematicians. Newton proved to be a bad loser taking Leibnitz to courts and lamenting over Leibnitz’ success acusing him of using his findings. The depth of Newton’s math work was way more simplistic than Gauss, Euler,Riemann,Kummer, Abel, etc.

Many with a background in phisycs come to this site to prove that one of them was greater than other matheticians. Newton’s great results are mostly in physical sciense while his discoveries in math came even earlier.

Kevin Reply:

February 20th, 2014 at 6:37 pm

Thanks Lrak for your insightful comment. It’s interesting to note how Newton’s mathematics were so closely related to physics. I agree with you that Riemann had great insights into the properties of primes.

Thanks, it helped a lot with my homework(:

And yeah, they are very influential mathematicians.

Alexa:)

Alexa,

Thanks for visiting here.

thanks man u helped me a lot by this……………………………..

Kevin Smith Reply:

July 6th, 2012 at 5:08 am

raghav

Your welcome.

very genius

it helps me in my homework i am very thanfull to this site.

it is short please give more information for my help with photo also

Riemann was the greatest genius that ever lived but has anyone dared to think of Ramanujan,original genius and probably the greatest of all mathematicians to have ever walked this planet

Any great mathematician was…great. About Gauss, Riemaann, Euler, it’s all clear. The next history making great mathematician si Shinichi Mochizuki! Very few understand his Inter-Universal Geometry theory which will prove two conjectures and FLT!

Kevin Reply:

December 6th, 2012 at 7:48 pm

Shinichi Mochizuki may have proved the ABC conjecture. Here is a video explaining how this works. See http://www.youtube.com/watch?v=RkBl7WKzzRw

I have been surfing online more than three hours today, yet I never found any interesting

article like yours. It is pretty worth enough for me. In my opinion, if all website owners and bloggers made good content as you did, the web will be much

more useful than ever before.

i agree

this site had helped me a lot…thanks

Marcus Tullius assesment about Riemann is quite correct. I think he was the greatest creative mind ever walked on the earth planet.

Riemann was very creative

this site help me so much inmy school work

It will be impossible to prove that Arhimede and Newton were greater mathematicians than Riemann, Euler, or Cauchy. Both were great but the depth of their work is far simpler than those I’ve quoted.And of course far simpler than the work of many others like Hilbert, Serre, Frobenius, Thompson, Mochizuki, Tao, etc. Nowadays very few math manuscripts relate to Newton’s math foundation work but it does not take long to find so many times Galois or Riemann are quoted. Especially Riemann who left a math revolution behind him.

Fabio Reply:

May 15th, 2013 at 6:54 am

Dear Gerd, maybe you should spend a little more time doing research on Archimedes and Newton’s works. Archimedes was too far ahead of his time and Newton was Gauss’ greatest hero. And most importantly, this article is about influential mathematicians, and not necessarily about the depth or difficulty of their works. All of those mathematicians that you have mentioned were at some point very much influenced by icons like Archimedes and Newton.

Nr. Fabio, I suspect that you operate in an area of science but not mathematics. What’s so dificult to undertsand in general combinatorics and basic calculus which was published by Leibnitz seven years earlier than Newton? Archimede, like Newton, was more involved in physics than in math. Sorry, but you don’t seem to grasp too well the idea “most influential” which I sketched a bit in my earlier comment..how many times is Newton’s name mentioned in today’s math works versus how many times you read about Riemann’s ideas in today’s math?! The point that Gauss had a good view of Newton is irelevant, let’s get to the facts not to the fairy tales. Gauss was also very enthusiatic when attended Riemann presentations of the fundaments of geometry and the distribution of prime numbers. Gauss also named Pierre de Fermat a genius which was correct.Newton was a genius of first class in physics but a genius of second class in math. To give another example, Euler did much more than Newton for the mathematics, this is undeniyable.

Fabio Reply:

May 15th, 2013 at 10:16 am

Dear Gerd, sorry but I am not interested on discussing my mathematical capabilities or knowledge with someone I do not know.I respect very much your opinion but strongly disagree with your concept of “influential”. The impact of the ideas of Newton and Archimedes over generations of mathematicians were so overwhelming that this discussion is worthless. No one would be stupid enough to lessen Riemann’s influence on today’s mathematics or discuss his “gloriously fertile originality” (again quoting Gauss), however Newton and Archimedes influenced Mathematics for many centuries, while Riemann’s work has mostly influenced 3 or 4 generations (which is still impressive). I am a big fan of Riemann, who lived a very short time but long enough to create a whole new mathematical world!

If we talk about students up to 14 year old then it is the case to limit the title to ” most influentuial mathematicians in arithmetics, elemenatary algebra, and euclidian geometry”, then we will find names like Euclid, Thales, Eratostene (..sieve), Pithagoras,Archimedes, etc. (all greeks, none from the UK)On a full scale math, even if those mentioned above remain on the list there is much more to add. In tend to agree with Marcus Tullius who brought a good view on what means influential.

How many times are Galois or David Hilbert mentioned versus how many times Newton is mentioned in the today modern math works?! Simple.

Kevin Reply:

June 27th, 2013 at 10:31 pm

Hi Luciano,

You make a very good point but I didnn’t want to limit the post to arithmetic and algebra.

you know mathematics more than michael atyah,that explain because newton and gauss are the greatest mathematicians of History

you know the work of riemann.omly listen to talk about

the work of his.

vasu and gigante are things of very fool without doubt

read the pricipias of newton,talk not for talk

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