The top five most influential mathematicians

by Kevin on April 7, 2009

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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March 7, 2010 at 1:10 am


1 Kevin Smith October 5, 2011 at 8:30 am

vishal ku ranjan,
Thanks for visiting. I see you enjoy mathematics also.

manan sharma Reply:

they were so intilegent and great

2 venu gopal rao up coming abel November 13, 2011 at 12:29 am

hey where is abel?

Kevin Smith Reply:


Niels Abel is on my next list.

3 Nick Nazari January 17, 2012 at 10:04 pm

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:

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.

4 Rajan February 17, 2012 at 5:23 pm

Paul Erdos is my hero!!

Kevin Smith Reply:

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

5 Marcus Tullius March 25, 2012 at 4:51 pm

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
“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:

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:

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:

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.

6 Alexa Claire Sanders June 15, 2012 at 4:25 pm

Thanks, it helped a lot with my homework(:
And yeah, they are very influential mathematicians.


7 Kevin Smith June 16, 2012 at 9:24 pm

Thanks for visiting here.

8 raghav July 5, 2012 at 1:38 pm

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

Kevin Smith Reply:


Your welcome.

9 hamza August 29, 2012 at 5:04 pm

very genius

10 sanjna November 2, 2012 at 8:05 am

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

11 rashika December 1, 2012 at 7:49 am

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12 nicco December 4, 2012 at 8:20 am

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

13 Rick December 6, 2012 at 8:45 am

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:

Shinichi Mochizuki may have proved the ABC conjecture. Here is a video explaining how this works. See

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15 pardeep singh December 8, 2012 at 2:46 am

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16 pardeep singh December 8, 2012 at 2:48 am

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17 Rajnikant Sinha December 26, 2012 at 6:31 am

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

18 nicco January 10, 2013 at 9:09 pm

Riemann was very creative

19 harry dhillon May 14, 2013 at 10:40 am

this site help me so much inmy school work

20 Gerd Mueller May 15, 2013 at 3:27 am

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:

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.

21 Gerd Mueller May 15, 2013 at 10:00 am

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 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:

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!

22 Luciano Gigante June 11, 2013 at 8:53 am

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:

Hi Luciano,

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

23 antoniocarlos motta June 11, 2013 at 9:40 am

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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