25 August 2008 @ 01:52 pm
The Mathematicians  
I think I spent almost two months just working on this. Excluding the time not working on this piece, it probably would have taken me about a month if I went at it non-stop. But now it's all finished.



Here are the mathematicians featured in this picture:

Gauss, Newton, Archimedes, Euler, Cauchy, Poincare, Riemann, Cantor, Cayley, Hamilton, Eisenstein, Pascal, Abel, Hilbert, Klein, Leibniz, Descartes, Galois, Mobius, Jacob, Johann and Daniel Bernoulli, Dirichlet, Fermat, Pythagoras, Laplace, Lagrange, Kronecker, Jacobi, Bolyai and Lobatchewsky, Noether, Germain, Euclid, Legendre

I'm not entirely sure of the accuracy of the biographical information below because it's just from what I remember mostly, but if anyone spots any errors, please point them out. Thanks.

Also note that the pictures might not actually represent how the mathematicians in real life looked like, either because I purposefully made tweaks to their hair or because there weren't good reference pictures of them (or authentic portraits were lacking).

Unfortunately, there are more mathematicians than there is space in this picture to give recognition to each and every mathematician in history that is worthy of it; most of the ones in this picture are mathematicians I am most familiar with from my math history class.


Karl Friedrich Gauss 1777 - 1855
Considered to be one of the three greatest mathematicians in history. Known for constructing a regular 17-sided polygon with only a compass and ruler (this feat was never discovered since the Ancient Greeks, who knew only up to 15 sides), concluding that any polygon with the number of sides equal to a Fermat prime can be constructed, works in his Disquisitiones Arithmeticae on number theory, developed the modulus notation, discovered the fundamental theorem of algebra, calculated the orbit of Ceres, various works on electromagnetism and geodesy, invented the heliotrope, and other contributions too numerous to mention. Did not publish his thoughts on non-Euclidean geometry for fear of being rejected. Considered to be the last universalist before Poincare.

Isaac Newton 1642 - 1727
The second of the three greatest mathematicians in history. Known for discovering gravity, various works in physics, co-inventor of calculus and his best works, Principia. He worked alone. He invented his own telescope and discovered the binomial theorem. He hates disagreeing with people because he hates being wrong; that's why people say he's nasty. But he claims that his work is akin to sitting on the edge of the ocean picking up seashells, never knowing what lies at the bottom of the ocean.

Archimedes ~ 287 - 212 BC
The last of the three greatest mathematicians in history. Known for developing the concept of the lever, inventing the screw pump, ratios of volumes between spheres and cylinders. Rumored to have run through the streets screaming "Eureka!" at the discovery of a method of determining gold from fake gold. He was killed by a soldier during war; the cause of this dispute is unknown; either the soldier had stepped on his work on the ground and angered him, or he had refused to go with the soldier in order to finish the solution to his math problem. He also liked doing math everywhere; if there was soot nearby, he'd write in it. He even wrote in the oils on his skin, which was applied after bathing as is the custom in Ancient Greece.

Leonhard Euler 1707 - 1783
"Analysis Incarnate", as some call him. Known for various works in number theory, the sum of 1/n^2, development of the concept of functions with D'Alembert, and capable of calculating large calculations entirely in his head. Liked children and had many of them. Slowly went blind, and was completely blind by the time he was 70. His blindness did not hinder his mathematical insight, but rather, it increased after he became blind.

Jules Henri Poincare 1854 - 1912
Considered to be the last universalist in mathematics. Known for conjecture on three body problem and concepts related to the development of relativity theory--some say that he should deserve all the credit for it instead of Einstein. The circle slightly above him is a Poincare disk model, used to visualize lines in a sphere in hyperbolic geometry.

Augustin Louis Cauchy 1789 - 1857
A contemporary of Gauss. Known for developments in calculus including certain concepts of limits and continuity, some algebra and complex analysis. The formula next to him is known as Cauchy's Theorem, used in complex analysis, and below it, the well known Cauchy's inequality.

Bernard Riemann 1826 - 1866
A German mathematician whose originality in thought impressed Gauss. Known for ideas in non-Euclidean geometry and integrals. He died young from illnesses. The sphere next to him is a stereographic projection of a Riemann sphere.

Georg Cantor 1845 - 1918
A German mathematician whose methods were consistently criticized by Kronecker. However, he is known for developing the concept of set theory. Though his ideas were accepted by Hilbert and other great mathematicians, he could not get over Kronecker's criticism and admitted himself to a mental institution. The fractal next to him is a Cantor set.

Arthur Cayley 1821 - 1895
A British mathematician. Found the theory of invariants with his friend Sylvester, and succeeded in having women admitted to Cambridge. Also known for the concept of n-dimensional geometry.

William Rowan Hamilton 1805 - 1865
Considered to be the greatest Irish mathematician. By the time he was 14, he knew as many languages as he was old. Known for discovery of complex variables in the fourth dimension and the algebra of quaternions, the former of which he discovered when he could not find a way to represent complex variables in the third dimension. Had drinking problems in his later life.

Ferdinand Gotthold Max Eisenstein
A brilliant mathematician and pupil of Gauss. His mentor considered him to be one of his greatest students and one of the greatest mathematicians. Unfortunately, he died young.

Blaise Pascal 1623 - 1662
Originated the mathematical theory of probability. Was a French mathematician who posed cycloid problems to other mathematicians and also known for his converse of Descargues' theorem in projective geometry. The triangular array of numbers in front of him is Pascal's triangle, and are also the coefficients of the terms in a binomial expansion.

Niels Henrik Abel 1802 - 1829
A Swedish mathematician who lived in poverty. He taught math and did some work on algebra. He died young before his contemporaries could give his work recognition.

David Hilbert 1862 - 1943
One of the successors to Gauss' former position as the director of the observatory at Gottingen. Made some contributions to algebra. Supported Cantor's set theory. Tried unsuccessfully to get Emmy Noether a faculty appointment at Gottingen. He was also known to be slow at grasping new concepts in an attempt to understand it completely.

Felix Klein 1849 - 1925
Another of Gauss' successors at the observatory of Gottingen. Made contributions to algebra, and also known for the concept of a Klein bottle (pictured).

Gottfried Wilhelm Leibniz 1646 - 1716
One of the founders of calculus with Newton. However, the competition between himself and Newton was bitter. He was also skilled in other areas besides mathematics, including philosophy, politics, law and history.

Rene Descartes 1596 - 1650
Well known for his phrase, "Cogito ergo sum" and the Cartesian coordinate system, thereby creating an entire system of geometry. The phrase is often misinterpreted to mean one exists because he thinks, but it means that the act of thinking is the only truth that exists.

Evariste Galois 1811 - 1832
A brilliant mathematician whose genius was not well recognized. His examiners had difficulty understanding his explanations, and he often proclaimed most of them were so easy as to not require an explanation. He wrote very little in his career and accurately predicted he would die in a duel. Known for work in group theory, Galois theory and algebra.

August Ferdinand Mobius 1790 - 1868
A German mathematician from whom the Mobius strip is named after. The Mobius strip is an object which has only one side. Also made contributions to algebra.

The Bernoullis (Jacob 1654 - 1705 (pictured left), Johann 1667 - 1748 (pictured right) and Daniel 1700 - 1782 pictured (below))
The Bernoullis are a family of brilliant people, some of which are mathematicians. Daniel Bernoulli was the son of Johann Bernoulli, and made many contributions to applied mathematics. His father and Jacob Bernoulli were in competition with each other, and fought often. One of their disputes involves the question of what shape a string should be in order for a bead to travel from one end to the other most quickly (the correct answer is a cycloid). Daniel Bernoulli was often excluded from disputes between Euler and D'Alembert.



Peter Gustav Lejuene Dirichlet 1805 - 1859
One of Gauss' pupils, whose works in number theory were inspired by his mentor. Apparently, on his jubilee lecture, Gauss wanted to burn the original of his Disquisitiones Arithmeticae, and was about to light his pipe with it, when Dirichlet saw him doing that and saved the original in time (I don't actually know if this is true though; I read it somewhere).

Pierre de Fermat 1601 - 1665
Considered to be the greatest mathematician of the seventeenth century. Known for his work in number theory, and his last theorem (which he claimed to have proven, but no evidence of this has been found), which has caught the attention of many mathematicians and other challengers. He also created the Fermat primes, which have later been shown not to be primes. Gauss was not interested in proving his last theorem.

Pythagoras 572 - 492BC
His well known theorem regarding right angle triangles is actually a proof of a Babylonian theorem. However, he is credited for his abstraction of numbers, including the property of even or odd numbers. He suggests that all things are considered to be numbers.

Pierre-Simon de Laplace 1749 - 1827
A French mathematician who made many contributions to mathematical astronomy and physics. Known for his Laplace equation in calculus and Laplace transforms. Some consider him to be as great a scientist as Newton, and call him a French Newton.

Joseph-Louis Lagrange 1736 - 1813
A mathematician with bad eating habits. He first proposed the mean value theorem in calculus, and did a little bit of work on number theory. However, his Mecanique is consider his best work.

Leopold Kronecker 1823 - 1891
A mathematician who did work in algebra and number theory. He mastered Galois' theory of fields before others, but was critical about using mathematicians using irrational numbers, and said mathematics should be based on relationships between integers; he said to Lindemann that irrational numbers don't exist. He was also critical towards Cantor, and did not agree with his concepts. this eventually caused Cantor to admit himself to a mental asylum.

Carl Gustav Jacob Jacobi 1804 - 1851
A mathematician whose reputation is often mistaken with his brother's. Known for his work in number theory, algebra and Abelian functions.




Janos Bolyai 1802 - 1860 and Nikolas Ivanovitch Lobatchewsky 1793 - 1856
Both mathematicians were the first to introduce the concept of non-Euclidean geometry to the public (remember that Gauss did not do this). Their ideas were challenged due to the popularity of Kant's Critique of Pure Reason, in which the idea of non-Euclidean geometry would be made absurd. While Gauss commended both mathematicians for their work, only Lobatchewsky received support from Gauss in being admitted to Gottingen, but in his letter to Bolyai, Gauss claimed that giving credit to him would be like giving credit to himself. Lobatchewsky also challenged Euclid's fifth postulate, using non-Euclidean geometry for counter examples.


Emmy Noether 1882 - 1935
A mathematician who was one of two female students out of a thousand students in the university of Erlangen. She was influenced by Hilbert and Klein, and although Hilbert tried to help her get an appointment in Gottingen, he did not succeed. She is known for her original work in noncommutative algebra.

Sophie Germain 1776 - 1831
A mathematician whose parents discouraged her from pursuing the sciences. She was influenced by Gauss' work in number theory, and when she made some discoveries on quadratic reciprocity, she wrote to Gauss about them under the disguise of a man (because she feared he would not accept her if he knew her gender). However, when she did reveal her identity, Gauss was impressed with her work and admired her even more because it would have been harder for a woman to succeed in sciences, due to society's prejudices.

Euclid ~325 - 265BC
A Greek mathematician known for his works in geometry in The Elements. His works, however, are restricted primarily to plane geometry, and some of his postulates, including the last one do not work on non-planar surfaces. However, his ideas in geometry have been well accepted for centuries.

Adrien Marie Legendre
A mathematician with some works in number theory. His theory of quadratic reciprocity was never successfully proven by himself, but by a younger Gauss, whom Legendre was mostly jealous of.
 
 
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( 49 Nachrichten — Schreiben ein Nachricht )
perculiousperculious on March 25th, 2009 03:49 pm (UTC)
Hey, my friends and I found this while researching a math project and we think it's seriously, seriously awesome. You rock.
Lyndaphoenixfire23 on April 14th, 2009 07:23 am (UTC)
Einstein?
I notice that you never list Albert Einstein with your list of mathematicians...why is that?
angelustenebraeangelustenebrae on April 15th, 2009 09:08 pm (UTC)
Re: Einstein?
Because we didn't study him in my math history class, and I thought he was a physicist. So I wasn't aware he was a mathematician specifically.
(Anonymous) on May 1st, 2010 12:34 am (UTC)
Re: Einstein?
Also Einstein was not good at math, he had to have most of his calculations double checked by others, specifically his wife.
(Anonymous) on March 16th, 2011 10:34 pm (UTC)
Re: Einstein?
to był fizyk, a nie matematyk ...
(Anonymous) on April 1st, 2011 11:40 am (UTC)
Re: Einstein?
Einstein is not a mathematician,he is a physicist.
(Anonymous) on February 27th, 2010 12:59 am (UTC)
Wow! Very nice picture!!!
But I have to say that I miss some brilliant mathematicians in your picture, like Weierstrass, Liouville, and Ramanujan. And maybe we could have some more XX century mathematicians like Cartan, Alexander Grothendieck, von Neumann, and Erdos. Also, even though you've pictured Germain and Noether, I missed more female mathematicians, like Hypatia of Alexandria, Sofia Kovalevskaya, Maria Gaetana Agnesi, and Mary Fairfax Greig Somerville.
But please, don't take my comment as either a criticism or a complaint. You made a great job!
axiom37axiom37 on June 25th, 2012 08:20 am (UTC)
And Noether~!
(Anonymous) on April 30th, 2010 01:38 am (UTC)
wow
wow!! i like it,,!!
hermitbikerhermitbiker on April 30th, 2010 01:53 am (UTC)
Mathematicians
.... cool article with image, but yep Einstein was another mathematician, but this is still a great article anyway !!
(Anonymous) on April 30th, 2010 02:56 am (UTC)
amazin
brilliant minds.....i wonder what would happen if they were to all be alive and meet up, wonder if they would solve problems or would they just disagree with each other and argue lol!
(Anonymous) on April 30th, 2010 02:56 am (UTC)
amazing
forgot to say AMAZING work dude
(Anonymous) on April 30th, 2010 03:20 am (UTC)
Algebra?
What about the father of Algebra Muhammad al-Khwarizmi, without him most of those people wouldn't even be here!
(Anonymous) on April 30th, 2010 09:46 am (UTC)
Re: Algebra?
He was probably a Muslim - you know follower of Islam the religion of Truth, so he doesn't compare with the 'Great minds' of a 'FREE THINKER'. Never mind I'm sure muslims prefer him not to be depicted so you can imagine their response when the Prophets of God are drawn.(Jesus included).
Cool link if anyone is interested - SCIENCE related. http://www.1001inventions.com/
(Anonymous) on April 30th, 2010 09:45 pm (UTC)
Re: Algebra?
Muslims turned the Dark Ages into the Golden Age. It shows you it's not a religion of only faith but also reason ;)
(Anonymous) on May 7th, 2010 02:07 am (UTC)
Re: Algebra?
The latest muslim contributions to society are:
stoning of women
beheadings
suicide bombings
assorted acts of terrorism
blaming jews for everything
Guess that makes islam a cult of death
(Anonymous) on March 16th, 2011 08:12 pm (UTC)
Re: Algebra?
Thank goodness the peaceloving and forward-thinking Christians and Jews are here to keep us safe. /sarcasm
(Anonymous) on March 16th, 2011 08:54 pm (UTC)
Re: Algebra?
Those things were all around long before Islam...
(Anonymous) on March 17th, 2011 01:56 am (UTC)
Re: Algebra?
Ah, a coward who comes into a thread about math and spouts hatred based purely on prejudice.
(Anonymous) on January 14th, 2011 02:41 pm (UTC)
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(Anonymous) on March 16th, 2011 07:41 pm (UTC)
Mandelbrot?
Mandelbrot?
(Anonymous) on March 17th, 2011 02:48 am (UTC)
Re: Mandelbrot?
Mandelbrot was famous because people like to look at pretty pictures of fractals. In terms of actual importance to mathematics, he was nowhere near as great as most of the people here. (I don't mean to disparage him as a mathematician or anything -- it's hardly an insult to say he's not in the same league as Gauss or Euler.)
(Anonymous) on March 16th, 2011 09:45 pm (UTC)
Abel
Niels Henrik Abel was Norwegian, not Swedish. Otherwise, nice work :)
(Anonymous) on March 17th, 2011 02:44 am (UTC)
Re: Abel
Indeed, and I think he also deserves some more mentioning on his works, since they have become so important in modern mathematics.
(Anonymous) on March 16th, 2011 09:53 pm (UTC)
Mobius
But that isn't a Mobius strip, just a regular one he's holding.

And yeah, otherwise you rock.
(Anonymous) on March 17th, 2011 07:25 pm (UTC)
Re: Mobius
This is a Mobius strip even if it doesn't look like. This is the problem of 2D paintings ;>
(Anonymous) on March 17th, 2011 10:10 pm (UTC)
Re: Mobius
Noticed the same thing. I suggest to get that fixed if there are any plans to reprint.

Nice work :)
(Anonymous) on March 16th, 2011 11:38 pm (UTC)
Archimedes
The significance of the sphere and cylinder that he is holding is that he discovered that the ratio of the volumes of the two solids is identical to the ratio of the surface areas, provided the sphere is inscribed in the cylinder. He felt this was his best result, and asked for it to be inscribed on his tombstone.

However, the cylinder and sphere that he is holding in *your* drawing do *not* have the required relationship, so they look wrong to me! (I teach History of Math at a university in California).

I appreciate your effort, but inaccuracies like this can ruin the piece for people like me. Sorry to be so anal--unfortunately, it goes with the territory of being a mathematician...
(Anonymous) on March 16th, 2011 11:51 pm (UTC)
Print
Any plans to sell prints of this?
(Anonymous) on March 17th, 2011 03:05 pm (UTC)
Re: Print
Yes please! I would love to hang one in my office. Please please consider having it printed up and sold!
Dougalldougallj on March 17th, 2011 12:40 am (UTC)
I would love a higher resolution copy of this. It's an amazing artwork.
doug_palmerdoug_palmer on March 17th, 2011 01:26 am (UTC)
High levels of awesomeness.

On the subject of who got included and who didn't, I'm imagining a fractal representation of your pyramid, where everybody budges up as new suggestions are put in.
(Anonymous) on March 17th, 2011 01:10 pm (UTC)
Stefan Banach
Where, for the God's sake is Stefan Banach?
(Anonymous) on March 17th, 2011 12:52 pm (UTC)
You include that Hamilton had drinking problems later in life, but say nothing of the huge impact he had on the study of classical mechanics. It probably worth mentioning about Galois that he did everything that he did before the age of 21, when he was killed in a duel.
papersteph.wordpress.com on March 17th, 2011 01:52 pm (UTC)
Beautiful!
I LOVED THIS! As a fan of beautiful artwork and a graduate with a Math degree, this was wonderful.
(Anonymous) on March 17th, 2011 03:38 pm (UTC)
Images copyrights
Can I use one of the pictures on my site ?
(Anonymous) on March 17th, 2011 05:11 pm (UTC)
Great work
Great work, really good. But, what about Banach?
(Anonymous) on March 17th, 2011 07:16 pm (UTC)
How dare you name Newton "the second greatest mathematician"? He was the greatest mathematician ever, and for sure more important than Gauss. Just think about all that physicists without calculus, they wouldn't be able to describe even simplest laws of the nature. Do you imagine Maxwell's equations without calculus?
Also, the equal character should be next to the fraction line, not next to fraction numerator.
(Anonymous) on March 22nd, 2011 02:01 pm (UTC)
You might call him the greatest physicist, then, but for mathematics, I'd argue Gauss was more important.
Eugene Kirpichovantilamer on March 17th, 2011 07:58 pm (UTC)
Thank you. Your pictures amazingly show not just geniuses, but real people who happen to be geniuses.
(Anonymous) on March 23rd, 2011 07:43 pm (UTC)
nice!
great read thank you.
btw the pics don't show.
(Anonymous) on April 1st, 2011 10:40 pm (UTC)
car owner pvt 323
801846
(Anonymous) on April 10th, 2011 08:55 am (UTC)
Brilliant
What a beautiful artwork! How beautiful it would look as a wall hanging in my office. Some amazing minds in that image, and some truly tragic stories, so many of these brilliant people died so young or untimely (Archimedes murder).
Just thought Janiszewski was a bit still to miss out, he was another tragic figure, 1888-1920, who worked with topology and started Fundamenta Mathematicae in Poland.
(Anonymous) on April 13th, 2011 07:49 pm (UTC)
Colors
¿What about the colors?
Is it red for Analysis, green for geometry and blue for algebra?
даняagvares on July 14th, 2011 01:35 pm (UTC)
you're awesome
Abhijeet Sai DasariAbhijeet Sai Dasari on February 23rd, 2012 08:29 am (UTC)
It is a great picture in artistic nature...but i was disappointed not to see a single INDIAN MATHEMATICIAN!! (even though,they had contributed so much to the field of mathematics in early BC's!!!)
Sebastian KaSebastian Ka on August 6th, 2012 05:43 pm (UTC)
seriously, i think there should be gauss and euler on top. and newton and leibniz almost on the same level. but this is debatable.

still ... a remarkable, astonishing picture. really.
Renan Maneli MezabarbaRenan Maneli Mezabarba on March 29th, 2013 06:47 pm (UTC)
Just amazing! Congrats!
Patrick: patrickwonderspatrickwonders on August 12th, 2013 03:49 pm (UTC)
Awesome. Wonderful!
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