The human mind is capable of great things. When the most brilliant minds of the world are concentrated for long periods of time truly amazing things can happen. Some math and science problems go unsolved for centuries because most of us lack the intelligence needed, most of us lack the concentration required, and the vast majority of us are tied up with other obligations. These men did not make excuses like most people. In these following instances, problems that have plagued many intelligent minds were solved by strokes of pure brilliance. None of the problems were guaranteed to have solutions.
Number 5: George Dantzig, 1939
Have you ever turned in a homework assignment late?
So has George Dantzig. He walked into his graduate study class late one day at California Berkley. On the board were two statistics problems. He took three days to complete them, and then threw them frantically on Professor Neyman's desk. He then apologized for turning them in so late.
The problems were not homework problems. They happened to be famous unsolved statistics problems, as in they had never been solved before by anyone. Within a few years both of his solutions were published. One was published by his own Professor Neyman, and another by Abraham Wald. Most human beings would have considered just solving one of these problems as a lifetime accomplishment, but he solved two in three days.
So what was your excuse for turning in your homework late?
George Dantzig wasn't finished. Among many awards, honors, and accomplishments, he worked on linear programming (top secret during WWII).
Among his most impressive solutions:
Most people would find it hard to best fit 70 people to 70 jobs. It might take you centuries to come up with all of the possibilities, decades to pick the best one, and another few years to prove that you were correct. However, he came up with an application of linear programming that involves a simple equation that would find the best fit for 70 people to 70 jobs very very quickly. That is of course very useful when the government you're working for is trying to wage a World War.
Number 4: Grigori Perelman, 2002
In the year of 2000, the Clay Mathematics Institute set aside 7 problems for the coming millennium that a bunch of mathematicians came together and decided were really frickin' hard. These problems were published in order to raise public awareness that math still has a promising frontier. They were dubbed the "Millennium Prize Problems" and set aside $1 million as a prize for a solution to each problem.
As of July 2011 when I'm writing this article, only one has been solved. To give you an idea of how difficult this problem was, here is a quote that is intended to simplify the problem from mathworld.wolfram.com:
"The Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense), where a three-sphere is simply a generalization of the usual sphere to one dimension higher."
Right. A topology problem. If that doesn't leave you scratching your head, then you're at least one step ahead of me. Anyway, this problem had been unproven since around 1904. Mathematicians are a special breed because they won't accept billions of examples as sufficient evidence. They have to have proof. So an American named Richard Hamilton made significant progress on the problem. He then advocated a program that would publicize and promote the problem. As a result it turned up on the Millennium Prize Problem list.
Grigori Perelman comes in and solves the problem by November 2002 (at most 2 years), although it is unclear when he started working on it. He published it very discreetly online on Cornell University's Library site. It simply claimed to have solved the toughest portion of the Poincaré conjecture. It took until 2003 to verify it, and others had to fill in some gaps in his work.
The story gets more interesting. After all of the buzz, he was awarded the Fields Medal, the highest award in mathematics. He declined. He declined awards from the European Mathematical Society and International Congress of Mathematicians in Madrid. He was then awarded the Millennium Prize Problem $1 million, and declined the prize and money. Perelman declined the Millennium Prize Problem money because he didn't think they gave enough credit to Richard Hamilton. He cited different reasons for declining the rest of the prize committees. He especially cited the reason that he did not enjoy any money or fame and that he did not want to feel like a zoo animal. Despite valiant attempts to persuade him to accept the awards, he stood firm. Would you decline $1 million because it made you feel like a zoo animal?
Side note: If Wikipedia is to be trusted, he is also proficient at violin, table tennis, and probably lives with his mother. Oh yeah, and it is likely that he has stopped doing math.
Check out 2:31 on the video
Number 3: Mohamed Altoumaimi, 2009
Bernoulli numbers are very famous in the mathematics world. They deal with prime numbers and exponents. They are also quite important to number theory. The Bernoulli numbers have many complex patterns and relationships that an untrained eye will probably not see easily.
Mohamed Altoumaimi, who would later become very familiar with Bernoulli's numbers, was forced to immigrate in 2003 to Sweden because of the U.S. invasion of his home country, Iraq. This would allow him to further study his favorite two topics, math and physics.
It took him only four months to find complex equations that solved and explained 300 year old relationships originally described by a Swede, Jacob Bernoulli. These equations he created were unique, and they were very advanced although albeit not completely new to the mathematics world. Altoumaimi's colleagues were puzzled about his complex equations, and so he took it to Uppsala University to have them checked. They were considered an amazing achievement there.
Keep in mind that Altoumaimi had his interesting beginnings in a war-torn Iraq.
Oh yeah, and he was only 16. A.K.A. a freshman in high school. His "colleagues" I described earlier: skeptical high school teachers (wouldn't you be skeptical too?).
So about the time you were perfecting a spitwad technique, dealing with acne breakouts, and being rejected to the school dance, he had already fled Iraq to Sweden and developed groundbreaking math equations. If Dantzig didn't make you feel bad about not doing your homework, Altoumaimi will make you feel bad for not achieving more than a little league championship or the honor roll by age 16.
Number 2: Andrew Wiles, 1994
This one sends chills up my spine. It was a big topic of discussion in my undergraduate Mathematician's Toolkit class. Gee whiz, where do I start?
Pierre de Fermat was a brilliant mathematician. If you haven't heard of him, you should have. He pioneered calculus (as in Newton specifically gave him credit for the idea), and like Grigori Perelman, didn't like money or fame. He didn't use his talents to specifically develop groundbreaking work (although he happened to do that as a biproduct of his math). Instead, Pierre de Fermat worked as a lawyer. He also spent most of his free time finding ways to torture England's Mathematical Society.
Fermat would do problems for his own enjoyment. He created a number of theorems, and then lazily wrote down the proofs. Most of his proofs were lost over time or he did not give them. Unlike a normal person, he didn't really care if he was given credit for solving them. He took more pleasure in watching others squirm as they themselves could not match his skill. This lead to disbelief on many accounts. Most mathematicians called bullshit. They didn't think Fermat himself could prove these theorems (often dealing with number theory). Not just the poor mathematicians, either. Even Carl Gauss said that Fermat was a load of bull. So was he? That's for you to decide.
The best example of this is Fermat's Last theorem. The problem even has its own blogspot page. It is simple enough for anyone to understand, but no one could prove it until 1994. The problem states, again thanks to wolfram.mathworld.com:
"As a result of Fermat's marginal note, the proposition that the Diophantine equation
Basically this means the Pythagorean theorem (x2+y2=z2) is the only equation in this family that has a solution. Replace the 2 with a 3 (or any whole number higher than 2), and it won't have a single solution.
Seems almost incredulous doesn't it? So Fermat scribbled in the margins "I have developed a truly marvelous proof which this margin is too small to contain." Once again, teasing mathematicians for hundreds of years. He didn't even published the theorem, his son published it posthumously.
So literally for hundreds of years the greatest mathematical minds worked on this. There was immense frustration by all accounts. The theorem was tested and tested, and no one could prove that it was not true. The full story on how it started to unravel is beyond the scope of this article. However, realize that it was a very slow process. Modern day mathematics proved areas of it, but came honestly nowhere close to solving it.
So Andrew Wiles, a very brilliant mind himself, locked himself in his attic for 7 years working on this in complete secrecy. He started in 1986, and didn't come out hardly ever until 1993. This of course threatened his marriage and had other unintended consequences. Just as professional musicians have an unwavering passion for music, and sports players have a fiery passion for sports teams, Wiles had that same drive for solving this problem.
After he announced his great accomplishment in 1993 to an audience of mathematicians (it took two days to explain briefly), he waited and waited. Everyone knew what came next: relentless scrutiny by "checkers" who would look for errors in his logic. A few of these mathematician checkers found the same discrepancy in his proof. Uh oh.
This discrepancy not only was available for other mathematicians to solve, but also presented a problem that no one had solved before. Wiles consulted others, and then locked himself in a room for another year trying to figure out this gap in his logic. Just when all seemed lost, and he was really close to quitting, his friend happened to mention a form of new math passively. Wiles ran home and developed his proof off of this. He published two papers fixing the problem.
It was done. Wiles had proven Fermat's Last Theorem. Had Fermat done it before 1660?
Most people agree that Fermat's proof was erroneous. However we can't be sure. If he did have a proof, it would be like a 17th century astronomer building a rocket that could reach the moon. The math that Wiles used was completely foreign to anything before the 19th century.
Cydro is a firm believer that Fermat did have a marvelous proof, but the margins were simply too small to contain it.
Number 1: Albert Einstein, 1905, 1916
I bet that you might have expected this one.
Albert Einstein is probably the most prolific mathematician/physicist of all time. You've probably heard of him. He made the number one spot by not rewriting physics laws once, but twice.
His most famous work, e=mc2, might ring a bell. If you don't know what this means, it means that there is a fundamental relationship between energy, mass, and the speed of light.
To put this in perspective, the heat from your microwave is energy. If you had 299,792,4582 (the speed of light in m/s, and then squared) Joules of this energy, you could produce 1 kg of mass. For 1 gram of mass, you have to have about 25 kilowatt-hours of energy. Think how much energy is stored in your couch.
Finding out that mass and energy are related in 1905, before there were cars, was purely a stroke of brilliance. It also had enormous consequences. An atomic bomb is created by releasing the energy within the atom. The bombing of Nagasaki had about 1 kg of plutonium in it.
This also means that heating an object makes it more massive, albeit minutely. It also means spinning objects are more massive than if they were not spinning. Lastly, it insinuates that a spring is more massive when it is compressed.
In 1916 he came out with his General Theory of Relativity. Why is that so special?
Well it has interesting consequences. It states, among other things, that if you speed up fast enough, time slows down. That means if you cruised in a spaceship around the world at 95% of the speed of light for 2 years, and came back to Earth, people on Earth would have aged many more years. You would be in the future.
So time is not constant for everything in the universe.
Also as you speed up and approach the speed of light, you become more massive. The universe has a speed limit (sorry future space travelers). This is because if you traveled at the speed of light you would have infinite mass and thus would require infinite energy. Sounds pretty hard to do to me.
It also allows for the existence of black holes (Newtonian physics does not), as well as gravitational lensing.This is just the tip of the iceberg. Einstein also solved the dilemma of Brownian motion, a problem that had plagued physicists for quite some time. Not to mention his revolutionary General Theory of Relativity has yet to be proved wrong at all (yet we're still experimenting on it).
Other hubs about the Einstein:
Heisenberg_Cat on August 21, 2014:
StevenMurphy, other than the anglo-bias evinced in your name, on what grounds is Isaac Newton "by faaar (!!)" the greatest mind to walk the earth"? Leibniz's version of calculus, for all intents and purposes, is what we use in teaching calculus today (BOTH Euler, Gauss, and Bernoulli used Leibniz's form of calculus in applied theory NOT Newtonian calculus -- due to the consistency of notation form). Leibniz also squared the equation f = mv, a HUGE deal. Laplace invented Pertubation theory to correct for some of Newton's lapses (mistakes), and Newton, as history has shown, stole his inverse square law of gravity from Robert Hooke (and later, as head of the Royal Society, attempted to destroy any memory of Hooke by burning/erasing his works from the office of the Royal Society). Einstein is the father of modern physics and no alibi can disprove it (a poetic variant of a wonderful quote by Max Born).
simi on June 13, 2013:
dat was reallly useful to me !!!! thanks hub i was in a gr8 need of it even though i dnt kno many of these maths concept but yea !! these guys did a wonderful job !!!!! hats off !!!!!!!! :) :) :)
StevenMurphy on March 14, 2012:
Laughable. Isaac Newton was by faaar(!!) the greatest mind to walk the earth as far as mortals go. (Jesus Christ doesn't count due to Him being the 2nd member of the Holy Trinity.)
Blake Atkinson (author) from Kentucky on July 12, 2011:
Thanks Simone! Yeah I chose to focus on math and physics because of my own personal background which has traditionally been male dominated (despite some really lucrative grad school scholarships for women). Marie curie is very worthy though so I might add her in an update.
Simone Haruko Smith from San Francisco on July 12, 2011:
Whoah, this is so cool! I hadn't known about most of these folks. Now... if only there were some women on this list! I guess that until recently, it has been more difficult for women to have the opportunity to become as highly educated as their male counterparts.
mactavers on July 06, 2011:
While I don't understand many of these math concepts, I can appreciate the fine job that you did on this Hub and those wonderful minds that were able to solve the seeming unsolvable problems.