Link to the life stories of four famous mathematicians

Click on this link to read the life stories of Archimedes, Newton, Euler and Gauss.

Link to the four great mathematician biographies

Here is the link to the biographies of Archimedes, Newton, Euler and Gauss.

Five eccentric 19th British mathematicians who started mathematical logic.

Mathematical logic got its first great boost forward in the 19th Century, though at the time there was little practical use to it.

George Boole is considered the originator of modern mathematical logic, so much so that the field is called Boolean Algebra. He wrote his important treatise The Laws of Thought in the 1850s.

Augustus de Morgan is another important pioneer. The ways to distribute a not sign ~ through parentheses are called de Morgan's laws.

~(p v q) = ~p ^ ~q
~(p ^ q) = ~p v ~q

He was one of the first professors at University College London, the first major school in Great Britain that accepted students who were not Church of England, which meant that Catholics, Jews, protestants of denominations other that Church of England and those who professed no faith whatsoever could get a first class education in Great Britain.

Charles Babbage was another British logician, and he wanted to take mathematical logic to the next step. He designed the world's first mechanical computers, the Difference Engine and the Analytical Engine, both of which were designed to run on steam. Problems arose when trying to build the machines and neither was ever completed.

This did not stop Countess Ada Lovelace, the only legitimate daughter of the famed British poet Lord Byron, from designing programs for Babbage's machines. The Countess Lovelace was educated by de Morgan and is given credit as the first computer programmer. the language Ada is named after her.

The best known of the British eccentrics fascinated with logic in the 19th Century was Charles Dodgson a.k.a. Lewis Carroll. While still famous for Alice in Wonderland, he was also a mathematician, clergyman and photographer, and enjoyed putting together logic puzzles based on the ideas of syllogism using silly but logical statements. For example:

(a) No ducks waltz.
(b) No officers ever decline to waltz.
(c) All my poultry are ducks.

Therefore (d) None of my poultry are officers.

Here is also a link to the biographies of five 20th Century mathematicians who made great contributions to the field of computer science when it was much more practical.

Five computer scientists

Here are the highlights of the life stories of five important people in the history of computer science. There are many others, but these folks made significant contributions and their lives have interesting and unique tidbits which will be shared here.



Born Janos Von Neumann in Hungary, he is known to posterity as John Von Neumann, though his friends always called him Johnny.

I give Von Neumann the first position on this list because he is the greatest mathematician on the list. The list of four great mathematicians I lectured about on the first day only takes us through to 1855, when Gauss dies. If we were listing great mathematicians since then, almost all mathematicians would put Bernhard Riemann, Henri Poincaré, David Hilbert and John Von Neumann on the list of the greatest of the great.

Not Albert Einstein. He is a great physicist, but not a great mathematician.

Von Neumann started his career in chemistry, but after he did the mathematical groundwork for the ideas of quantum mechanics, he switched to mathematics. This is some of the strangest and least intuitive mathematics ever done, and it shows that at the sub-atomic level, it is possible for some small objects to be in two places at the same time. When people would ask him how he understood some of the strange ideas he came up with in his life, Von Neumann said: "You don't really ever understand higher mathematics. You just get used to it."

Besides his work in mathematical physics, Von Neumann solved a conjecture of Borel and created the field now known as game theory. A century before, a Prussian tactician named Von Clausewitz put forward the idea of total war, that a country at war must put forward every available resource or it wasn't truly war at all. Von Neumann's game theory proved Von Clausewitz wrong, that successful war strategies include bluffs and strategic ways to put forward only part of the available resources and still meet your objectives.

Among his practical inventions include the trigger for the hydrogen bomb, which makes an atomic explosion "slow" enough that it begins a larger chain reaction instead of obliterating all matter in a radius of several hundred yards instantly. The larger chain reaction makes for an explosion thousands to millions of times stronger.

The reason Von Neumann is on this list is because he invented the idea of software. When the first computer were created, they had to be re-wired by hand every time a new problem was to be solved. There was computer memory, but it just stored data. Von Neumann put forward the idea that some of the memory hold instructions, and the computer should be hard-wired to understand these instructions. It is nearly impossible to overestimate the importance of this idea.

Von Neumann died of cancer in 1957 at the age of 53. The amount of important work he did in such a short life is as amazing as any of the great composers who died young, like Mozart or Chopin.



Alan Turing was born in England, and he was an excellent math student before the innovation of computers. He is given credit as one of the people who proved the Central Limit Theorem, a key fact that makes statistics work.

Turing's most famous practical work was breaking the German codes during World War II using some of the first computers ever built. The Germans had a code machine called Enigma, which could scramble a message in a way that was very difficult to unscramble without another Enigma machine at the other end AND the particular starting position of the machine when the operator began typing the message in. The British code breaking team was housed during the war at Bletchley Park, and some of the things that happened there have only been de-classified in the past ten years of so. All the information points to Turing as being the intellectual star of the team.

Turing also came up with theoretical concepts in early computers, including the Turing machine, an idealized computer with two tapes, one for input and one for output, and the Turing test for artificial intelligence.

Turing was also very openly gay at a time when that was illegal. He was charged in a court of law with engaging in homosexual acts and found guilty. He was given the option of going to jail or taking a "cure" of estrogen treatments. He chose the cure. It did nothing to change his feelings, but it did make his breasts bigger.

Turing died in 1954 at the age of 41 from eating a poison apple. He was working on electrolysis, a way of plating one metal on top of another, in this case silver plating, and absent-mindedly picked up an apple and took a bite when his hands were covered with poisonous chemicals. The authorities ruled it a suicide, though Turing's mother believed it was just an accident.



Back in the day, the actual work of programming was considered "woman's work", and many of the programmers back in the era of the huge mainframes were women, who were considered better suited to the painstaking work of making sure there were no errors in a piece of computer code. This stereotype made it possible for some women to get employment other than secretarial work in business in the middle of the century in the United States, and the stereotype continued in Japan well into the 1980's, when I was a programmer of video games in the U.S. In the era of Pac-Man and Donkey Kong, the video game designers in Japan were men, but the programmers were women.

Grace Hopper was born in New York City in 1906. She was a good math student, getting her bachelor's degree from Vassar and her doctorate at Yale. During World War II, she worked for the Navy and was on the team creating some of the first computers used by the U.S. Military, including the Mark I.

She is given credit for finding the first computer bug, which means a mistake in the program which keeps it from running properly. The bug she found was an actual bug, a moth that found its way into the computer and died when it hit the exposed wires, causing a short circuit.

Her ideas about designing a software language gave rise to COBOL, a language that was the standard for business software for many decades. Though it has been eclipsed by more modern languages, there are still listings for jobs for people who program in COBOL to this day.

She wanted to understand the connection between the speed of light and the workings of the computer that work on electricity, which moves at very close to the speed of light, so she had engineers cut pieces of wire that would show how far electricity would travel in a nanosecond, a billionth of a second, and she would hand these wires out when she gave lectures.

Hopper kept her Navy commission throughout her life, and retired with the rank of Rear Admiral.

She died in 1992 at the age of 85. She was buried with full military honors at Arlington National Cemetery. The U.S.S Hopper is one of the few ships in the Navy named after a woman, and the ship has the same nickname that the admiral had in life, Amazing Grace.


Edsger Dijkstra was born in Holland in 1930, about a generation after Hopper and Turing and Von Neumann, and his contributions to computer science dealt with changing computer programming from a haphazard practice to a well-structured and defined set of proper practices.

He started working in computers in the 1950's, and computers were still strange and exotic devices to the general public. When Dijkstra applied for his wedding license, her put "computer programmer" down as his line of work. The clerk at the registrar's office made him change it, saying that nobody programmed computers for a living. He crossed it out and wrote "theoretical physicist", which the registrar accepted as a real job people get paid for.

While Dijkstra is given credit for developing some important methods for solving problems, his main influence today is the idea that a computer program should be completely designed before anyone ever starts typing in code into a machine. There were some computer languages he felt caused people to fall into bad habits, including Grace Hopper's COBOL and other popular languages of the 1960's, including BASIC and FORTRAN. A more modern concept in programming called object oriented programming also met with his disapproval. "Object oriented programming is an exceptionally bad idea that could only have originated in California."

Another famous quote attributed to him is: "Computer Science is no more about computers than astronomy is about telescopes."

Dykstra died at the age of 72 in 2002. When asked by an interviewer what he would like to be remembered for, he replied: "If some day, someone is writing a computer program and is thinking about how to do a quick and sloppy job, and for a moment that person considers 'What would Dykstra make of this?', then decides to design the program carefully, that will be immortality enough for me."


Donald Knuth was born in Wisconsin in 1938. He was a very good student and at an early age he showed how obsessed he could be with solving a problem. He skipped nearly a week from high school trying to win a national competition to find the most words that could be made using the letters in the phrase "Ziegler's Giant Bar." Knuth found 2,500 words. The second place competitor found about 600. He said he could have found more if he had realized he was allowed to use the apostrophe. The prize was a television set, which he donated to the high school.

Knuth's best known work is the textbook series The Art of Computer Programming. The first four volumes have been around since the 1970s and 1980s. The fifth volume was released only a few years back. When people send Knuth corrections to his textbooks, he send the first person who correctly spots an error a check for $2.56. The number 256 is the number of different patterns an eight bit binary string can create. Most people who get the checks frame them and hang them on their walls as souvenirs.

Donald Knuth is still alive and is professor emeritus of computer science at Stanford University. A devout Lutheran, his web page lists his public speaking engagements, and includes the Sundays when he will give a sermon as the deacon of his church on some text from the Bible.

Four great mathematicians

Archimedes of Syracuse: born 287 BC, died 212 BC. The greatest thinker of antiquity. Known for inventions for centuries, including weapons he developed for his relative King Hieron of Syracuse and a famous method for irrigation called the Archimedes Screw, still used to this day, he was proudest of the mathematics he did, and asked for one of his discoveries, the relation between a cylinder and a sphere inscribed in it, to be put on his tomb. There are three famous stories about him that include quotes.

"Eureka!": King Hieron was given a gift of a gold crown, but he wanted to make certain it was really gold without melting it down. He asked Archimedes if he could come up with a test. Archimedes has in his bathtub when he saw the level of the water rose when he entered, and thought about why a large boat would float while a small rock would sink. He came up with the laws of displacement and realized it could be used to see if the crown was really gold or just another metal with gold plating. He was so excited by this, he ran through the streets of Syracuse to the palace of the king naked, yelling "Eureka!" which means "I have found it!"

"Give me a lever and a place to stand and I could move the earth.": Archimedes challenged a mighty warrior to move a massive stone brought to the palace. The warrior could not, but Archimedes took a long piece of wood, and using a small rock as the fulcrum, he was able to move the large weight using leverage. Many of his inventions used leverage, either directly like a lever and fulcrum or indirectly like turning screw.


"Don't disturb my circles!": The Roman general Marcellus was invading Sicily and laid siege to Syracuse. He gave specific orders that Archimedes was to be captured and brought to him alive. With the battle raging in the city, Archimedes, then in his seventies, was working hard on a geometry problem and paid no attention to the clamor around him. A soldier burst into his home and found him on his patio working on math. Archimedes did not notice the soldier until the man's shadow cast on the work Archimedes was doing, and when that happened, Archimedes spoke sharply at the young man. "Don't disturb my circles!" the old man snapped, and the soldier, unhappy with the disrespect, stabbed and killed Archimedes. Marcellus was very upset by this, and paid for lavish tomb to be built for the great inventor, with the cylinder and sphere put on top of it.

As great as his reputation has been for more than two thousand years, Archimedes had a new work "discovered" in the 20th Century, when an illuminated prayer book from the 10th Century was discovered to be a palimpsest of one of Archimedes' lost works, which is a book written over the paper of another book. This work shows that he understood the basic concepts of integral calculus, a field of study not fully understood by the rest of mankind until our next great mathematician comes along.


Sir Isaac Newton: born 1642, died 1727. Born in England prematurely on Christmas day, 1642, Newton's father was quoted as saying that Isaac could fit in a pint mug when he was born. His father died soon after and his mother re-married, and the family struggled to make ends meet. Newton's cleverness showed itself early as he designed toys for himself that actually worked, like a toy wagon whose wheels turned and whose axle could be steered. The owner of the land on which Newton's father worked decided to sponsor the boy to go to Cambridge, which was then and is still now one of Britain's great universities. Late in his studies in 1666, plague swept through Europe and the universities were closed. Alone on the farm from 1666 to 1669, Newton did much of the great work of his life, including the three laws of motion, the laws of optics, the laws of universal gravitation and the mathematics behind it all, integral and differential calculus. For this, he is considered the father of modern physics.

For all his talent at theoretical work, Newton was also a practical man. He invented the reflecting telescope, the kind that you find at large observatories. He was knighted for his work at the Royal Mint, where he developed ways to catch makers of counterfeit coins.

Personally, he was very shy, and there is some speculation that he had a mild form of autism known as Asperger's Syndrome. He would rock back and forth when in intense concentration and disliked being touched. He wrote to a friend that he was proud and happy that he would die a virgin.

While his great work was finished by 1670, Newton did not like dealing with people and had to be coaxed into publishing his findings, which he finally did in 1687 in a book called the Principia Mathematica, short in Latin for the mathematical principles of physics. While the book had its detractors, soon enough the world saw how important a work it was, and Newton's became world famous.

He actually spent much more time studying the Bible and alchemy than he spent on math, but he never published these other works. Some of his religious scholarship was heretical at the time, like his proof that the Holy Trinity was physically impossible, and his calculations that the end of the world prophesized in the Bible would come in 2060 was only written in a letter to a close friend.



Leonhard Euler: born 1707, died1783: Leonhard Euler (pronounced Leonard Oiler) was born in Switzerland. His talent at math was seen at an early age and he became fast friends with the Bernoulli family, a famous few generations of Swiss scientists. He became renowned in his time as the greatest mind of his generation, and worked for both Frederich the Great of Prussia and Catherine the Great of Russia. He is a close contemporary of Ben Franklin (1706-1790), but his reputation as a scientist is much greater. He fathered 13 children, only 5 survived infancy. His first wife died and he married her sister. He went blind, but kept working until he died. In these situations, Euler has parallels with the life of the great German composer Johann Sebastian Bach (1685-1750).

His reputation during his life was very strong. The French mathematician and astronomer Pierre-Simon LaPlace wrote to his students, "Study Euler, for he is the master of us all." His place in history faded somewhat, but there was a strong comeback after all his works were finally published in a single place, 80 quarto volumes of math. (A quarto volume is about the size of a phone book.)

There are so many mathematical ideas that he pioneered, if all of them were named after him the confusion would be too great.A famous function sometimes known as the Riemann zeta function is now more accurately called the Euler-Riemann zeta function. Riemann was alive about a century later than Euler.

The base of natural logs, a very important number in calculus, is named e in honor of Euler, who did a lot of work with the number.


Carl Friedrich Gauss, born 1777, died 1855. When Gauss was born, Germany did not exist, but that is the country that now includes his home region of Brunswick. Gauss was the greatest mathematician in the first half of 19th Century. Like Newton, he wasn't rich, but the Duke of Brunswick became his mentor, and out of respect, he went to the University of Gottingen instead of the most important university in the German speaking work, the University of Berlin. Because he went there and stayed there and his best students stayed there, Gottingen became one of the top math schools in the world until it was destroyed by Nazi policies in 1933.

There is a famous story of him showing his math skills while very young. His class was being noisy, so his teacher told all the students they had to add the numbers 1 through 100 and find the sum. In less than a minute, little Carl raised his hand and gave the correct answer: 5,050.

He had his practical side as well. He is credited with inventing the telegraph and had a working model before Samuel Morse got a patent in the United States. He worked as a surveyor and an astronomer. He "re-found" the largest asteroid between Mars and Jupiter mathematically after a Sicilian astronomer found it and gave several sightings but lost it. He did it solving a difficult equation and didn't tell anyone his method. He was accused of witchcraft.

In his lifetime, Gauss' reputation was so great that when Napoleon conquered most of Europe and imposed a tax on all professors at all schools in conquered territories, the French Academy paid Gauss' tax.