History and Mathematicians Section

You will begin a long journey that extends from the emergence of the first civilizations in the Nile Valley (Egypt), the most fertile place in North Africa, and in Mesopotamia (Tigris and Euphrates), where a product of these civilizations was mathematics.

Among other things, the ancient Egyptians developed a numerical system for the purpose of counting, based on different symbols for ones, tens, hundreds, and thousands. Inscriptions of sequential numbers are found on the wall of Thutmose III in the Temple of Karnak. Later, the Babylonians surpassed the Egyptians in arithmetic and created the first modern numbering system.

In 500 BC, the oldest school of mathematics was founded by Pythagoras in southern Italy. It was particularly concerned with the study of the properties of numbers and the measurement of objects and gave importance to the triangular numbers 1, 3, 6, 10, 15 and the perfect square numbers 1, 4, 9, 16, 25. The study of pictorial numbers was passed on to us from Hippolytus’s Arithmetic to the age of globalization.

Later, the solution of Fermat’s Grand Theorem was introduced as a fine example of global collaboration in our time, and as one of the most important mathematical achievements of the 20th century.Portraits of mathematicians are scattered throughout the museum, and you will meet the people who are credited with this wonderful science such as Greeks, Arabs, Germans, Indians and others from all over the world who were united by their marvelous mathematical intellect, and their theories are the living witness to their immortality.

1) Pythagoras

All things are numbers and the whole cosmos is a scale.

A philosopher, and the first pure mathematician, Pythagoras was strongly influenced by Egyptian priests. He founded a secret mystical society – the mathematikoi – who lived a communal life and practiced vegeterianism. To numbers they attached personalities – masculine or feminine, perfect or incomplete, beautiful or ugly. Among their many discoveries in arithmetic, geometry and astronomy, were the existence of irrational numbers, and the Pythagoras theorem. They were the first to show that Venus as a morning planet was the same as Venus as an evening planet.

2) Archimedes

Give me a lever long enough, and a fulcrum on which to place it, and I shall move the world.

Perhaps the greatest mathematician of antiquity. It is said that when he discovered the laws of buoyancy, he jumped naked from his bath, crying “Eureka” in the street. A rare manuscript, discovered in a monastery in Jerusalem, contained a letter of Archimedes to Eratosthenes, in which he explains his method for computing volumes, anticipating calculus by almost 2000 years. His last wish, before dying at the hand of a Roman soldier, was to finish some computations he was making in the sand.

3) Al-Khawarizmi

What is the square, which combined with ten of its root will give a sum total of 39?

A scholar at the “House of Wisdom” established by the caliph Al-Mamun in Baghdad, Khawarizmi translated the Greeks, and was the writer of an important treatise on equations, Hisab al-jabr w’al-muqabala, in which the word “algebra” appeared for the first time. In his second famous book, On the Hindu Art of Reckoning, Khawarizmi popularized the decimal system, and the standard methods of arithmetic. The word “algorithm” is derived from his name.

4) Omar Khayyam

…In the science of algebra one encounters problems dependent on certain types of extremely difficult preliminary theorems…

Better known as the author of some 600 poems – the Rubaiyat, Khayyam was firstly a mathematician and an astronomer working under difficult conditions in the Seljuq empire. He calculated the length of the sun year to within a few seconds, and laid out a general theory of cubic equations. His claim that such equations cannot be solved by geometric methods involving ruler and compass was only proved by Abel and Galois in the 19th century!

5) Fibonacci

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair, which from the second month on becomes productive?

This famous problem, from the Liber abaci, is an example of situations that give rise to the Fibonacci sequence 1,1,2,3,5,8,13,21… Working in Pisa under the patronage of Frederick II (founder of the University of Naples, and the crusader King of Jerusalem) Fibonacci was responsible for spreading algebra and the decimal system in Europe during the Middle Ages. His contributions to number theory were surpassed only by Fermat, 450 years later.

6) Fermat

I have discovered a truly remarkable proof, which this margin is too small to contain.

A lawyer in Toulouse, Fermat was preoccupied with number theory. Many of his deep discoveries he wrote down in the margins of a Latin copy of Diophantus’ Arithmetica. Fermat’s Last Theorem is the assertion that the sum of two third powers of positive integers cannot be itself a third power, and the same for fourth powers, fifth powers etc. Generations of mathematicians tried to prove it, attempts that led to fundamental developments in number theory. Andrew Wiles finally found a brilliant, but long and complicated, proof in 1995. It now seems likely that Fermat himself did not have a valid proof.

7) Newton

To explain all nature is too difficult a task for any one man… It is much better to do a little with certainty, and leave the rest for others.

Thus in mechanics Newton “only” explained gravitation and the motion of the planets. In optics he “only” discovered the nature of light. In mathematics he “only” invented (along with Leibnitz, with whom he quarreled endlessly) calculus, the analysis of infinitely small quantities, on which a large part of modern mathematics rests. A difficult person by most accounts, Newton was a self-taught genius. His Principia Mathematica is considered the greatest scientific book ever written.

8) Euler

Now I will have less distraction (upon becoming blind in his right eye).

Swiss by birth, Euler moved to St.Petersburg (Russia) where he teamed up with some of the greatest scientists of his age. Although his duties included state projects related to ship building, cartography and other applications, his main contributions were in number theory, differential equations and mechanics. The most prolific writer of mathematics of all times, Euler described himself as the happiest man in the world, when Frederick the Great invited him to be “the King’s Professor”.

9) Gauss

I have had my results for a long time: but I do not yet know how I am to arrive at them.

At the age of nine Gauss amazed his teachers when he summed all the numbers from 1 to 100 by observing that the sum was 50 times 101. Nicknamed the “Prince of Mathematics”, he made fundamental discoveries in number theory, non-Euclidean geometry, differential geometry, astronomy and magnetism. War in Europe and death in his family did not prevent him from transforming Goettingen into the most important center for mathematics, up till World War II.

10) Hilbert

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

One of the last giants who worked in almost every field, from logic to relativity, Hilbert concentrated his efforts in one area at a time. His address to the 1900 International Congress of Mathematicians in Paris, containing his famous 23 “problems”, shaped the course of mathematics in the 20th century. Hilbert contributed to a major trend of abstraction, where seemingly remote examples were shown to obey similar rules, yielding new structures, and even new fields of research.

11) Emmy Noether

After all, the university senate is not a bathhouse!

This was Hilbert’s response to the professors at the university of Goettingen who objected to the appointment of Emmy Noether to the faculty, on the grounds that she was a woman. The daughter of a mathematician, Emmy Noether became one of the leading algebraists in the early 20th century, when algebra was rapidly becoming more abstract and more geometrical. Hilbert won her case at the end, but being a Jew, and a leftist, forced her eventually to flee from Germany to the United States.

12) Ramanujan

No – it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.

G.H Hardy tells that he was riding a taxi whose license plate number was 1729. He remarked that this was a rather dull number, to which Ramanujan immediately replied with the above. A self-taught genius, Ramanujan’s phenomenal computational abilities allowed him to make amazing discoveries in number theory, without any formal background. Suffering from illness and poverty, he came to Cambridge, England, where he and Hardy started an exceptionally fruitful collaboration.

13) von Neumann

In mathematics you don’t understand things. You just get used to them.

A pioneer in many areas of mathematics, “Johnny” was a founder of game theory and of theoretical computer science, and an important contributor to statistical mechanics. Educated in Hungary and Berlin, he moved in 1930 to Princeton, U.S.A., where with other European immigrants he conducted his research at the Institute for Advanced Studies. In 1945 he designed one of the first computers, the “von- Neumann machine”.

Al-Quds University