Tag Archives: Mathematics

Jew of the Week: Avraham bar Chiya haNasi

The Rabbi Who Discovered the Quadratic Formula

Avraham bar Chiya (c. 1070-1145) was born in Barcelona to a Sephardic Jewish family. It appears that his family was persecuted by its Christian rulers, so they fled to the neighbouring Arab kingdom of Zaragoza. Bar Chiya came from a long line of rabbis, and was also extensively trained in science, math, and astronomy. Famed for his wisdom, he became the court astronomer of Al-Musta’in II. Eventually, he was appointed minister of police and given the title sahib al-shurtah, “city governor”. This is why he was known in the Jewish community as HaNasi, “the prince” or “the president”. Al-Musta’in II was unable to defend his domain from the Christians, who soon took over. Bar Chiya moved to southern France for a while and lived in Narbonne and Provence. There he composed some of the most important scientific texts of the Medieval era. He translated a number of Arabic works into Latin, opening their study for Europeans, and played a key role in introducing the Hindu numerals we use today (by way of Arabia) to Europe, and thus to the rest of the world. Bar Chiya also synthesized ancient Greek wisdom with contemporary Arabic knowledge, and published new discoveries in number theory, arithmetic, geometry, optics, astronomy, and music theory. His Treatise on Measurement and Calculation inspired later greats like Plato of Tivoli and the world-famous Fibonacci. Meanwhile, Bar Chiya also served as the chief rabbi of the Jewish communities he presided over, and composed two important Jewish commentaries and texts. He is credited with being the first person to write a scientific book in Hebrew, and played an instrumental role in the development of the Hebrew language. His disciples included both Jews and non-Jews, among them the great Rabbi Abraham ibn Ezra, and the Flemish astronomer Rudolf of Bruges. The first historical appearance of the quadratic equation (with a complete solution of x2 – ax + b = c) appears in one of Bar Chiya’s works! He is also referenced in many philosophical works as “Abraham Judaeus”. All in all, his impact on the development of science, mathematics, and human history is unparalleled.

Jew of the Week Turns 10 Years Old Today!

What I Learned from 10 Years of Writing Jew of the Week

Words of the Week

The mind of man plans his way, but God directs his steps.
King Solomon (Proverbs 16:9)

Jews of the Week: Murray Gell-Mann and George Zweig

Discovering the Quark

Murray Gell-Mann

Murray Gell-Mann (1929-2019) was born in Manhattan to Austrian-Jewish immigrants from what is now Ukraine. Passionate about math and science from childhood, he graduated high school at the top of his class years ahead, and began studying at Yale when he was 14 on a full scholarship. He had his PhD from MIT by 22. He did research at multiple universities before moving to Caltech in 1955, where he became the youngest professor in the school’s history, and taught there until retirement. In 1958, together with Richard Feynman, he made a huge discovery with regards to the weak nuclear force (one of the four fundamental forces of nature). He went on to make many more important discoveries in the field of quantum physics. He is most famous for proposing the quark model – revolutionizing the world of sub-atomic particles – and for coining the term “quark”. Gell-Mann won a Nobel Prize in 1969 for his work. He is also credited with defending and popularizing string theory. In the 1960s, Gell-Mann was a co-founder of the Jason Division which advised the US military and helped to develop anti-ballistic missiles. He was a science adviser for presidents Nixon and Clinton, and was an editor of the Encyclopaedia Britannica. Later in life, he delved into “complexity science”, tackling some of the most challenging problems in nature (especially biology). He even co-founded the Santa Fe Institute for researching this kind of complex science. Gell-Mann wrote a best-selling science book called The Quark and the Jaguar, and inspired the Gell-Mann Amnesia effect (see below). Sadly, Gell-Mann passed away last month.

George Zweig

Gell-Mann was not alone in his proposal of the quark model. The same model was devised independently by George Zweig (b. 1937), who was born in Moscow to German-Jewish parents fleeing Nazi Germany. The family moved to the US in 1938 and settled in Detroit. Zweig earned a bachelor’s in math in 1959, and a PhD from Caltech in 1964 (a graduate student of Richard Feynman). He then went to work at the world-famous CERN, where he developed the quark model. (He called quarks “aces”, but Gell-Mann’s name stuck.) Zweig continued to do important work in quantum physics for some time before switching to neurobiology. He helped uncover how the cochlea in the ear transduces sounds into nerve impulses, and how the brain maps sounds, and made other key discoveries with regards to the amazing complexity of the ear. He also invented a device called a signiscope. Zweig was a professor at Caltech for over three decades. Nominated for a Nobel Prize, he has yet to win one, though he has won multiple other prestigious science prizes.

A Jewish Take on the Classic Moral Problem of the Trolley

Words of the Week

The Gell-Mann Amnesia effect is as follows: You open the newspaper to an article on some subject you know well… You read the article and see the journalist has absolutely no understanding of either the facts or the issues… you read with exasperation or amusement the multiple errors in a story, and then turn the page to national or international affairs, and read as if the rest of the newspaper was somehow more accurate about Palestine than the baloney you just read.
– Michael Crichton

Jews of the Week: Edmund Landau and Lev Landau

Two Math Wizards

Edmund Landau

Edmund Georg Hermann Landau (1877-1938) was born in Berlin. As a young boy, he was recognized as a math prodigy, and earned his Ph.D from the University of Berlin by 22. He immediately received a teaching position at the university, where he taught for the next ten years. Meanwhile, Landau married the daughter of Nobel Prize winner (and past Jew of the WeekPaul Ehrlich. In 1812, Landau presented four complex math problems at the International Congress of Mathematicians. The problems remain unsolved to this day. After over a decade teaching at the University of Göttingen, Landau joined the new Hebrew University. He was a co-founder of its math department, and played a key role in the construction of its Mathematics Institute. He taught himself Hebrew so that he could present a novel math lecture at the University’s grand opening in 1925. Two years later, Landau and his family made aliyah. He taught at the Hebrew University for several years before returning to Göttingen. After being removed from his position by the Nazis, Landau settled back in Berlin and occasionally traveled outside Germany to teach. He died four years later. Landau is renowned for his work on distribution of prime numbers, and on what is now called Landau Prime Ideal Theorem. It was once said that “no one was ever more passionately devoted to mathematics than Landau.”

Lev Landau

Edmund Landau is not to be confused with another Jewish math prodigy, Lev Davidovich Landau (1908-1968). Born in Azerbaijan (then part of Russia), Lev Landau started university at 13, published his first paper at 18, and got his PhD in math by 26. He received a scholarship from the Soviet government as well as the Rockefeller Foundation to travel and study abroad. He was soon fluent in German, French, Danish, and English. Much of his time was spent working in the lab of Nobel Prize winner (and past Jew of the WeekNiels Bohr. After returning to the Soviet Union, Landau was put at the head of the physics department at Kharkiv Institute of Physics and Technology. He taught at the University of Kharkiv, and at the same time worked with his student Evgeny Lifshitz on a ten-volume textbook. The Course of Theoretical Physics is still one of the most popular graduate physics textbooks used today. In 1938, Landau was arrested for comparing Stalin to the Nazis. After the intervention of other physicists, he was freed. Ironically, he won the Stalin Prize in 1949 and again in 1953, for his work on building the first Soviet nuclear bomb. Landau is famous for, among many other things, his theory of superconductivity, theory of Fermi liquid, for plasma physics, quantum electrodynamics, and most of all for his theory of superfluidity, which won him a Nobel Prize in 1962. Unfortunately, he couldn’t personally collect the prize because he was in a severe car accident and spent two months in a coma. He ultimately died from his injuries in 1968. Several years before this, his students established the Landau Institute for Theoretical Physics near Moscow. It is still one of the most prestigious physics labs in Russia. Landau was featured in the latest Google Doodle. There is a crater on the moon named after him.

The Torah: A Comprehensive Overview

Words of the Week

Both religion and science require a belief in God. For believers, God is in the beginning, and for physicists He is at the end of all considerations… To the former He is the foundation, to the latter, the crown of the edifice of every generalized world view.
– Max Planck

Google Doodle for January 22, 2019, the birthday of Lev Landau.