Mathematics – part 2

Nowadays, life is a giant numbers game. Every breath we take is registered in a giant database and added to the gargantuan calculations that will decide whether the world is heading for an ice-age or global roast. This is nothing new.

Back in ancient Greece, Pythagoras of Samos believed that numbers were the basis of everything including music. The story goes that he was once strolling past a blacksmith and noticed that instead of harsh cacophony, his ears were registering what sounded like a pleasant harmony. Striding inside to investigate, he discovered that the smiths’ anvils were all simple ratios of each other. Each anvil was half, a third, or a quarter the size of the other.

Through this he theorized that numbers are part of a cosmic symphony and that even planets and stars were governed by musically related mathematical laws, singing a silent symphony as they circled their infinite trails.

Don’t be too surprised if this seems similar to Pirkei Shira’s description of the Creation’s song of praise to Hashem. Josephus reports that Pythagoras was influenced by Jewish teachings. Sefer Yetzira, too, indicates that numbers are an integral part of creation, albeit on a spiritual level, stating in chapter one, “He created His universe with three books (seforim), with letters (sefer), with counting (sefar), and with communication (sippur),” and in his commentary the Vilna Gaon demonstrates how the total gematria of the letters of alef beis adds up to 6,000 years of creation. The Ramban in his introduction to the Chumash expresses a similar idea in his famous statement that the entire creation is encapsulated in the Torah. After explaining how Hashem taught Moshe all the secrets of Torah and creation in 49 gates of understanding, the Ramban continues,

“Everything handed to Moshe Rabeinu in the gates of understanding, all is written in the Torah explicitly, or hinted through words or gematrios or the forms of letters, etc.” Because of the critical importance of gematria, the Ramban at the beginning of Sefer Hageulah warns that people must know what gematria is and what it is not: “A person should not think that the calculation of letters that we call gematria is nonsense because a person could transform many verses to strange, evil ideas because a person may not use the gematria methodology and reach conclusions that arose in his head. But we have a kabbala (tradition) that Moshe was given certain gematrios to be a zecher (reminder) of a matter said orally. Thus the calculation of gematria is to upkeep (what was given) and not to destroy.”

The Degel Machaneh Efraim issues a similar warning, insisting that truly valid gematria is based on ruach hakodesh: “‘Therefore the moshlim say, come to Cheshbon.’ When great people want to reveal a secret, the moshlim, that is, people who learn the Torah as a parable, say… come to Cheshbon… they derive (a hidden matter) it through calculations and gematria in order to understand the secret of that matter, how it (the Torah) hints that secret. But in truth they understood it from the light of the thing itself that Hashem illuminated for them with His great chesed to enable them to understand that secret.”

In other words, true chiddushim are principally derived not from the gematria but from ruach hakodesh. Nevertheless, many seforim demonstrate how well-known Torah facts coincide with the most incredible gematria. For example: Rav Yosef Chaim Sonnenfeld said that “Tzion B’mishpat Tipodeh” is the same gematria as “Talmud Yerushalmi” (1,076) and “V’shoveho B’tzedaka” is equal to “Talmud Bavli” (524) hinting to the fact that we will be taken out of golus through the merit of Torah.

Of course, Jews have their own history of number conundrums. On the Gemara Sanhedrin (39a), Rashi cites Rabbi Meir’s parable of a fox that told a wolf, “Come with me and I will show you a place where you can eat to satiety.” The fox took him to a well that had two buckets arranged on one rope so that as one bucket went down the other bucket came up. The fox went down in one bucket and called up to the wolf, “There is meat and cheese to eat to satiety here!” The wolf entered the top bucket and the fox came up in the other bucket, leaving the wolf trapped below.

The Maharsha is puzzled by this episode. If the fox was so smart, how could it take the risk of leaping into the first bucket? What would happen if the wolf ignored the invitation to go down and left the fox in the lurch! The Maharsha explains that the cunning fox had a mathematical solution – he took two stones heavier than himself and placed one in each bucket. That way, if the wolf refused to cooperate, all the fox had to do was jettison the stone in his bucket. Then the stone in the other bucket would hurtle down and lift him to the top.

Either the fox made these preparations in advance, or the wolf was too dim witted to realize what his crafty friend was up to.

Another Jewish based puzzle is based on the report of Second Century historian Hegesippus, who reports that Josephus once saved his life through a cunning calculation.

The story begins after the Romans conquered Jotapata (now known as Gamla) in the Golan, and Josephus and other rebels were hiding in a cave. Josephus reports what happened next: “The Romans began to search for Josephus who had leapt down into a deep well, branching into a great cavern. Here he had found thirty-nine of the chief men of the city with a store of provisions sufficient for many days. (After Vespasian found the hiding place) Josephus prepared to come forth when his companions announced: ‘If you die willingly you are still our leader, but if unwillingly you art a traitor!’

“Josephus then said, ‘Since you are resolved to die so that each man may die by the hand of his companion.’ And in the end Josephus was left alive with one other and when these two were about to draw the lot, Josephus persuaded him that he should live.” (abridged)

Hegesippus claims that Josephus’ escape was not through chance, but by cunningly suggesting that the forty men in the cave gather in a circle and proceed to count around the circle, dispatching every third person. By placing himself and the other survivor in the 31st and 16th places from the beginning of the count, Josephus guaranteed that they would be left until last.

An even later story concerns Rav Yehonasan Eibshitz when he was rav of Metz and it was decreed that the Jews must leave the town. Rav Eibshitz went to the local bishop to appeal for mercy.

“How many words are there in this verse from the New Testament?” the bishop challenged, reading it out.

“Seventeen!” replied Rav Eibshitz.

“The same as the statement, ‘Am Yisroel chai le’olmei ad” (the Jewish nation lives forever).

“And how many Jews live in Metz?” the bishop asked.

“45,000!” replied the Rav.

“If so,” said the bishop, “If you can write Am Yisroel chai le’olam 45,000 times on a scrap of paper within one hour, I will nullify the decree.”

Within the hour, Rav Eibshitz returned with a scrap of paper divided into ten columns and eight lines, completely covered with letters.

“Start with the ayin in the middle,” he told the bishop, “and by reading the letters in every possible permutation you will fi nd the statement you want written 45,670 times!”

It took the bishop a year to check this out.

Jewish mathematics was imbued with sinister meaning during the regime of the Nazis who invented a ridiculous theory of Nordic mathematics that was volkish verwurzelt (rooted in the German nation) and not infested by Jewish and foreign elements. This helped lead to the firing of Germany’s greatest mathematicians in the 30s, including the famed Felix Hausdorff who felt that his exalted position as professor in Bonn University would keep the Nazis off his tail. He was wrong! The Germans fired him without a qualm, denouncing his theoretical math as Jewish and useless. For him and his wife, a self inflicted end in 5702/1942 was the only way to escape deportation to a concentration camp.

In Germany’s renowned Göttingen University, the Nazis fired their world-class mathematicians with Jewish connections, including Hermann Weyl, Emmy Noether and Edmund Landau because, as Bernard Rust, Nazi Minister of Education explained, “We must have a new Aryan generation at the universities, or else we will lose the future.” He also held that “the whole function of education is to create Nazis.”

The results of this great purge were disastrous. Shortly afterwards, the Nazi minister asked prominent Göttingen mathematician, David Hilbert, “How is mathematics in Göttingen now that it has been freed of the Jewish influence?”

To this Hilbert replied,

“Mathematics in Göttingen? There is really none any more!”

This preponderance of Jewish scientists had developed ever since the Haskala when the phenomenon of Jews transferring their talents from Torah to science led to Jews becoming such a formidable scientific force that they outweighed every other ethnic group in mathematics. This is easily noticeable by surveying the Jewish recipients of major mathematics prizes such as the Wolf Prize in Mathematics (40% Jewish), the Bocher Memorial Prize (42%), and the Frank Nelson Cole Prizes in Algebra and Number Theory (44%).

If only this intellect was utilized to produce gedolei Torah!

(Sources: “Chochmas Hatashbores. Hamatematike be’Aspaklaria haYehudis” by Rachel Rosenbaum, Mossad Harav Kook, Jerusalem, 2003. Excerpt about Hilbert: “Hilbert” by Constance Reid, Springer 2004.)

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