Oy vey,
how?

What is mathematics, anyway?
What is “the world”?

Questions from the furnace of creation itself (what is a world?)—matters that are not discussed individually. And if I weren’t afraid, I would have said that the gentleman mixed up Iyar with Adar…

What is “understanding the world,” and how does basic mathematics (fractions, exponents, etc.) help with that?

I remember that Rabbi Shach was very fond of mathematical thinking; he said it instills the “quality of order,” which is important for Torah study.
And the Vilna Gaon also wrote a book on the “science of measurement” for some reason.

But aside from acquiring thinking tools for analyzing ideas, do you think it helps with anything else?

It is very worthwhile to be proficient in mathematics when approaching the study of logic; translating statements into logical language and analyzing them requires similar skills.

Aharon—
Yes, that’s what I wrote. The question is whether there is reason to invest time in mathematics just because it helps analytical skill, or whether there is some additional reason to invest time in the subject.

It helps with orderly thinking, precise definitions, analytical skill, and the content is also important for various needs (even in Jewish law). Beyond that, mathematics has theoretical value, and I don’t see why that is inferior to many chapters in the Guide for the Perplexed that deal with philosophical issues that are, in my opinion, far less relevant, and based on various strange external sources together with Maimonides’ personal conjectures.

With God’s help, 4 Iyar 5778

To Shai—greetings,

For most of the big questions in life, philosophy has no answer. On the contrary, philosophy is built on foundational assumptions whose grounding is intuitive.

Mathematical thinking is good for the natural sciences, but the world of spirit and values does not operate according to “proofs of the science of measurement” (in secular language: mathematical proofs). A person reaches one conclusion or another because that is what sits better with his heart.

Philosophical inquiry can help a person understand the complexity of the questions, and from that he can understand “what exactly they disagree about” among the various opinions. And from understanding the foundations of each and every approach, a person can choose the path that better accords with his heart.

When a person’s outlook is well ordered, he understands the reasons for the differing views and can define what he connects with most. It may very well be that he will remain in doubt—but not out of a vague feeling.

Another reason that can bring a person to “mental chaos” is the feeling that his life is “stuck.” When a person feels that his life is drifting without any horizon, everything becomes confused and blurry for him. Someone who sits for hours and hours over study that gives him neither interest nor a practical horizon will obviously begin to “climb the walls” and enter a sense of dizziness.

To return to mental order, one should invest time first and foremost in study that will give him a stable and clear picture: the central approaches in Jewish faith; the Bible with Rashi, Nachmanides, and Radak; the Kuzari; Maimonides’ introductions to his commentary on the Mishnah and to the Mishneh Torah; Sefer HaChinukh; and the basic books of Ramchal, Mesillat Yesharim and Derekh Hashem. Once the foundations of Jewish faith are clear to him, a person can enter deeper inquiry and also make comparisons with other approaches.

And since a person was also created to engage in settling the world, and as the Sages instructed: “Torah study is good together with worldly occupation, for the effort of both makes sin forgotten”—therefore a person should prepare himself for a profession through which he can earn a respectable living and also increase his Torah study from a position of financial ease, and basic mathematics can open quite a few “gates of livelihood.”

When a person is settled in mind on the material side, it is easier for him to be settled in mind on the spiritual side as well, and even to deepen his understanding of intellectual matters!

With blessing,
S. Z. Levinger

Regarding books of Jewish thought, it would also be worthwhile to add: the homilies of Ran; the books of Rabbi Samson Raphael Hirsch—Horeb, The Nineteen Letters, and his commentaries on the Torah, Psalms, and the prayer book; Chapters in Jewish Thought by Rabbi Shaul Yisraeli; and the book by Rabbi Yehoshua Enbal, may he live and be well, Introduction to the Oral Torah.

With blessing,
S. Z. Levinger

Our Generation Facing the Eternal Questions by Dr. Aharon Barth.