For me in learning Mathematics, I found a lot depends on understanding certain key concepts. I was in Hebrew University trying to restart math [because of the Rambam's opinion as I mentioned earlier] and I was looking at math and physics books. A certain girl, Michal, came over to me and explained the basic concept of a derivative. That is, she showed the basic way that Newton had come upon the concept, and then showed how it in fact worked to get the derivative of x^2 to be 2x by taking the limit. [She actually sat down with me and showed me step by step the exact derivation.]
That one basic concept turned out to be the key concept that later made Calculus clear to me.
Same went for Algebra. It made no sense to me either until I think it was the same girl that showed to me how 2 (x+y)= 2x+2y. Again it was one simple key concept that made everything clear.
Again in Quantum Mechanics I really had no idea what was going on on until one day I stumbled across a book by Eyal Buks from the Technion in Israel that said simply the inner product is equal to the delta function (that is one when both vectors are equal, and zero otherwise.).
[I am not saying one should be stuck until he understands every concept. Just the opposite. I hold from what is called דרך גירסה-to say the words in order, and go on. Eventually, one will understand. And even if he does not get it, he still has the mitzvah of listening to the Rambam and having אמונת חכמים belief in the wise.
[Using Torah to make money made no sense to me, so I decided to start afresh with learning an honest occupation like Physics. I also had seen most people that make money by using the Torah, just do not seem kosher or decent in any sense. Seeing that people using Torah for money turn out really nasty, gave me a lot of incentive to find a different path. This is in any case exactly what the Torah itself says. Take a look at Pirkei Avot ch 4 ולא קרדום לחפור בה מכאן אמרו כל הנהנה מדברי תורה נוטל את חייו מן העולם and the Rambam explains there מן חיי העולם הבא. [Pirkei Avot brings the statement in ch 1 "Do not use Torah to make money." Then it repeats it in ch 4 an adds, "From here they said he who uses Torah to make money takes his life out of the world," and the Rambam adds "from the life of the world to come"]. (For the majority of people in yeshivas, learning Torah is a career choice. It is a way to plan ahead by using Torah to make money and get a shiduch. Outside of the implausible excuses, it is exactly what the Mishna in Pirkei Avot says not to do. Another thing they do is to make as much as they can to be forbidden unless under their control. By adding countless restrictions they get everyone under their thumb.]I wish I could say otherwise but the truth needs to be told: yeshivas are disaster zones. Even the best. It has gotten to be just a business. A business that produces nothing but heart ache for those people naive enough to think the products of yeshivas have anything to offer but the swiftest way to break up homes and families. [It was not always like this and it does not have to be. I remember a time at the Mir in NY and in many places in Israel learning Torah was in fact known to be the highest goal and people did it with sincerity.]
In any case. it was kind of late to start a new career, but I did have some nice experiences in math. As I wrote on this blog, I did have a nice opportunity to give a few seminars in HU on Differential questions, and to spend time at the Polytechnic Institute of NYU.
Same went for Algebra. It made no sense to me either until I think it was the same girl that showed to me how 2 (x+y)= 2x+2y. Again it was one simple key concept that made everything clear.
Again in Quantum Mechanics I really had no idea what was going on on until one day I stumbled across a book by Eyal Buks from the Technion in Israel that said simply the inner product is equal to the delta function (that is one when both vectors are equal, and zero otherwise.).
[I am not saying one should be stuck until he understands every concept. Just the opposite. I hold from what is called דרך גירסה-to say the words in order, and go on. Eventually, one will understand. And even if he does not get it, he still has the mitzvah of listening to the Rambam and having אמונת חכמים belief in the wise.
[Using Torah to make money made no sense to me, so I decided to start afresh with learning an honest occupation like Physics. I also had seen most people that make money by using the Torah, just do not seem kosher or decent in any sense. Seeing that people using Torah for money turn out really nasty, gave me a lot of incentive to find a different path. This is in any case exactly what the Torah itself says. Take a look at Pirkei Avot ch 4 ולא קרדום לחפור בה מכאן אמרו כל הנהנה מדברי תורה נוטל את חייו מן העולם and the Rambam explains there מן חיי העולם הבא. [Pirkei Avot brings the statement in ch 1 "Do not use Torah to make money." Then it repeats it in ch 4 an adds, "From here they said he who uses Torah to make money takes his life out of the world," and the Rambam adds "from the life of the world to come"]. (For the majority of people in yeshivas, learning Torah is a career choice. It is a way to plan ahead by using Torah to make money and get a shiduch. Outside of the implausible excuses, it is exactly what the Mishna in Pirkei Avot says not to do. Another thing they do is to make as much as they can to be forbidden unless under their control. By adding countless restrictions they get everyone under their thumb.]I wish I could say otherwise but the truth needs to be told: yeshivas are disaster zones. Even the best. It has gotten to be just a business. A business that produces nothing but heart ache for those people naive enough to think the products of yeshivas have anything to offer but the swiftest way to break up homes and families. [It was not always like this and it does not have to be. I remember a time at the Mir in NY and in many places in Israel learning Torah was in fact known to be the highest goal and people did it with sincerity.]
In any case. it was kind of late to start a new career, but I did have some nice experiences in math. As I wrote on this blog, I did have a nice opportunity to give a few seminars in HU on Differential questions, and to spend time at the Polytechnic Institute of NYU.
