Product of Mathematics
1.Introduction to Product of Mathematics-It has been said in this article that insight is needed in abstract mathematics. Abstraction means not being visible to our eyes. Such as math numbers are 58,39 etc. We cannot see them the way the existence of road, house looks like. But we know very well how important is the importance of numbers in our lives. The suffixes of abstract mathematics exist at the level of thought, but we accept them because they have importance in daily life. It has been further explained in the article that we exist on the level of abstract suffixes, so we need insight to make any development or advancement in it. Our worldly means for both physical and spiritual world require insight and knowledge.
The mystery of human life is very esoteric and spiritual which requires very high knowledge and experience to know and understand. It is very important to understand what is the importance and use in human life because without it we do not have any knowledge about ourselves and abstract suffixes of mathematics. Any thought done without insight ends. Any opinion, principle, rule or discipline, etc. given without insight, is of two codi, it has no importance. We should keep in mind mind, word and deed with insight, if we do it according to the inner sense then our life will improve. The principles, rules, which are given in mathematics and science etc. without any knowledge, are broken up one day or the other. Intangible suffixes require the most insight. In the inner sense, good-bad, good-bad and right and wrong are identified. There have been many great philosophers, scientists who have discovered the principles, laws of mathematics and science etc. based on their insight. While those rules or principles were already in place, then why did not ordinary people come to know them? The reason is that they do not have proper insight which is disorderly, which limits their knowledge and one who becomes emotional. He cannot discover these rules and principles. All the great men who have been, may have been ordinary in their childhood, but they have attained the highest position on the strength of their tenacity and practice. Therefore, as soon as the disorders that are inside us are removed, we become enlightened.
2. Product of Mathematics"When you need to know what you want, you will get to the beginning of what you should do"
- Cahill jibran, sand and foam
In some sense, abstract mathematics is the art and science of discovering real insights about things that do not exist. When I say "things that don't exist," I mean things that actually exist only in the context of your thoughts.
Consider prime numbers as an example. They don't "exist" the way your chair does, or I do. You will never hit 37 on the road and yet, mathematicians have discovered all kinds of truths about crimes.
So to do mathematics well, you need to learn how to reliably and repeatedly discover the truth about things that do not exist. This is not an easy task. You are essentially in the business of pulling symbolic truth from the ether, such as some sort of pre-psychic book-NARD.
Nevertheless, mathematicians do this regularly. Their livelihood depends on it. So how do they manage?
I do not claim to know all their ways. Certainly they are huge, and some methods work better than others. Srinivasa Ramanujan, for example, is widely regarded as one of the greatest mathematicians in world history. Ramanujan said that his family goddess gave him all his formulas and he was not the least interested in any equation until he thought of the divine. If you doubt it - note that it works well enough for him. When he died at the age of 32, he left behind some 3,900 mathematical results, but left evidence for most of them. Since his death mathematicians have looked and found that almost all of them are true. Some of his works are now used to describe the physics of black holes, even though the very concept of black holes does not exist during Ramanujan's life.
For those of us without Ramanujan's seemingly divine progress in pulling towards the truth, there are more worldly and accessible ways. One such method is to learn how to generate intuition systematically.
Step 1: Gather relevant facts and clarify.
Step 2: Stop trying.
The problem solving problem in any domain, not just math, is that it is really tempting to just sit there and "find it really hard." But any person who has sat down and "thought" for 12 hours is of no avail, will tell you.- It does not take any real effort to solve the problem when you are thinking about real hard work. This is when you have stopped thinking completely. It comes upon you as a kind of emotion, as an intuition.
I wish, once you know that intuition is the key to real insight, despair waits. Contrary to your intelligence, intuition is not push-to-start. It is like a beautiful woman working hard to get perennials. You never stop needing to earn his trust and presence in your life.
And so the question is how? How do you need to show and juice you to arrive at real insight?
The essence of the skill is to overcome the "desire to think real hard" and instead understand how to use what you can demand (your intelligence) to prime what you need, but Cannot reach demand (your intuition).
The systematic production of intuition is straightforward.
Step 1: Gather relevant facts and clarify.
Step 2: Stop trying.
In mathematics, collecting and clarifying relevant facts is straightforward. You clarify your definition of mathematical object. You remind yourself of the results that other mathematicians have proven about it. You study related mathematical structures that you think may prove useful. And you just keep on going, constantly trying to learn more and more relevant facts, making sure that you understand them as clearly as possible.
And then you stop trying. You play football, or dance, or sleep, or go swimming. You completely and completely forget that math ever existed in the first place.
And then when you're in the middle of your 15th lap in the pool, pssst. Intuition gently strokes you and "tries it out." And you get out of the pool, and you try it and lo and behold, it leads you to a fundamental new approach to the problem and then you get there. You have taken the truth out of the ether. You are a mathematical magician.
To use the analogy, it is completely akin to cooking a meal with an A-list chef who does not tell you what he is going to make. You all know that this cook is going to cook food if you give him a bunch of ingredients and then leave the kitchen. But you don't know what materials he needs and when he wants you to leave the kitchen. So you just go on collecting and preparing the material. You buy some broccoli and some onions and some chicken and prepare it all and then leave the kitchen. But you come back the next day and the chef does nothing. So you go back to the store and you buy some tomatoes and zucchini and sweet potato and a little bit of parmesar. You come home and prepare all this and leave the kitchen again. And then you come back the next day and the chef has left you a note with a recipe and nothing else. He didn't bother to say hello and he certainly didn't cook because that's how it is. But he tells you "do it, then that and then this." So you follow the instructions and before you know it you have made broccoli / chicken / sweet potato with chopped parmesan as a compliment. It is delicious, and you are at once satisfied and confused. You never knew such a conch shell was possible.
Contrast this with sitting in the kitchen and "try to work real hard" to make something delicious, and you see that there is a subtle but important difference between the discipline of reliably inviting your intuition to come and play , And approach the difficult task of thinking your way through problems.
As a product manager and entrepreneur I am curious at the beginning of my career that this line of problem solving translates quite well, especially to one core aspect of product creation: finding out where in the first place What to make in
Oddly enough, to find out what to construct is something like knowing something new about prime numbers (or any other mathematical object for that matter). Like prime numbers, the future version of your product is actually in your mind. However, there are aspects of your product that you can deal with right now.
And so the systematic process is almost fine. Instead of collecting and clarifying mathematical facts, you do research on your user, you check usage rates on your current features, and you clarify how the product fits into your user's daily life. You can learn anything about your product, your user, business, vision and market. And you maintain your understanding about all those things.
And then you go for a walk with your director of engineering, or you sit down to dinner with the family. You completely forget that this whole "product" thing exists in the first place.
And when you least expect it, intuition "builds up".
Now at this point stating that your intuition does not always correct you. (Part of this is due to the mental agility of the underdeveloped mind and the inability between intuition, but this is a story for another time). This is why in mathematics, you must produce intellectually rigorous evidence to justify your spontaneous leap of faith. In the product, it is equivalent to creating MVP (or some other type of under-worked test case) and see how users respond to it.
If they respond well, you "prove" your product. (I use quotes here because truth is a fuzzy thing in the product world. It works more than an accurate description of reality, although the two are interconnected).
If they don't, you go back to the grocery store and expect the chef to come to you again tomorrow.