Did majoring in mathematics improve your logic and thinking skills? If this is true, what are some examples you can provide?

Let me go way off base on how it improved my thinking skills.

My Mathematics classes required using creative avenues to apply logic if I did not know the answer to a proof. I use logic in a less explicit way. Not proofing by contradiction, induction, but in a more creative way. Allowing faulty generalization fallacies, but good enough for non mathematical subjects.

In subjects such as sociology which has it's hands dipped in psychology, I have been able to find answers. Though individuals can be hard to explain, using statistical analysis to I can provide not only socioeconomic, but senario anal

Let me go way off base on how it improved my thinking skills.

My Mathematics classes required using creative avenues to apply logic if I did not know the answer to a proof. I use logic in a less explicit way. Not proofing by contradiction, induction, but in a more creative way. Allowing faulty generalization fallacies, but good enough for non mathematical subjects.

In subjects such as sociology which has it's hands dipped in psychology, I have been able to find answers. Though individuals can be hard to explain, using statistical analysis to I can provide not only socioeconomic, but senario analysis of on macrosociety issues. A measurement fallacy in Mathematics, but we aren't looking for a Mathematics proof.

It does not help me much with psychology of society. I have to make inferences about that, but data is data.

If having a PhD in mathematics improved your logic, then it doesn’t show. Mathematical logic has been in existence for about 170 years and it is still wrong today as it was wrong at the time of Pierce and Boole.

All students in mathematics get a class on mathematical logic and yet, of all the literally several millions of professional mathematicians since the middle of the 19th century, not one could get up and say out loud the truth that mathematical logic was wrong AND offer a better alternative. Well, at least it is true some have said things implying mathematical logic is wrong but only to

If having a PhD in mathematics improved your logic, then it doesn’t show. Mathematical logic has been in existence for about 170 years and it is still wrong today as it was wrong at the time of Pierce and Boole.

All students in mathematics get a class on mathematical logic and yet, of all the literally several millions of professional mathematicians since the middle of the 19th century, not one could get up and say out loud the truth that mathematical logic was wrong AND offer a better alternative. Well, at least it is true some have said things implying mathematical logic is wrong but only to produce more of it themselves.

I would grant that mathematicians make a more intensive use of logic. However, they learn wrong logic at university and apparently don’t realise it is wrong.

The bit they are competent at is essentially in their use of the Modus Ponens—or some other logical truth—as a rule of inference. Yet, every human being does it without the benefit of a PhD in mathematics.

Here, on this forum, you can see, often enough, PhD’s justifying the principle of explosion. I still have to see one explain that it is wrong and why exactly it is wrong. And this is just one of many examples. The same goes with papers published on the Internet.

From the question you are asking I assume you are still in school. This question can be answered in many ways. This is my suggestion.
First of all, I would seek help in learning math in the way I think. There are qualified teachers that do that, I’m sure. Visual tools help a lot to create picture in your mind and it works for the rest of person’s life.
You have to learn math, because it is involved in anything you want to do. You don’t have to go to higher math if it is not for you. But to be a carpenter, mechanic, hairdresser, sewing, cooking, farmer, forest ranger, craftsman, etc., no matte

From the question you are asking I assume you are still in school. This question can be answered in many ways. This is my suggestion.
First of all, I would seek help in learning math in the way I think. There are qualified teachers that do that, I’m sure. Visual tools help a lot to create picture in your mind and it works for the rest of person’s life.
You have to learn math, because it is involved in anything you want to do. You don’t have to go to higher math if it is not for you. But to be a carpenter, mechanic, hairdresser, sewing, cooking, farmer, forest ranger, craftsman, etc., no matter what, you will needs math of some level.
As you put the effort to do the above, ask yourself what you enjoy doing? Pursue that with great effort and joy. Laziness has to come out of your vocabulary and character, because no matter, male or female, you have to be ready to provide for the necessities of a family later on, or for yourself. Doing what you enjoy as a job it will make your life pleasant and joyful. Do not be intimidated by social pressure. That makes many unhappy people pursuing big money, prestige, and fame.
We humans are selfish beings. We want to do what gives us pleasure. The good part of this selfishness helps us find our gifts and talents instilled in us from birth. Developing them to full potential is up to us for our own good and for the good of all the others. Trampling on others to achieve that is totally wrong and there is no joy in it.
Talk to your teachers and seek advice how can they help you achieve your dream. They help the students that think about their future and are focused.

Good luck

Logical thinking and problem solving skills, contrary to much public opinion and even college classes, etc. has nothing to do with how much knowledge or information is in your head it also isn’t just a trick in the way you think… it takes serious wisdom and understanding the big-picture about how things work, in reality, generally and specifically. You can’t ever get that from anyone else. The best teachers are people who guide you to discover truth. Actual teaching is becoming extinct in our society. Our schools, k-12 and even colleges are filled with “tellers” and very few actual “teachers”

Logical thinking and problem solving skills, contrary to much public opinion and even college classes, etc. has nothing to do with how much knowledge or information is in your head it also isn’t just a trick in the way you think… it takes serious wisdom and understanding the big-picture about how things work, in reality, generally and specifically. You can’t ever get that from anyone else. The best teachers are people who guide you to discover truth. Actual teaching is becoming extinct in our society. Our schools, k-12 and even colleges are filled with “tellers” and very few actual “teachers” any more.

For that reason, serious problem solving and logical thinking skills, are some of the most rare virtues around. Working in nature, where you begin to reap the cause and effects of your own labor, is one of the best habits you will ever develop. Plant a garden, learn how to build things, work with animals, work with your hands and discover for yourself how nature works and the universe operates… but then relate everything to your own life in practical application. It is a good thing to learn from others but learning is not about memorizing, it’s about discovering.

What you want to focus on is discovering principles. Principles are the most precious treasure on earth. they are always hidden beneath and in between what you think you already know. That doesn’t mean that simply working with your hands is the magic. Most people who work with their hands, still haven’t discovered principles.

Only wise and worthy mentors can help to uncover principles for you and then guide you how to discover them through your own practical experience with life. But you must be willing to do the work and discover them for yourself.

Unfortunately, even the vast majority of people who make a living helping to solve problems actually end up creating more problems than they solve because they lack the big-picture of life and reality. That only comes to a small few who have discovered that wisdom is a totally different thing than knowledge. The two are acquired in very different ways. Knowledge is based on information that can be memorized and passed from one person to another. You can stumble upon knowledge through experience but knowledge is all about “answers,” it breeds arrogance and inflated, false pride (most assumed knowledge today is not really knowledge at all but only naïve assumptions, which is really foolishness).

Wisdom on the other hand, is founded on principles. Wisdom is never contented with “answers,” because it knows there is always more…. Wisdom is entirely based on discovering better questions. Answers stop growth, questions demand and perpetuate growth… Since every piece of real truth is totally interdependent on every other truth, there is always more, better, greater improvements to make, regardless of whether you are at the bottom, top or anywhere between-of what you are trying to understand.

The great masters through time, became great masters because they never stopped learning, discovering and evolving. The only way they remain great masters is by never losing track of their leaders, mentors, masters….

Beware, however many, many today believe (and/or try to convince you) that they are wise and flaunt their money, positions, knowledge, influence, etc. Many even believe they have risen above ordinary mortals (talk about ego). But the truly wise and their followers are the ones willing to do what the masses are not willing to do… the hardest work they will ever undertake—their own self evolution. Even though difficult at first, it is only way to live with real fulfillment and genuine happiness that doesn’t fade with the lights and the music….

I have come to call, what everyone wants, but only a few have been willing to discover, the most valuable and precious treasure on earth… “The principles that birth intelligence, lead to wisdom and harness the laws of creation.”

Since you are a creator—that’s what you do, every moment of your life—create your own future reality, You can learn to create something much greater than you have done so far, regardless of how little or far you have come.

Once on that path, you will naturally see what is, over ride your ego that desperately tries to get you to find what will pacify you for the moment, so you don’t have to risk failure, and claim whatever rewards you want most. Intelligently taking those risks is the only path to wisdom and wisdom is the only environment that enables one to solve problems and see the perfect logic in the universe—and align your thoughts and behaviors with it…

There is no way to cut corners to gain wisdom—but it is the great shortcut to super success. Everything else is settle-for. You just must make the decision.

The efforts will pale by comparison to the rewards—IF you recognize and accept that it is all up to you, no one can ever come to your rescue, and then make it a life-style. There is no gimmick or tactic or trick, but once you make those commitments, the right mentors will show up and make all the difference.

Learn to love being uncomfortable, pushing yourself out of your comfort zones IN THE RIGHT DIRECTION and the world will be yours.

Let’s go catch your dreams .

Eldon Grant

The day you start doing is the day you start improving.

For improving any skill you need to get a hang of it and that can be attained just by Practicing!

But the paradox is how many of the people really want to improve their skills by actually doing and not just by wishing for attaining a mastery in your desired skill.

We are so much obsessed by the end product that we just keep on thinking about achieving that mastery but are not actually ready to give our heart out to learn what we want to.

So , if you have really made your mind and ready to go beyond your potential then just Start doing ….

Now!

Y

The day you start doing is the day you start improving.

For improving any skill you need to get a hang of it and that can be attained just by Practicing!

But the paradox is how many of the people really want to improve their skills by actually doing and not just by wishing for attaining a mastery in your desired skill.

We are so much obsessed by the end product that we just keep on thinking about achieving that mastery but are not actually ready to give our heart out to learn what we want to.

So , if you have really made your mind and ready to go beyond your potential then just Start doing ….

Now!

You will surely ask ,

How do I start ?

Then my dear friend , we have our Bible with us which we carry almost 24×7 with us .

Our mobile phones!

Yes , every skill can be learned from Google and youtube if you really wish to give your efforts.

Now for e.g. you want to excel in your academics then just take one subject , try to make hand written notes.

If you're finding difficulty in making notes of some typical topics then again take help of Google. There are ample of websites which provides the best of the matter.

Try to keep separate copies for different subjects.

Use highlighters ,black pen to focus on the vital topics.

Keep your notes concise.

There's no point in writing your whole course book again.

100 pages should be converted into 10 pages and then at last in one page.

Once you're done with making notes then 70% of your work is done. Now you just need to revise them on alternative days and then on weekends.

They'll get print in your head.

And whenever you're finding hard to retain any challenging topic then not just recite it but try to learn it by writing.

Trust me ,

Writing is the key for excelling in academics .

So this was just one example!

The idea is simple , to divide your goal in fragments and your way to acquire any skill will be sorted!

Happy Learning. ^•^

Not really.

It cannot hurt…but, the logic aspect is a bit different.

With math, you can check to see if the answer is right, and, try something else if it doesn't check, etc. You can do a proof, etc.

With logic, the basic problem is that the brain evolved to take short cuts, as brains are very expensive in calories and nutrients, and, starvation is the most common cause of extinction.

:D

So, we are HARDWIRED to make certain types of mistakes.

Basically, things that “make sense”, and sound “right”, can be wrong, and, wrong in the same way, for the same reasons, because when were were evolving, it did

Not really.

It cannot hurt…but, the logic aspect is a bit different.

With math, you can check to see if the answer is right, and, try something else if it doesn't check, etc. You can do a proof, etc.

With logic, the basic problem is that the brain evolved to take short cuts, as brains are very expensive in calories and nutrients, and, starvation is the most common cause of extinction.

:D

So, we are HARDWIRED to make certain types of mistakes.

Basically, things that “make sense”, and sound “right”, can be wrong, and, wrong in the same way, for the same reasons, because when were were evolving, it didn't matter yet.

This is why optical illusions work at all, for example…we KNOW the types of mistakes the brain makes, and, we can trick it into making them.

So, that’s just a visual example, but, the principle applies to arguments, etc, as well.

So, “learning logic” is less about learning to think, as about learning how NOT TO think… and learning what mistakes our brain WILL make, if we don't reel it in.

Think of it as proactive thinking…LOOKING for the booby traps, by learning what they look and sound like, their properties, etc, so, you can recognize them in any environment.

That means when others present an argument, (Which can be a TV commercial/sale pitch/religious pitch or an editorial or the news, a philosophical argument, etc..)…you are scanning it for booby traps…the things the brain will latch onto and fall for, etc.

It also means scanning what YOU say, for the same thing, to avoid SAYING them too.

:D

Some common examples include confusing causation and correlation, and sunk cost errors, etc.

If you are NOT aware of these sorts of things, they will convince you of things without merit…or, you will say things without merit.

So, a logic class, for example, teaches you the types of errors, or fallacies, and, warns you to be on the lookout.

APPLYING that mental rigor to you life is actually not that easy at first…its easy to let your guard down… but, as it becomes habit, and you drop the human tendency to take the short cuts… you find that many things suddenly become quite clear, and, you can cut through the BS and get to the heart of an issue.

So, math is related to all of this, but, not in the way that you were thinking.

The main way, is that math has its own rules, and, ways of checking your work… but they are not the same rules, or ways, as logic has.

:D

That part about it being your brain and unchangeable is malarky.

I had math phobia for many years, and was convinced that it was one subject I'd never really master. But because so many other subjects came easily to me and it didn't, it was the one that tantalized me and that I had to conquer.

Finally I realized that my problem hadn't been inadequate learning, but inadequate teaching. Never take math from a mathematician unless you too desire to be a mathematician. Take math from an engineer or other tangential practitioner who stresses practical applications.

Math, you see, is only a modeling la

That part about it being your brain and unchangeable is malarky.

I had math phobia for many years, and was convinced that it was one subject I'd never really master. But because so many other subjects came easily to me and it didn't, it was the one that tantalized me and that I had to conquer.

Finally I realized that my problem hadn't been inadequate learning, but inadequate teaching. Never take math from a mathematician unless you too desire to be a mathematician. Take math from an engineer or other tangential practitioner who stresses practical applications.

Math, you see, is only a modeling language. And my introduction to true mathematics came via statistics, which is the ultimate in applied mathematics, because it frankly admits, unlike most of mathematics, that you can know only so much for sure. It joins hands with physics at that point. When I finally realized that all those symbols and equations were just stand-ins for real-world items, math came into focus for me. It became a compact, "lossy" modeling language for the real world. I suddenly had power that most other people declined to seize.

I recommend that you investigate statistics for a starting point. It uses data to tell stories, and considering that you've written that you're a verbal thinker, it may be the most effective path in to the subject of mathematics. In my view, it does the best job of evoking rigorous thinking in non-mathematicians. It has everyday power to predict things, which is why it's widely used in the sciences, economics, and business. You'll quickly run into algebra, of course, which for most of us is the base language and worst learning experience in all of mathematics, but having once tasted the power of statistical thinking, you may be more interested in mastering algebra. A book I often recommend to beginners is The Cartoon Guide to Statistics by Larry Gonick and Wollcott Smith.

QUORA changed the original question that I answered. It’s been a while, but I believe the question was something along the lines of : “Should I study engineering or theoretical physics to expand on my ability to interpret and understand nearly anything I put my mind to?”

_______________________________________

I had a similar dilemma 37 years ago. My favorite subject in school was physics but I was young and also looking for adventure and excitement. I considered getting a degree in physics, however, I ultimately decided that I wanted to fly fighters in the military and then to become an astrona

QUORA changed the original question that I answered. It’s been a while, but I believe the question was something along the lines of : “Should I study engineering or theoretical physics to expand on my ability to interpret and understand nearly anything I put my mind to?”

_______________________________________

I had a similar dilemma 37 years ago. My favorite subject in school was physics but I was young and also looking for adventure and excitement. I considered getting a degree in physics, however, I ultimately decided that I wanted to fly fighters in the military and then to become an astronaut. As a result, I chose to get an aeronautical engineering degree since that's the path that many astronauts had taken.

My priorities and career goals changed while I was still in the military and I decided to change career completely after I served. Do I regret my decision not to go into physics? Not really. Aeronautical engineering is a scientifically based field based mostly on math and physical properties (not pure physics per se). It taught me how to approach, understand, and solve complex problems. It gave me skills that I use everyday in most aspects of my life.

I believe that either one of the degrees, in theoretical physics or engineering, will allow you to achieve your goal to "expand on my ability to interpret and understand nearly anything I put my mind to".

That being said, I really believe that the best path is to follow your heart when choosing your career. What do you really like or love more? Theoretical physics is fascinating but may sometimes seem like mental masturbation. Engineering is challenging and more practical but may lack the wonder of theoretical physics. What about combining the two? Maybe consider going into engineering physics, that is physics with a practical bias. Here is a link that lists a bunch of US schools that offer this program Engineering Science / Engineering Physics .

Do what you like/love at this moment. That may change as you grow older but you can also change directions later in life. Or you may decide that you've found your true calling and remain in one field forever. Either way, do what you like/love at the moment and you will lead an interesting life.

There are several ways a prior grasp of Logic can help one learn maths with greater confidence: It can give one a deep understanding of the use of quantification; it can give one a deep understanding of the logical structure of different proof strategies; it can help you understand how to structure natural language assertions to reflect their logical structure more clearly; it can help you understand how to unpack the language of a theorem’s antecedent(s) and use them to satisfy the antecedent conditions of another theorem that could help you in your current proof; finally, it provides an oppo

There are several ways a prior grasp of Logic can help one learn maths with greater confidence: It can give one a deep understanding of the use of quantification; it can give one a deep understanding of the logical structure of different proof strategies; it can help you understand how to structure natural language assertions to reflect their logical structure more clearly; it can help you understand how to unpack the language of a theorem’s antecedent(s) and use them to satisfy the antecedent conditions of another theorem that could help you in your current proof; finally, it provides an opportunity to become versed in the language of proof.

One major challenge for students new to post-school maths is the structure of proofs. Logic can help you with this challenge by presenting you with the opportunity to understand quantification deeply. For example, “For each x, there exists a y such that…” is a common type of assertion. To prove it, one sometimes assumes its negation (assumes that its false) and derives a contradiction from this assumption to show that it can’t be false (therefore, it must be true). In logic, you would learn the forms of the negations of such assertions.

Another challenge is to disprove assertions. Sometimes after attempting mightily, yet unsuccessfully, to prove an assertion that seems obvious or likely to be true to your intuition, you suspect that it might not be true, after all. To prove the negation, you need to understand the structure of the quantifiers, which can be learned by studying logic.

A third challenge arises when, while proving some theorem, you reach a point where a proven result will help you prove the theorem you want to prove. You have to understand how to apply that known theorem to your proof. Studying Logic can help you accomplish this application.

Logic can help with proof strategies, generally. For example, to prove that two sets are identical, you have to show that if every element of one set belongs to the other set. You accomplish this objective by showing that x belongs to S if and only if x belongs to T. To accomplish this objective, you show, first that if x belongs to S, then x belongs to T; then, you show that if x belongs to T, then x belongs to S. From these statements, you can infer that x belongs to S if and only if x belongs to T. Then, you can infer that S = T. In studying logic, you would prove the theorem, “(S → T) & (T → S) → (S ⟷ T),” in propositional logic.

Knowing some first-order logic can help you overcome some early challenges that you are likely to meet in your Maths courses. But, nothing will help you more than just attacking the proofs of theorems directly and seeking collaborators along the way.

Personally I’d probably distinguish between logical thinking and abstract thinking, and say that mathematics helps a lot with both.

Logic is “the rules of inference,” it tells us what conclusions are justified (or not) given the information we start with, whereas abstraction is more the ability to conceptualize things. In his essay A Mathematicians Lament, Paul Lockhart explains how mathematics isn’t so much about learning to blindly apply the rules we’re taught in grade school to solve a problem, it’s really about creative problem solving, he makes the comparison to music—which is not about si

Personally I’d probably distinguish between logical thinking and abstract thinking, and say that mathematics helps a lot with both.

Logic is “the rules of inference,” it tells us what conclusions are justified (or not) given the information we start with, whereas abstraction is more the ability to conceptualize things. In his essay A Mathematicians Lament, Paul Lockhart explains how mathematics isn’t so much about learning to blindly apply the rules we’re taught in grade school to solve a problem, it’s really about creative problem solving, he makes the comparison to music—which is not about simply learning the notes and how to read sheet music and so on, but has a creative component like all art forms—mathematics is much the same, though the creativity is about abstract problem solving, rather than composition or color or melody as it is in other art forms.

Lately I’ve been watching a lot of youtube videos by 3blue1brown, who does a fantastic job producing his videos, but also covers fascinating problems and breaks them down into easy to follow chunks.

These are two of my favorites:

The hardest problem on the hardest test

(Note, I think there are probably many other skills people could point to that mathematics can help with, but I think to me this is probably the central benefit.)

Let me just assert that mathematics at the college level is basically comparable in logical training and critical thinking as philosophy. The only difference is mathematics courses and the material are much less verbose or use less words to study the material. And that philosophy and courses use more passages and reading comprehension, to study their material about issues, philosophers, or important works. The math taught in college is really intended for common courses, usually applied to sciences or engineering, as well as technology. And can be used as a liberal requirement for subjects int

Let me just assert that mathematics at the college level is basically comparable in logical training and critical thinking as philosophy. The only difference is mathematics courses and the material are much less verbose or use less words to study the material. And that philosophy and courses use more passages and reading comprehension, to study their material about issues, philosophers, or important works. The math taught in college is really intended for common courses, usually applied to sciences or engineering, as well as technology. And can be used as a liberal requirement for subjects interested in more artistic or verbal pursuits, the common fine arts like drawing or painting, or the writing and reading found in English or a foreign language. You basically need logical talks in math courses, and the material and properties studied will reflect the discussion. You are basically studying, as you have always been since grade school in math class, the same properties with more variations, applications, problems, and coherent developments. It should not get too complex, as to be incomprehensible. We are basically studying numbers, space, change, structure, logic, computation, and discrete objects and relations. These are not all studied or explained with such terms or words in the younger grades, though when we are studying them in college with a maturity of conversation, then we can further explain and comprehend their applications within and without a math curricula.

Math is by definition logical/abstract thinking, so I'm going to go with yes.

Now, if you want to become a professional Mathematician, there is this other small matter of 10+ years of training in specific mathematical disciplines, proof-writing (and reading), collaboration, teaching, a dissertation, and more. But none of that is required if you just want to enjoy math recreationally.