Becoming a mathematician - I am so depressed

[AdrianZ]

I know this sounds awful. I know this is just a bunch of whining to you guys, but this really upsets. I have almost entered a state of depression, simply due to this issue.

Im a 17 year old high school student, living in denmark. I live and breathe mathematics! It is my passion, my way of life, and i feel it always will be. It is my greatest hobby, and my dearest pastime. And like luther, i have a dream - i want to obtain a math PhD, and become a mathematician working with mathematical research and teaching at college. I want to become a college professor so hard, that its basically all i care about.

There is just some complications involved in my dream:

1. My iq is approx. 135. When i first found out, it was devastating to me. I had done a lot of reading about mathematicians, and to me it seemed like you would have no chance what so ever to be competitive in higher end mathematics, if you are not 150+. I have tried to forget that i am of low intelligence, but i simply can't. Everytime i work with math, i am always reminded reminded that i am not smart enough to accomplish my goal.

2. Instances have been seen, where low iq ppl (like feynman) are excellent at their field of study. This is just not my case - i have never been a child prodigy, learning calculus at age 12 and so on. I did teach myself calculus at age 16, but that is only 1 year prior to our high school introduction to the subject. It seems that i am of low intelligence, and i do not have a mathematical talent.

3. People around me keep saying that if someone can complete a math PhD, then it must be me. This is of great annoyance to me! Out of all the 600 pupils on my school, i am the best at mathematics. I teach in the schools "homework help cafe", even the 3. year students despite the fact I've just started 2nd year. My math teacher says i am the most brilliant math student he has encountered in 20 years of teaching A level high school math (the 3 year course).

I have created proofs on my own for the Taylor series, the arc length formula etc. I can solve differential equations such as y''(x)+xy'(x)+y(x)=0 by series solutions and understanding what i am doing.

In my head the guy described in the above paragraphs sounds like someone capable of completing a math phd - but the truth is, that's not enough! Why is it that in our subject, mathematics, you have to be an utter genius in order to qualify for a phd program? You can't imagine how discouraged i get, when i read about studying mathematics on the internet. Higher education math seems to be something reserved for the high iq geniuses, and the rest might as well just apply for another job. Why do you have to be able to complete your bachelor at age 10 in mathematics, but not in other fields? I am no child prodigy. I am just a young guy, with a passionate dream about contributing to the world of mathematics.

This text turned out to be one big whine i know - but this issue is ruining my life. You guys - who are so unfairly gifted - have no idea what it is like to have a mind that is so determined to contribute to mathematics, but is simply lacking the raw processing power to do so. I would give everything for a drug capable of eradicating my passion. This sounds horrible, but you have no idea how hard it is to want something so much, but knowing you will never be able to achieve it.

Im sorry, but i had to get this out to someone who understands me. Everyone around me seem to think I'm crazy. If i couldn't complete a math phd, who could? The answer is: The prodigies, the naturals and the people who are born to do maths. I cannot say that i am among equals on this board, but at least i am among people, who understand my deep frustration. Imagine if your mathematical talent was taken away from you, leaving only the deep desire to do and practice math - how would you feel?

I'm happy to see that there is someone out there who feels exactly the same way as I. I'm at the same situation, the difference is that I gave up med. school after studying one year there for becoming a mathematician at the age of 19. Now not only I feel that there's little chance that I become a great mathematician, but I sometimes regret myself that I have ruined my life by switching to a field that there is no job future in it. I've promised myself to continue studying medicine after I have obtained a PhD in mathematics and I hope that I could achieve it. This sense of regretting goes soon though, because I truly love math and I'm happy that I'm studying it now.
I believe both of us can complete a PhD but if you want to be someone like Euler (who is like a hero for me, even more than Gauss or any other mathematician) then you'll fail and I'm honest. I believe when you want to measure the quality of a great mathematician, then you must take a lot of factors into account. I usually say great mathematicians are usually grouped into 3 major branches: some mathematicians are good when it comes to creating new theories, some mathematicians are good only at problem-solving and some mathematicians are good at both. I believe only the later can be real great mathematicians and in each generation the number of such people is very few. so if your goal is to obtain a PhD in mathematics, then I'm sure that you can complete it. but if you dream of being someone like Euler, Gauss, Galois, Newton, Archemedes or other great mathematicians, then I doubt you could achieve that goal easily. I should add that I totally agree with micromass that your efforts are more important than your talent and if you try hard, you'll be better everyday.

 

[Dembadon]

Spend less time thinking about your I.Q and more time brewing coffee and proving theorems.

Yes! I like this.

 

[FredericGos]

Hej,

Here is something that helped me a lot and changed my view of inteligence and what's important etc.

You are Danish, so am I. The greatest scientist our country ever produced was Niels Bohr. If you read a bit about this guy, you will realize that he was known as a notoriously slow thinker. He became great anyways. Not because of speed, but because he kept thinking about it and working at it. He eventually reached a level of insight most cannot.

Hope that helps a little. :)

 

[Levis2]

I apologize for not getting back to you, but I've had a lot on my plate the last few days - especially after the visit at the professor's.

So i went for the meeting, and it turned out really nice! There were no examination, no "trying me out" or anything.. we just spent 2.5 hours talking about math, future plans and how i can study more math. He has now set me up on a real analysis course, and damn - I've finally found some mathematics, that i find difficult... This stuff is rather complex, mainly because I'm use to "invent" and come up with formulas, relations and so on.. That has been my "line of work" for a long time - addressing a problem, then coming up with a solution/formula or a relation. Now my real analysis books wants me to prove things directly, an approach i find slightly more difficult. I haven't had much time to look at it yet, but I must admit that i have trouble with some of the inequalities ... Its rather annoying :) I have also been given the offer to follow a real course at the university, and get assignments and homework. I just can't attend the classes, since my high school won't let me skip 3 hours to attend the lectures.

I don't know if I'm going to sign up for the course though, since i don't think ill be able to keep up .. This real analysis is tough on top of loads of other crappy kinds of homework, i get from my regular high school :)

But i just wanted to say that i am going to pursue math, and see where it takes me :) Even though i still have my doubts, mostly because I'm having a bit of trouble with the analysis hehe :)

 

[cobalt124]

Fantastic! Good Luck!

 

[Levis2]

Fantastic! Good Luck!

Thank you! My mood is slightly better than the beginning of this thread hehe :)

But - have any of you guys struggled with the material in the first 5-15 hours of your real analysis courses? Be cause i sure am .. Can one get better at doing proofs, or is it just some native ability you're born with? Its funny i am struggling with these proofs .. I have no problem creating a proof for some geometric formula or something, but i seem to have problems proving inequalities once in a while :(

 

[Fredrik]

I think everyone struggles with analysis. The kind of proofs that you may encounter there are really hard. You may think that your professor must be much smarter than you because he seems to find them easy, but he probably had to work hard to make it through a difficult analysis course at some point, and then he spent a few months working just as hard on a topology course. He probably didn't start to find this type of proofs easy until he got to the end of the topology course, and even then, there were probably at least a few theorems the wouldn't have been able to prove in less than an hour without peeking in a book. He probably didn't get to the level where he could prove every theorem with ease until he had taught the subject a few times.

I wrote the above before I saw your post before this one. Can one get better at doing proofs? Of course. We all suck at it at first, and it takes a long time to get good at it. As I said, you shouldn't expect to be really good at it until you have taken a course in topology (something you're not expected to do in your first year, and probably not the second either). Did we struggle during the first 5-15 hours? Of course. We struggled a lot longer than that.

 

[micromass]

Thank you! My mood is slightly better than the beginning of this thread hehe :)

But - have any of you guys struggled with the material in the first 5-15 hours of your real analysis courses? Be cause i sure am .. Can one get better at doing proofs, or is it just some native ability you're born with? Its funny i am struggling with these proofs .. I have no problem creating a proof for some geometric formula or something, but i seem to have problems proving inequalities once in a while :(

Real analysis is a notoriously hard subject. Almost everybody struggles with real analysis at one stage or another. But on the other hand, real analysis is also quite fun once you get the hang of it.

Do take the univsersity course. It'll be quite hard for you, but in the end you'll be in a better position to say whether you actually like the math there. A lot of (very smart) people drop out of math because they just don't like it. If you take the course then you can experience first-hand what mathematics is really like!

 

[deluks917]

Real analysis is a very fun subject to have studied (not necessarily to study). After the course is over problems that seemed impossible will seem easy once you have the hang of it.

 

[GregJ]

Levis2:

Glad you are making progress and that everything is heading in the right direction. You'll make a fine mathematician yet ;)

Just remember to focus on the here and now and let nothing else steal your thoughts. Master the present and you will master your future.

 

[Fredrik]

...in the end you'll be in a better position to say whether you actually like the math there. A lot of (very smart) people drop out of math because they just don't like it. If you take the course then you can experience first-hand what mathematics is really like!

This is a very good point. I remember that the differences between university math and what we had seen before had different people reacting in different ways. I like this type of math much better, but others hated it.

 

[Functor97]

I apologize for not getting back to you, but I've had a lot on my plate the last few days - especially after the visit at the professor's.

So i went for the meeting, and it turned out really nice! There were no examination, no "trying me out" or anything.. we just spent 2.5 hours talking about math, future plans and how i can study more math. He has now set me up on a real analysis course, and damn - I've finally found some mathematics, that i find difficult... This stuff is rather complex, mainly because I'm use to "invent" and come up with formulas, relations and so on.. That has been my "line of work" for a long time - addressing a problem, then coming up with a solution/formula or a relation. Now my real analysis books wants me to prove things directly, an approach i find slightly more difficult. I haven't had much time to look at it yet, but I must admit that i have trouble with some of the inequalities ... Its rather annoying :) I have also been given the offer to follow a real course at the university, and get assignments and homework. I just can't attend the classes, since my high school won't let me skip 3 hours to attend the lectures.

I don't know if I'm going to sign up for the course though, since i don't think ill be able to keep up .. This real analysis is tough on top of loads of other crappy kinds of homework, i get from my regular high school :)

But i just wanted to say that i am going to pursue math, and see where it takes me :) Even though i still have my doubts, mostly because I'm having a bit of trouble with the analysis hehe :)

Proofs are the in my opinion the most beautiful aspect of mathematics. Pretty formulas may be interesting, but thinking that this is mathematics is somewhat mistaken. Mathematics is about understanding, not calculating. Maybe you are more of a Ramanujan than a Hardy?

 

[SuchABohr]

Hey bro, just wanted to say don't worry about iq scores or any of that... I'm extremely confident I don't have a high iq at all (I'd be satisfied if I was average, lol) ... and I got the "coveted" masters in math ... I felt like an idiot in my first couple years at school... The "naturals" can do a lot of stuff in their head - and have a habit of showing off too, lol - but don't let it phase you... Hard work, and perseverance are all you really need... Honestly, after a while, you start to see the the patterns, and the techniques, and it's really more about creativity, which you develop just by rigorous practice, and reading and understanding... but it will come eventually

 

[Intervenient]

This thread has been extremely enlighting for me as well. During my first quarter of university I switched from being an English major to a statistics major, but felt I wasn't quite up to scratch with the rest of the competition. However, talking to professors and TAs and undergrad students, the majority of these people aren't geniuses at all, but "regular" people who are interested enough in the subject of math who have or want to make a career about it. No going to college at 12 and getting a Ph.D. at 15 and inventing lauded theorems: just dedication and interest. As for Real Analysis, I haven't taken the course yet (soon though), but from the talk on these forums and on campus, it seems that succeeding in higher level mathematics requires you to build up a strong mathematical intuition. I'm sure you'll do well :)

 

[whyee]

Is this a joke? An IQ (if it even means much) of 135 is not enough? Richard Feynman had an IQ of 124, and look at how much work he did in such advanced physics topics.

 

[sandplasma]

Keep thinking this way and you will end up quitting and working at a grocery store when you could have contributed to Math. Stop it, get to it. One other thing to keep in mind is that as you study mathematics you will get better at pattern recognition at least slightly thereby increasing your IQ possibly. Which again, doesn't really matter much.

 

[dijkarte]

Levis2, if you are confident that you are not smart enough to do math then I agree with you, it would be a big waste of time and effort trying to excel in a subject that you think you are not qualified enough for.
However if you are uncertain about your abilities and you tend to believe some stupid "IQ test" then do the real test yourself. Study math and if you failed the courses then try another uni, because failing the first time is not the end. I know friends who tried several uni's until finally they got PhD.
I have an IQ of -250, I got straight F's at university exams, but I consider myself a great mathematician because I believe in my talents and abilities, even if many disagree, and regardless of what the "academia standards" are.

 

[Shackleford]

Levis2, if you are confident that you are not smart enough to do math then I agree with you, it would be a big waste of time and effort trying to excel in a subject that you think you are not qualified enough for.
However if you are uncertain about your abilities and you tend to believe some stupid "IQ test" then do the real test yourself. Study math and if you failed the courses then try another uni, because failing the first time is not the end. I know friends who tried several uni's until finally they got PhD.
I have an IQ of -250, I got straight F's at university exams, but I consider myself a great mathematician because I believe in my talents and abilities, even if many disagree, and regardless of what the "academia standards" are.

Is this a serious post? I detect a bit of facetiousness/sarcasm towards the end, but you never know. Haha.

 

[dijkarte]

I quote myself here:

...even if many disagree, and regardless of what the "academia standards" are.

I would say it's a bit of humor.

 

[Shackleford]

I quote myself here:

I would say it's a bit of humor.

Yes, that indeed was the trigger. Haha.

 

[nucl34rgg]

I live and breathe mathematics! It is my passion, my way of life, and i feel it always will be. It is my greatest hobby, and my dearest pastime.

You will succeed in math.

 

[R.P.F.]

I have to say that people on this forum are extremely nice and patient. I feel like a jerk.

 

[SolsticeFire]

Wow you guys managed to turn a confused, fearful and depressed teen who was obsessed about the destination and not the journey, a boy who almost gave up his dream because he deemed himself not worthy because of some worthless IQ score, into an young aspiring learner who is now doing Real Analysis at a university and pursuing his obsessive passion for nature's language? I sincerely applaud you guys. And Levis: Keep working my friend.:) If you truly are sincere about learning, you'll always find people like these who will support and guide you. :) Don't care about IQ scores, don't care about what great theorems you'll come up with or whether you'll be the next Ramanujan or Gauss; just keep exploring and learning, and you'll definitely come to great insights. If you fail at some things or the journey gets hard, get back up and keep going. Maybe you are not a prodigy who blazes through everything, you are not a genius with innate affinity for mathematics, but you still can be a genius - genius of hard work! And that in my opinion is the greatest genius we can find within us :D. Keep working and don't stop till you have quenched your thirst! :D

 

[mathwonk]

If IQ = mental age/ chronological age, does that mean a 70 year old with IQ = 135 has the mental age of a 95 year old? If so, I am a little worried.

 

[dipole]

Go talk to some math professors, lots of them can be real dummies outside of math and not at all the geniuses you think they are.

 

[NeptuniumBOMB]

Why do you have such a fictional type veiw of mathematics and mathematicians? (its the media i tell you).
95% of people in their fields weren't prodigies when they firsts studied it. Look at Joan Birman, she went to grad school in math in her forties and is now one of the top researchers in knot theory.
Look at Robion Kirby, as an undergraduate, he was far more interested in sports then mathematics and did poorly in his masters exam and barely got into a good graduate school. Know he's a proffesor at University of Berkeley

Are there any PhD holders here, who has actually struggled with the material in some point of their education, or have they just aced through EVERYTHING?

Of course people struggle with education at many points in their life, you might think math right know at high school is easy, wait till you get to university and graduate school, you'll be really surprised. No one could possibly not struggle at anything he/she meets.

 

[Dr_Scientist]

I can't believe.. I read this thread to the end..

What I learnt:
1. A mathematician is not equal to a genius
2. You do maths because you like it. nothing else. no need for honors

 

[Kalidor]

If you wish to further investigate the relationship between IQ and mathematics, check out the already mentioned Marilyn vos Savant making a complete and utter fool of herself.

http://www.dms.umontreal.ca/~andrew/PDF/VS.pdf

 

[SolsticeFire]

If you wish to further investigate the relationship between IQ and mathematics, check out the already mentioned Marilyn vos Savant making a complete and utter fool of herself.

AHAHAHAHA The Quotable Quotes from the book had me on the floor (lol). Especially these ones:
4) Using inductive logic, F.L.T. is proved after enough examples have been found
and
2) The square root of +1 is a real number because +1 x +1 = +1; however, the square root of -1 is imaginary because -1 x -1 = +1.

Ahahahaha. Who's reading this crap anyways.

 

[chiro]

If you wish to further investigate the relationship between IQ and mathematics, check out the already mentioned Marilyn vos Savant making a complete and utter fool of herself.

http://www.dms.umontreal.ca/~andrew/PDF/VS.pdf

You know it's odd since the wiser people that I have experienced personally and also observed not in person (like forums, videos, and so on) are the ones that have the courage and the sense to say "I'm sorry, I don't understand X,Y, or Z".

If you guys ever want to see where this has gone bonkers, take a look at the movie idiocracy and listen to how people try and hide their stupidity by pretending that they know so they don't look stupid.

I admit that I do this from time to time, but eventually it always ends in the way that accepting my wrong notions is the best thing in the end.

I feel that she should do the same and just say that she is at the very least, unfamiliar with a lot of mathematics in particular research mathematics. It's not a character flaw, just a realization that sometimes, we get it wrong.

 

[StatOnTheSide]

This is a very long thread and I did not read it completely. I have a recommendation for you.

Thinking Mathematically -- J. Mason, L. Burton, K. Stacey

It is a fantastic book. Thinking process can be divided into two categories. Thinking by analogy and thinking by originality. Most contest problems are based on analogy. You try to solve 10 tough ones based on a trick. You won't go anywhere with it. You look at the solution and then you solve the later problems using the same trick.

Original thinking on the other hand involves inventing the trick. It might sometimes not even be based on a trick and will be a very rigorous approach completely based on recognizing a pattern and then formally providing the proof for it.

This book helps you to think originally. He walks you through the process of thinking mathematically. I think that solving problems by analogy in Olympiads and Putnams, though very much a great achievement, especially for a high school kid, is still not same as thinking originally. Srinivasa Ramanujam is a classic example of an original thinker. Who taught him all the tricks? He was in India during the British Raj and there was nobody to talk to let alone get training in mathematics. He basically thought of everything in the most original way and must have had an extremely good cognitive ability based on which, he could see patterns very well. Based on that, he made conjectures and proved them.

There is IQ and there is also the testosterone. People with high testosterone just go ahead and do it without caring for anything else. I think that unless you develop a don't care attitude to what others say when they are being negative and unless you have love for mathematics, you will find it hard to do mathematics. If you love mathematics, I am sure you will find your way out like most of the others have done.

I am not sure if you are looking for a response at this time as this is a very old thread but I just thought of sharing my thoughts on this.

 

[H2Bro]

AHAHAHAHA The Quotable Quotes from the book had me on the floor (lol). Especially these ones:
4) Using inductive logic, F.L.T. is proved after enough examples have been found
and
2) The square root of +1 is a real number because +1 x +1 = +1; however, the square root of -1 is imaginary because -1 x -1 = +1.

Ahahahaha. Who's reading this crap anyways.

I read the review and its hilarious. I read up a bit on the Marilyn vos Savant lady as well. She seems clever but she makes mind-boggingly stupid mistakes and then has the audacity to not acknowledge them - a sure sign of a very limited kind of intelligence.

This is an old thread, but sometimes I get down myself when I read the bio's of famous physicists and see they independently created their own notation for vectors or integration in their teens. It's good to get some reality check once in a while.

IQ tests are probably one of the most persistent forms of pseudoscience around. They are practically near to meaningless, especially for children and teenagers. The assumption that people develop mentally at the same pace, and can therefore have standardized adjustments for age, is patently false.

Do some reading on the history of IQ tests. They appeal more to our love for easily digested and compared numbers than any real understanding or valid measurement. Indices are the destroyers par excellence of accuracy...

 

[StatOnTheSide]

Mathematicians have proved incredibly great theorems. Godel has shown that no set of axioms are consistent as in there will always be a paradox no matter which set of axioms you start with. I am sure that is the case with other sciences too. There are great scientists just as there are great mathematicians.

For that reason, I wonder as to what scientists have to say about IQ. When I browse google about IQ, I do find that many scientists believe that IQ has a strong correlation to success in academic career even though that may not be the only factor.

Even though I will not stop doing math under any circumstances and my advice will still be that do what you feel like doing, I am curious to know what the truth is. It would be ironic to shy away from the truth for me as one of the qualities of a mathematician or a scientist is to consider all the possibilities with no bias and try to discover the truth. If the question is regarding the importance of IQ in being able to do math, then a scientific approach would be to figure out the truth without bias.

It might be true. It might be a bad news for all of us who do not have a good IQ. As I have said again and again, I will not stop doing math under any circumstance; however, I am really really curious to know THE answer to this question. What is IQ? Why is it important OR not important?

Whether or not IQ matters, I do not want to be unscientific about this matter and I will accept whatever is the truth. But knowing that Einstein had a very high IQ and so do many geniuses in math, there is a very strong likelihood that IQ does matter to a great extent.

 

[H2Bro]

Whether or not IQ matters, I do not want to be unscientific about this matter and I will accept whatever is the truth. But knowing that Einstein had a very high IQ and so do many geniuses in math, there is a very strong likelihood that IQ does matter to a great extent.

High IQ score is more likely to be something associated with mathematical ability rather than determinative or a necessary condition. It's quite clearly not a sufficient condition if you read the above post reviewing a book by the lady who currently holds the highest IQ score on record.

I'm betting its unlikely to find mathematicians with a very low IQ. And I bet a lot of successful one's have a high IQ. However, finding even a few successful mathematicians with only slightly-above average IQ is enough to demonstrate that a high IQ is not at all necessary for success in mathematics. This is simply something demanded by the scientific method.

One of the most influential effects of education is not just knowledge and networking, but actually instilling confidence in oneself and one's abilities. I have a feeling IQ scores can operate in a similar manner where those who find themselves with lower scores self-select out of the process, while those with higher scores assume they have fair to reasonable odds. When you go and do the measurement, it would appear only high IQ holders go on to maths success.

 

[StatOnTheSide]

It sounds very much similar to the case where some of the Olympiads go on to become great mathematicians and win the Field's medal. They usually have like 5 gold medals in Olympiads. It makes sense because for kids who do not get through Olympiads, there is no boost in confidence at that time. Success very much depends on how hard one works along with intelligence.
Hard work comes with motivation. The entire problem is with motivation.

Contests are good for people who make it through to the top but for the others, it leaves them with a very strong sense of diffidence. It is the same everywhere. A "successful" incumbent president almost surely wins the election while a president who was not able to "lift the economy" will almost surely fail with some exceptions. The economy may not even depend on the president but the candidate's success depends on the state of the economy. The analogy is loose and may be not directly applicable here but the the point is that if someone succeeds in a difficult endeavour, there is a h___uge ego boost which pushes them greatly in their career while it has the EXACT opposite effect for the ones who fail early on.

Animals have the same problem. A dominant male lion cub will show early signs of being a successful leader and that perception alone helps him become one after he grows up as the motivation is present in him which is the result of an early ego boost. Now the question is that for someone without that ego boost early on in life, what are the chances that he or she will succeed later? Failure, in whatever form it maybe, is like a thorn that keeps pricking in your mind every time you try to come out of that notion and try to do mathematics. On one hand, you cannot succeed in solving problems in the text. On the other hand, you will always have it in the back of your mind this thought that is working against you saying "I failed at Olympiad and I am not intelligent" or "I have a low IQ and I am not good enough for math". Under these circumstances, what is the likelihood of someone succeeding when all the factors "seem" to work against you?

It is about psychology. It is about emotions. Even though math is highly logical, or rather it is about formalizing the logic in a given setup, the factor that drives someone to the successful end is an emotional or a psychological one. Remember that you have to work for years and work hard to succeed and if you have these notions like failing in contests or low IQ etc, it is like trying to run a marathon thinking that the leg is broken or that it is not strong enough.

The irony is that for someone who wishes to know the truth about IQ, if he says things like "I have low IQ so I will fail", without even considering the validity of that statement, just the fact that a person thinks that way is very unscientific and may not qualify to become a mathematician. It is the question about his outlook and thinking. Math on the other hand needs you to be an EXTREMELY scientific person. You have to dispassionately try to figure out the truth. Talk to really wise people. Read books. Think and think and think. Before you even go onto becoming a math major, take this as your very first problem and demonstrate to yourself the ability to think logically.

I believe that as long as you have legs which are strong enough to carry your body for 26 miles, you are fine. It may take longer for you than the others but you will reach the target. Worse comes to worst you can walk if not run and cover the distance unless there is a rule stating that walking is not allowed. In real life, nobody cares if you are walking.

I think the reason why a lot of people do not succeed in math is that it is very intimidating, and yes, it requires intelligence. For most people, it requires a strong character too. I believe that a strong character is equally hard to find.