How do you find that math problem that is worth working on?

[Trurl]

What are your methods to find that great math problem to invest your time to work on? Or any other project.

 

I have my own methods but I want to hear others before I share my own.

[Trurl]

Well I thought this would be:What is the best way for an amateur to find math problems?

Math and drawing take less resources compared to other sciences. But the amateur still wants meaningful problems. Obviously ideas can come from anywhere, but it would be nice to be working on the most current needs. For example BitCoin is valuable, then it is not. Twitter following can tell you what is popular, but reaseach takes time and still how do I know the problem is worth the effort?

Journals list abstracts but the amateur doesn't really have access to them.

I know ideas are found everywhere. I am just looking to grow as an amateur. Am I looking in the right areas?

[Sensei]

On 3/19/2019 at 4:14 PM, Trurl said:

What are your methods to find that great math problem to invest your time to work on? Or any other project. 

I have my own methods but I want to hear others before I share my own. 

...during writing computer programs and algorithms..

 

 

Do you want my recent inspiration ...?

Suppose so we have function taking string as input parameter. It suppose to calculate quantity of the all possible combinations excluding repetitions..

Imagine example input word "ab". It can have only two outputs "ab" and "ba". It's simple n! so far..

Imagine example input word "abc". It can have outputs:

"abc", "bac", "acb", "bca", "cab", "cba". Again it's simple n! so far..

But there are possible combinations after exclusion of one of the letter! So remove "a" and work with "bc", remove "b" and work with "ac", and remove "c" and work with just "ab".

...with 4th letters it's already too complex for me to bother to list the all possible outputs (at least in Friday night hmm.. Saturday morning.. )

 

Your job is to make equation (preferably non-recurring procedure) returning number of the all possible combinations excluding repetitions of n-th word input (to be able allocate enough size array for the whole dictionary and order computer threads to work with specific portion of words, each thread with their own portion of data from dictionary).

 

Edited March 23, 2019 by Strange
Correct bc to ba

[studiot]

7 hours ago, Trurl said:

Well I thought this would be:What is the best way for an amateur to find math problems?

Math and drawing take less resources compared to other sciences. But the amateur still wants meaningful problems. Obviously ideas can come from anywhere, but it would be nice to be working on the most current needs. For example BitCoin is valuable, then it is not. Twitter following can tell you what is popular, but reaseach takes time and still how do I know the problem is worth the effort?

Journals list abstracts but the amateur doesn't really have access to them.

I know ideas are found everywhere. I am just looking to grow as an amateur. Am I looking in the right areas?

Since this was obviously a serious question, let me wish you well in your search.

As I don't know what you mathematical level is it is difficult to advise, but here are a few thoughts.

An amateur would not have the resources to attack the Millenial Maths Problems, or the ones introduced by Riemann, who originated the idea a century before with his list.
Further I would question if they are fun.

http://www.claymath.org/millennium-problems

 

Also I don't know if you are a reader. This route perhaps offers more fertile ground.
Take heart, Napoleon was an amateur mathematician and even discoverd a minor theorem which is named after him.

You will find Napoleon's theorem along with a lot of (mostly) easy to assimilate fun stuff in

The Penguin Dictionary of Curious and Interesting Geometry

David Wells.

David has also written lesser titles - TPD of Numbers and TPD of Mathematics.

 

Another modern book is

Things to Make and Do in the Fourth Dimension

Matt Parker

 

Martin Gardner was the most famous author of Maths Puzzles and explanatory maths articles with many books to his name.

 

You you also try some overview books from famous Mathematicians which range more sidely and interestingly than academic courses.

 

What is mathematics?

by Courant and Robbins

 

A survey of Modern Algebra

by Birkhoff and Lane

 

Come into this category

Another category lies in applied maths here

From Calculus to Chaos is brialliant

as is

The Mathematical Mechanic

by David Levi.

 

Other than this you will need to tie things down to a much smaller area.

 

 

 

[StringJunky]

1 hour ago, studiot said:

Since this was obviously a serious question, let me wish you well in your search.

As I don't know what you mathematical level is it is difficult to advise, but here are a few thoughts.

An amateur would not have the resources to attack the Millenial Maths Problems, or the ones introduced by Riemann, who originated the idea a century before with his list.
Further I would question if they are fun.

http://www.claymath.org/millennium-problems

 

Also I don't know if you are a reader. This route perhaps offers more fertile ground.
Take heart, Napoleon was an amateur mathematician and even discoverd a minor theorem which is named after him.

You will find Napoleon's theorem along with a lot of (mostly) easy to assimilate fun stuff in

The Penguin Dictionary of Curious and Interesting Geometry

David Wells.

David has also written lesser titles - TPD of Numbers and TPD of Mathematics.

 

Another modern book is

Things to Make and Do in the Fourth Dimension

Matt Parker

 

Martin Gardner was the most famous author of Maths Puzzles and explanatory maths articles with many books to his name.

 

You you also try some overview books from famous Mathematicians which range more sidely and interestingly than academic courses.

 

What is mathematics?

by Courant and Robbins

 

A survey of Modern Algebra

by Birkhoff and Lane

 

Come into this category

Another category lies in applied maths here

From Calculus to Chaos is brialliant

as is

The Mathematical Mechanic

by David Levi.

 

Other than this you will need to tie things down to a much smaller area.

 

 

 

What resources does one need, apart from a brain and the knowledge of those that have been before on a particular maths problem?

[studiot]

7 hours ago, StringJunky said:

What resources does one need, apart from a brain and the knowledge of those that have been before on a particular maths problem?

Some problems in modern maths have only been solved by super computer trial and error to exhaustion.

For example the four colour problem.

Not all mathematicians accept these methods.

[Sensei]

1 minute ago, studiot said:

Some problems in modern maths have only been solved by super computer trial and error to exhaustion.

Brute-force method, easy to program, is a good way of verification of whether some equation is giving good results.

2 minutes ago, studiot said:

Not all mathematicians accept these methods. 

Good luck in searching e.g. the biggest Mersenne Prime without computer farm..

[Trurl]

Thanks guys. There is some good advice here. I do like the permutation of a and b as a stating point. Usually it given the abc then find ab ac and so on. I have a reoccurring problem on my trucks speedometer. I am at 71000. But I was thinking when do numbers repeat. For example 71071 or 71171. This is considering how large the odometer is that the numbers occur linearly. So my hunch on the abc Sensei mentioned is a modulus problem and I would treat it as if it were an odometer. I know I problem misworded this idea but it is just an intuitive idea I have not done any work but it would be very applicable to computer computation.

The reason for me to ask this question is that I was stuck on a problem. The problem led to other problems but essential part of the larger problem I was stuck on. But I continued to work on it because it was "my problem". I like the idea of the abc problem because if each letter is given it's own spot across the odometer if it spins linearly all letters will result. But putting that into an equation is a different story.

 

 

 

[Trurl]

Ok, so I ask about a different math project because I have been stuck on my semi-Prime project for years. Actually it is several dozen of projects in one. But still the same problem.

So I have been searching for a new project. I will be moving on to computer modeling and computer graphics. I was reading an article from a math journal that mentioned solving math problems with “brute force” using computers. Basically it discussed the use of computers to eliminate or find patterns then offer the result as proof the math problem s or is not solvable.

I don't know if I agree computers testing every possible numbers results as proof. However it does seem interesting especially in response to cryptography and computer security.

So I will work on the Prime project in the background. I still have many new project possibilities. I just wish someone would agree that cryptography algorithms that rely on the least common multiple are now less secure.

[Sensei]

7 minutes ago, Trurl said:

I just wish someone would agree that cryptography algorithms that rely on the least common multiple are now less secure. 

..which cryptography algorithms rely on the least common multiple.. ?

 

[Trurl]

Well the first public key cipher, RSA, relies on the product of 2 Prime numbers. No pattern in Primes but you can solve the least common multiple and that will find the small Prime number of the product.

I don't know them all but several public key crypto relies on the product of 2 Primes.

I refer to RSA because it was the first and one of the most popular. Other crypto relies on logarithms or curves. But as far as I know the strength of RSA is still relevant. Most attacks are brute force and not on reversing the cyphering algorithm.