Is there a guide to inventing mathematical theories?

[hatemalnaggar]

Hello
Sometimes I want to invent a new theory just as Newton invented calculus
I use wide imagination and organized thinking
For 4 years, I didn't invent any thing mathematically correct
Can anyone tell me how to invent a mathematical theory?
Are there any resources on the internet?
Thank you

 

[bhillyard]

To modify a quote from Newton:
First find a suitable giant on whose shoulders to stand.

 

[dkotschessaa]

It's a noble goal. I'd say don't lose it, even if it evolves to something a little less glamorous sounding.

Remember that "necessity is the mother of invention." If you want to "invent" (not just discover) something new, there has to be a need for it. Newton invented calculus because he needed it to deal with questions in physics.

-Dave K

 

[waldganger]

I don't get the point of wanting to discovering something new. The contemporary obsession for "new ideas" is creating monsters in a lot of fields. A discovery should just happen.

 

[dkotschessaa]

I don't get the point of wanting to discovering something new. The contemporary obsession for "new ideas" is creating monsters in a lot of fields. A discovery should just happen.

I'm not trying to make you sound ridiculous, but you basically said it's OK to discover something, so long as it's not new, and it should happen by accident!

I'm sure you mean something else.

If I try to read into this, probably what you mean to say is that we shouldn't be trying to make "new for the sake of new" but we should be discovering things because they suit some existing need or purpose. If that's what you mean, I agree, sort of.

Though I think it's wrong to quash somebody's dream of making a new discovery. Maybe that doesn't ultimately mean what he thinks it means, but if that early impulse is a driving force to learn and study and discover something then it should be encouraged.

Science is *all* about discovering new things, even in the tiny little nooks and crannies of inquiry.

-Dave K

 

[1MileCrash]

Inventing math is pretty easy. Inventing math that no one else has before just requires you to get...weird.

 

[interhacker]

Unless you're Ramanujan, I think it's better to get at least a bachelor's degree in mathematics or a related field first (assuming you don't have one already).

 

[interhacker]

if you think people will care, they wont, people couldn't care less if you solved the Riemann hypothesis, and if they do, they will treat you like an animal in a Zoo, just look at what happened to the guy who proved the Poincare conjuncture.

Even I, a layman, care about the solution of the Riemann hypothesis, and I'm pretty sure professional mathematicians working in the field care far more.

Secondly, in spite of the fact that Perelman refused the fields medal and the Millennium prize because he "didn't want to be treated like an animal in a Zoo ", I find that analogy somewhat flawed.

There's a difference between being put on exhibition for other people's entertainment and being celebrated for an amazing achievement one has done.

 

[johnqwertyful]

Being a genius is only a small part of making discoveries in my opinion.

 

[johnqwertyful]

Even I, a layman, care about the solution of the Riemann hypothesis, and I'm pretty sure professional mathematicians working in the field care far more.

Secondly, in spite of the fact that Perelman refused the fields medal and the Millennium prize because he "didn't want to be treated like an animal in a Zoo ", I find that analogy somewhat flawed.

There's a difference between being put on exhibition for other people's entertainment and being celebrated for an amazing achievement one has done.

Besides, even if "no one cares", solving this problem contributes greatly to the mass of human knowledge. People care about the Riemann hypothesis not because "people care about it", but because it's an important problem.

I respect Perelman as a mathematician of course, but I think all the drama about not wanting to be treated like an animal was kind of silly and his decision to not take the money was extremely privileged. There are a lot of people who can't afford to not take money.

 

[dkotschessaa]

Lots of cynicism here and people that want to tell it like it is. I get that.

But I respect the spirit of the original poster's wish, and I still would encourage it.

My advice is pretty much the same:
1) Study lots of math (and probably science too, for scientists often need math that doesn't exist yet)
2) Find a need, and fill in the gap.

 

[phinds]

Am going to have to agree with this answer.

You also have to ask yourself why, why do you want to invent a math field?

if you think mathematicians will care, they wont, there isn't enough mathematicians to fill the subjects and inventing a new math field is a joke compared to solving problems in existing fields.

if you think people will care, they wont, people couldn't care less if you solved the Riemann hypothesis, and if they do, they will treat you like an animal in a Zoo, just look at what happened to the guy who proved the Poincare conjuncture.

Always nice to see when people have chosen a suitable handle for themselves

 

[dkotschessaa]

Being a genius is only a small part of making discoveries in my opinion.

I'd say it's almost no part of it.

 

[1MileCrash]

I'd say it's almost no part of it.

Yep, an interest and determination are what matters.

 

[phinds]

Personally, I think folks like Newton and Einstein had WAAAAYYYY more than just "interest and determination", otherwise there would be more of them.

 

[1MileCrash]

Personally, I think folks like Newton and Einstein had WAAAAYYYY more than just "interest and determination", otherwise there would be more of them.

I'm not sure I follow you.

From my point of view, passion, determination, and willpower are very much rarer than raw intelligence. I think there would be more of them if intelligence played a larger part.

 

[phinds]

Well, we'll just have to agree to disagree on this one.

I DO agree w/ you that simple intelligence is reasonably common. Genius on the level of Newton or Einstein is not.

 

[jedishrfu]

This reminds me of the Monkey King story where he tries to show the Buddha how powerful he is by flying for ten thousand li (1 li = 1/2 km nowadays but back then who knows).

He spots four big pillars pointing to the sky, stops and makes his mark o one triumphant that he has flown beyond the reach of the Buddha until the clouds vanish and he finds himself standing in the Buddha's hand with his mark on one of the Buddha's fingers.

The moral is who needs giants when a big palm and a beach-side seat with appropriate refreshments will do.

Here's a clip from Alakazam The Great:



and at 23:50 in is his interaction with the Buddha.

 

[jedishrfu]

With respect to the OP here. Its good to want to discover something new and great to discover something no one has discovered before. The danger here is that the desire to discover may blind you from ever discovering anything. We run into this all the time when something goes wrong and we are totally perplexed and can't fix usually because we're looking in the wrong place.

A classic example, were the programmers trying to figure out why their code was giving them the wrong answers to select computations on Intel Pentiums only to discover that some chips had an arithmetic flaw. that Intel had failed to disclose to anyone.

http://en.wikipedia.org/wiki/Intel#Pentium_flaw

Pentium flaw
Main article: Pentium FDIV bug

In June 1994, Intel engineers discovered a flaw in the floating-point math subsection of the P5 Pentium microprocessor. Under certain data-dependent conditions, the low-order bits of the result of a floating-point division would be incorrect. The error could compound in subsequent calculations. Intel corrected the error in a future chip revision, but nonetheless declined to disclose it.[citation needed]

In October 1994, Dr. Thomas Nicely, Professor of Mathematics at Lynchburg College, independently discovered the bug. He contacted Intel, but received no response. On October 30, he posted a message on the Internet.[71] Word of the bug spread quickly and reached the industry press. The bug was easy to replicate; a user could enter specific numbers into the calculator on the operating system. Consequently, many users did not accept Intel's statements that the error was minor and "not even an erratum." During Thanksgiving, in 1994, The New York Times ran a piece by journalist John Markoff spotlighting the error. Intel changed its position and offered to replace every chip, quickly putting in place a large end-user support organization. This resulted in a $500 million charge against Intel's 1994 revenue.

Ironically, the "Pentium flaw" incident, Intel's response to it, and the surrounding media coverage propelled Intel from being a technology supplier generally unknown to most computer users to a household name. Dovetailing with an uptick in the "Intel Inside" campaign, the episode is considered to have been a positive event for Intel, changing some of its business practices to be more end-user focused and generating substantial public awareness, while avoiding a lasting negative impression.[72]

Instead you should develop an active curiosity, always questioning what you observe, what you learn and what you do and from that may come a good or great discovery. Sometimes you need to go at things in different directions from the conventional ways to discover a new way of doing things or a new invention. Sometimes you need a question to be answered or a problem to be solved, or some stress or drive to solve it quickly.

 

[dkotschessaa]

Personally, I think folks like Newton and Einstein had WAAAAYYYY more than just "interest and determination", otherwise there would be more of them.

Interest and determination is a necessary condition, but not always a sufficient one.

 

[phinds]

Interest and determination is a necessary condition, but not always a sufficient one.

Oh, I agree w/ that completely. I don't think Newton & Einstein ONLY had genius

 

[1MileCrash]

Oh, I agree w/ that completely. I don't think Newton & Einstein ONLY had genius

Of course. I just think their devotion was of higher importance and a more rare thing.

I mean, I can think of many people I know who I think, if put in Newton's shoes in Newton's time, and devoted all of their time to these studies, could do the same thing.

 

[dkotschessaa]

Not to speak a blasphemy, but reports of Einstein's genius may be overblown as well. There was a lot of hard work involved and not a small degree of luck.

 

[phion]

As one kind soul put it for me when I was new to PF years ago, "shoot for the stars and you'll land on the moon."

 

[interhacker]

As one kind soul put it for me when I was new to PF years ago, "shoot for the stars and you'll land on the moon."

The probability of your spacecraft just happening to land on the moon after failing to complete an interstellar journey is almost nil, but I get your point. :-D

 

[phion]

The probability of your spacecraft just happening to land on the moon after failing to complete an interstellar journey is almost nil, but I get your point. :-D

These rules don't apply, haven't you ever seen The Hitchhiker's Guide to the Galaxy?

 

[interhacker]

These rules don't apply, haven't you ever seen The Hitchhiker's Guide to the Galaxy?

Yeah. The improbability drive, lol. :-D