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In summary, the most complex present-day math includes coupled systems of non-linear partial integro-differential equations and the study of number theory. It offers the challenge of applying mathematical maturity and discovering new methods to solve unsolved problems. However, the concept of "complexity" is subjective and can vary depending on individual perspectives and knowledge. Despite this, the field of mathematics continues to evolve and make connections with other subjects such as physics and computer science.

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Lifter0569

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I've currently enrolled in Calculus II and have been thinking lately how far does the most complex present-day math "go"? When I say how far, I mean how complex is the "most complex" math in present time and what does that type of math offer? This topic really is hard to create a search on, so I've resorted to asking in a post. I realize this is relative to the person being asked the question, but generally, there must be an answer widely agreed to. Thanks in advance!

Now that I think about it..I have a part 2 for this question. Many physicists agree that physics needs a "new type" of math for any hope to solve some of the present day equations because of the sheer complexity of the problems. When they say new type of math would they mean one that did not base itself off of integers and their units? Thanks again.

Mathematics news on Phys.org

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Mithal

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From my own experience , I find abstract mathematics is hard like abstract algebra or topology . The more advance you become , the more abstract it gets .

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Icebreaker

If by the "end" of math you mean where you can begin contributing new knowledge, the answer is anywhere and at any level. A professor here published quite a few papers on something as "trivial" as critical points.

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ComputerGeek

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Mithal said:

From my own experience , I find abstract mathematics is hard like abstract algebra or topology . The more advance you become , the more abstract it gets .

I love abstract algebra.

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saltydog

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Lifter0569 said:

I've currently enrolled in Calculus II and have been thinking lately how far does the most complex present-day math "go"? When I say how far, I mean how complex is the "most complex" math in present time and what does that type of math offer?

Personally I'd think coupled systems of non-linear partial integro-differential equations.

Many physicists agree that physics needs a "new type" of math for any hope to solve some of the present day equations because of the sheer complexity of the problems.

Would be nice to be around to see that happen. Perhaps we'll reach a critical-point qualitatively different than what we have now: A new non-linear computational device will be designed along the lines of the human brain unlike any linear digital computer we have today. The spark of creativity and discovery emerges from it and soon begins to design novel solutions to some of the intractable problems we face today. Just a hunch.

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neurocomp2003

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math never ends...you can apply math to any other subject field frm business to sociology to psychology to medicine to the other sciences and comptuer science.

As quantum and relativity grow so does math

as computer science and technology grows so does math.

As ALife grows math will also.

Now if your talking the math that studies math...like analysis...it also continues to grow that's why their are so many university professors...otherwise there would be no research in math.

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hypermorphism

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Lifter0569 said:

I've currently enrolled in Calculus II and have been thinking lately how far does the most complex present-day math "go"? When I say how far, I mean how complex is the "most complex" math in present time and what does that type of math offer? This topic really is hard to create a search on, so I've resorted to asking in a post. I realize this is relative to the person being asked the question, but generally, there must be an answer widely agreed to. Thanks in advance!

There aren't really levels of complexity to higher math. After learning analysis and algebra, everything else just requires mathematical maturity and the drive to discover new methods and apply new axioms. Basic topology can be taught to almost anyone, but without knowing analysis or algebra, the power of the methods of topology will not be immediately apparent.

However, number theory generally is held to have the most easily stated unsolved problems to the new mathematician.

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Gokul43201

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saltydog said:

Personally I'd think coupled systems of non-linear partial integro-differential equations.

You know how an algebraist would react to that !

I know one math department in India that was so...(ahem) arrogant, they didn't offer any courses in DE, and had their students take courses on DEs from the physics dept.

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saltydog

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Gokul43201 said:

You know how an algebraist would react to that !

I know one math department in India that was so...(ahem) arrogant, they didn't offer any courses in DE, and had their students take courses on DEs from the physics dept.

Very well Gokul. I yield. Might you be so kind to offer your opinion as to what you consider to be the present pinnacle of mathematical sophistication?

I would be genuinely interested in your thoughs about the matter.

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amcavoy

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I don't know if "complex" is the best choice of words.

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mathwonk

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i cannot easily even venture an answer to your question, although I am tempted to try.

instead let me remark that as you may know, the material you are studying in calc II is about, let's see, 150 years old? at least.

so to you everything done since then is new.

i study geometry, and in that field riemann and his followers made great strides in understanding diomension one geometry. then it took another 60-75 years to understand well the simpler parts of 2 diemsnional geometry, and only in the last 20-30 years has a beginning been made in three diemnsional geometry.

all the while peopl have been going back snd drawing connections between geometry of lower diemsnions and other subjects like analysis and physics: e.g. string theoiry is a n elaboration of the physics of (comkplex) one dimensional geometry, and much of modern number theory is likewise an in depthm study of a very special chapter of one dimensional geometry.

...etc etc,,,,

## Related to Where does math end presently?

## 1. Where does math end presently?

Math is a constantly evolving field and there is no definitive end to it. As our understanding of the universe grows, so does our use of mathematics to describe it. Therefore, math will continue to expand and develop as long as we continue to explore and discover new things.

## 2. Is there a limit to the complexity of mathematical problems?

It is believed that there is no limit to the complexity of mathematical problems. As mathematicians continue to push the boundaries and explore new concepts, the complexity of problems will continue to increase. However, our ability to solve these complex problems may be limited by our current technology and understanding.

## 3. Will we ever reach a point where all mathematical concepts are known?

It is highly unlikely that we will ever reach a point where all mathematical concepts are known. As mentioned before, math is constantly evolving and there will always be new concepts and theories to explore. Additionally, the vastness of the universe means that there will always be unknowns that require mathematical understanding to explain.

## 4. How do mathematicians determine if a mathematical concept is valid?

Mathematicians use a rigorous process of proof and logical reasoning to determine the validity of a mathematical concept. This involves breaking down the concept into smaller, more manageable parts and using established theories and principles to prove its validity. The concept must also be consistent with other established mathematical concepts.

## 5. Is there an ultimate goal or purpose for studying math?

The ultimate goal of studying math is to better understand the world around us and to solve real-world problems. Math is used in a wide range of fields such as physics, engineering, economics, and more, making it an essential tool for advancements and innovations in society. Additionally, studying math can also improve critical thinking and problem-solving skills, which can be applied in various aspects of life.

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