# Is Mathematics Research Useless?

# Preface

Last article I wrote about Markov Chain, this article is about why some people consider mathematics research useless.

# What is mathematics ?

This is a very deep and controversial question, however I will attempt to give a very simple answer to this question.

**For me, mathematics is a branch of knowledge that studies logical patters, these patterns can originate either from the human mind or from the world around us.**

# What is mathematics research ?

**Mathematical research is the process of discovering and studying the patterns** above-mentioned, these discoveries are typically done either in public and private institutions or independently.

# Is mathematics research useless ?

To give my two cents on this one, I will have to dissect a couple of points that come to my mind.

## Applied Research

When it comes to Applied Research, we have to dissect this into 2 topics:

**Short-Term**

There is applied mathematical research that is immensely applied to the real world, this typically stems from problems around us that have a very **specific question asking for a very specific answer of theoretical and practical importance**.

Typically, these are papers that give a theoretical contribution to the mathematical community as well as, for example, some code that solves a very specific problem in our society.

In my opinion this is the mathematical research that adds up something to society immensely and so it is an immediate ROI; This type of mathematical research is very important and useful. In fact, it is so useful that it is even done in R&D departments in private institutions.

**Long-Term**

There is applied mathematical research that is made for the long game, typically these are very big research projects that **attempt to solve questions of major society importance**.

As an example we have research in new AI architectures these; As in opposition to the upper ones, the ROI is not immediate, however they typically need many years to start giving anything.

In my opinion, this type of research is very significant to society, as some questions are not solved from day to night and require many heads on them.

**Why we should be careful with applied research?**

**There is a lot of applied research that is never applied**. In fact, I used to study nearby an Operations Research department, and they would say that most of what they do is lucky if it is read by an academic and mostly impossible to be useful in industry. This is outrageous, after all these researches are doing applied research for a reason: To be applied !

**CASE STUDY**

Your research needs to have a case study, otherwise your research is not applied, it is fundamental. Make sure to implement your ideas in the real world with real people. That is what dilettantes a useful applied research article from one mid-article.

Make sure your work:

- Contains or provides a direction of implementation
- Does not over specify
- It is relevant for society and academics.
- CASE STUDY

If you tick these 3 boxes, you are onto a very good paper!

## Fundamental Research

So at first sight, one might argue that any piece of fundamental mathematical research is worth a read, however in practice **this is very far from the truth!** I will point out 3 reasons why this is the case.

In my opinion, a paper which ticks any of these is not worth publication nor your time!

- Over Specific Topics
- Useful for the mathematical community
- Not disruptive

**Over Specific Topics**

If you open a maths journal, probably you will find over specific topics, these tend to be niche cases of a given big result or a very small aspects of a given topic that need to be shown.

The problem with these is that **people will not care** about what you have written, this is the experience of many of mine colleagues and friends, even if you are from the field. Sometimes, these specialisations are either to farm publications or just because of the sake of curiosity. But if you do not write for the others, then what are you doing exactly ? Writing a diary ?

**Useful for the mathematical community**

Mathematicians tend to be sometimes solely driven by curiosity, do not get me wrong doing maths for fun is very nice. However, I have seen some deemed** difficult or interesting questions that in the end are just a flex of intellectual showcase**, being difficult or funny does not mean useful; mind that in your writings.

**Lack of a common vision can tear apart a field**, in maths this is very much a thing, simply professionals from different fields do not talk with each other. I have heard stories in some departments where I have been where even the same office colleagues did not know what each other were doing. In my opinion, writing should be maximised for a larger number of readers, trying to connect our research with others (maybe in fields other than yours) is key, do not go on an alone path unless it fits in the following point.

**Not Disruptive**

Today is publish or perish.

This is something I listen a lot, however this will affect this point, which is: *Being disruptive requires time and patience.*

Disruptive articles in maths have been drowning (just check last century progress and compare with ours), some claiming that the field is starting to die! If you publish, try to give an actual contribute, connect the dots differently or add an all new class of problems to the maths building.

We need interesting questions more than answers.

Overall, fundamental research can easily be very useless for the reasons above. However, if you do not tick all those boxes, you are off to a decent piece of research. Furthermore, **history shows us that good pieces of fundamental research are what advances the world**, after all. Just look at General Relativity or Quantum Mechanics or the Theory of Computing.

# Conclusion

Mathematical research is a very hot topic of debate these days. In this story I tried to convince you that **applied research is VERY useful** if done properly and that **fundamental research can be useful** if done with a set of good principles in our mind.

Lisbon, Portugal