#Mathematician #Math #DayintheLife #MathDaily #Mathematics
Have you ever wondered what mathematicians do on a day-to-day basis? 🤔 It’s a question that many people often ponder, as the field of mathematics can seem mysterious and esoteric to those on the outside. Contrary to popular belief, mathematicians don’t spend their days just solving the same old math problems over and over again. In fact, their work is quite dynamic and varied, involving a range of activities that contribute to the advancement of mathematical knowledge and theory.
So, what does a mathematician actually do in their day-to-day life? Let’s take a closer look at the intricacies of their work and shed some light on the daily activities of these dedicated professionals.
##Research and Exploration
One of the key aspects of a mathematician’s daily routine is research and exploration. Just like scientists in other fields, mathematicians are constantly working to expand the boundaries of their discipline and develop new theories and concepts. This involves a variety of activities, including:
– Exploring existing mathematical theories and theorems to identify areas for further investigation
– Formulating and solving complex mathematical problems to gain a deeper understanding of mathematical principles
– Collaborating with other mathematicians to exchange ideas and work together on complex research projects
– Attending conferences and seminars to stay up-to-date with the latest developments in the field
It’s important to note that research in mathematics is not limited to just solving equations or working with numbers. Mathematicians also explore abstract concepts, such as topology and geometry, as well as theoretical frameworks, such as group theory and number theory. This diversity of research areas ensures that mathematicians are constantly engaged in exploring new horizons and pushing the boundaries of mathematical knowledge.
##Teaching and Education
Another important aspect of a mathematician’s day-to-day work is teaching and education. Many mathematicians work in academic settings, such as universities and research institutions, where they are responsible for educating the next generation of mathematicians and scientists. This involves a range of activities, including:
– Teaching undergraduate and graduate-level courses in mathematics and related fields
– Mentoring and supervising graduate students and postdoctoral researchers on their research projects
– Developing and delivering lectures and seminars on advanced mathematical topics
– Engaging with the broader community through outreach and educational programs
In addition to their work in formal education, many mathematicians also contribute to the development of educational materials and resources. This may involve writing textbooks, creating online tutorials, or designing interactive learning tools to make mathematics more accessible and engaging for students of all ages.
##Application and Problem-Solving
In addition to their work in research and education, mathematicians also play a crucial role in applying mathematical principles to solve real-world problems. This involves collaborating with industries, businesses, and government agencies to address a wide range of challenges, such as:
– Developing algorithms and mathematical models to optimize complex systems, such as transportation networks or financial markets
– Analyzing large datasets to identify patterns and trends that can inform decision-making processes
– Contributing to the development of new technologies and innovations, such as cryptography and data encryption
– Consulting with policymakers and stakeholders to inform evidence-based decision-making in areas such as healthcare and environmental sustainability
By bringing their expertise to bear on practical problems, mathematicians help to drive innovation and progress in a wide range of fields, from engineering and computer science to economics and social policy.
##Finding New Theory
Now, let’s address your question about how mathematicians “find” new theory. Contrary to popular belief, the process of developing new mathematical theories is not about stumbling upon a eureka moment or discovering a revolutionary idea out of thin air. Rather, it involves a systematic and methodical approach that relies on a combination of creativity, rigor, and collaboration. Here are some key steps that mathematicians take to “find” new theory:
– Identify a Gap: Mathematicians start by identifying an area of mathematics where there is a gap in existing knowledge or a unresolved problem.
– Formulate a Hypothesis: Once a gap has been identified, mathematicians develop a hypothesis or conjecture that aims to address the gap and expand the boundaries of existing theory.
– Test and Refine: Mathematicians then embark on a process of rigorous testing and refinement, using a variety of mathematical techniques and tools to validate their hypothesis and refine their ideas.
– Collaborate and Communicate: Throughout this process, mathematicians collaborate with their peers, seeking feedback, and input from other experts in the field. This collaborative approach helps to ensure that new theories are robust and well-grounded in mathematical principles.
– Publish and Peer Review: Finally, mathematicians publish their findings in academic journals, where they undergo rigorous peer review by other experts in the field. This process helps to ensure the quality and validity of new mathematical theories before they become widely accepted.
So, as you can see, the process of “finding” new theory in mathematics is not so much about hunting for something elusive, but rather about a systematic and collaborative approach to exploring new territory and expanding the frontiers of mathematical knowledge.
In conclusion, the daily life of a mathematician is far from mundane or repetitive. From conducting groundbreaking research to educating future generations and solving real-world problems, mathematicians are engaged in a diverse and dynamic range of activities that contribute to the advancement of knowledge and innovation across a wide variety of fields. So, the next time you think about what mathematicians do on a daily basis, remember that their work is as varied and exciting as the ever-expanding universe of mathematics itself.
In an academic setting, they are trying to solve a problem, any problem, so they can publish their solution and get credit for it.
In a commercial setting, they are trying to solve a specific problem from a short list the company needs solved.
Generally discovering any kind of new math basically boils down to asking some question and hunting for an answer. A fun example might be something like the [Millennium Prize Problems](https://en.wikipedia.org/wiki/Millennium_Prize_Problems). This is a set of unsolved problems in math that each have a million dollar prize to anyone who can solve them. The Navier-Stokes problem, for example, is actually a really straightforward equation to write down if you know some basic physics, but it’s a differential equation, which isn’t necessarily very useful for many practical applications. And so the million dollar question is basically whether or not we can take this impractical equation and rewrite it as a practical one instead. [Numberphile did a video](https://www.youtube.com/watch?v=ERBVFcutl3M) on this topic if you’re interested.
Sometimes, people state a theory that they haven’t proven – most famously, Fermat’s Last Theorem. They might work on this to solve it.
There are “problems” in which we can predict what the answer can be, but we haven’t conclusively proven it yet.
They might also take problems or demonstrations from more [practical examples](https://youtu.be/rXfKWIZQIo4?si=x-1fb13y8xBE5_x1), or applied fields like physics, and work out the maths for them.
There’ll also be a lot of teaching, marking, writing, supervision, grant applications etc. going on.
I really like the channel [Numberphile](https://youtu.be/d8TRcZklX_Q?si=GwQwk_C3wIBbYwMx) if you want to find out more about both serious and more whimsical stuff – a lot of it just seems “ooh cool!”, but may have practical applications in the future.
Some answers about what mathematicians do in general, but here’s some more detail about day to day.
First of all, there’s all the non-research stuff: teaching and prep, meetings, mentoring grad students, etc.
But for actual research: reading papers (keeping up with what’s new in the field and looking for a gap in existing research to work on), working out examples by hand or with code to find interesting questions and form conjectures, using those examples to build intuition and work towards a proof (often starting with a simple case and then working to generalize and strengthen the result), writing out the proof and working out details.
Mathematicians may be working on several projects at once in different stages. Some work alone, some do a lot of collaboration and bouncing ideas off of each other.
Statistician, actuary, data scientist, financial analyst, economist, systems engineer, etc., are all jobs where a math major is quite valuable (but you do need a second degree, in a practical field). A ‘pure’ mathematician will usually dwell in academia and live grant to grant.
Probably math.
jokes aside I’ve seen some lucrative jobs in hedge funds for Math PhDs… like quantitative analysis and such. I’m thinking most go that route that want to pursue money
Understand the difference between what I’ll call problems and exercises.
Exercises are what you do in math class when you are learning. The method for solving them is known and you just have to follow the right steps to get the answer. This is most people’s experience of math so they tend to envision mathematicians sitting around all day doing problem sets. Mathematicians do not do this. This would be like an author spending their time spelling random words.
A true problem is one where you don’t know how to solve it when you start. Finding a solution takes creativity and hard work. Sometimes years. The frontiers of math where the cutting edge research is happening are often so advanced that it might take years of study just to understand what the problem is (consider [this list](https://en.m.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics) of unsolved problems; I have a BS in math and it’s Greek to me).
One math phd I knew was creating an actually-random number generator as a fun side project. Because any mathematical approach you use has rules, so it isn’t perfectly random. You need to add chaos. Quite fun actually.
Start the process, get a relatively random set of coordinates, fetch the current temperature of that place and keep going with that number. But temperatures only come in a relatively narrow range.
The next idea was to use the movements of an animal as the start value. Entry code defined by which pieces of peanut the mice eat in which order today.
I’m a grad student studying math and so I work closely with a lot of professors. Mathematicians typically have *some* sort of teaching duty. This varies dramatically between schools and professors. Some people mostly want to teach, so they teach a lot of undergrad courses, while others mostly just want to do research and will only sometimes teach a course (and typically it’ll be a graduate-level course). Some people *only* want to teach, so they won’t even publish papers anymore. I know a few professors who haven’t published in over a decade. But if you’re a professor who is hired for your research, you will absolutely be expected to publish a certain amount each year (hence the academic phrase “publish or perish”). While teaching more lessens this burden, teaching can be extremely time consuming. Grading in general is tedious, but grading math takes so long to read through and understand peoples’ mistakes. Not to mention preparing lessons for all your classes each day and answering emails.
Outside of that, there’s also a lot of administrative duties that are just left up to professors. Hiring committees, department chairs, etc. are all made up of professors who have to spend a lot of time on these more mundane tasks that people typically forget about.
Then you have things like conferences. Mathematicians will go attend different math conferences through out the year and speak at a few. The more known you are within your niche subfield, the more talks you’ll be giving. While the talks themselves aren’t very long, they take a lot of preparing and traveling.
*Then* we can get to actually writing new math research. This will basically start with you asking some question that hasn’t been solved yet that you believe you can solve. While this can be difficult, when you’re one of the very few people who even understands the papers published in your subfield, it’s not as hard as you may think. You’re also working on solving *modern* math problems. People aren’t really working with high school geometry here. They’re using techniques that have only been used for the last few decades, so there’s less of a chance of others coming up with the same idea. There’s even times where you’ll think of a lot of questions while writing one paper and save some of them for your next paper to reach your department’s expectations that year.
Once you have your question or concept that you want to explore for a paper, you just start asking natural questions and seeing where things go. If you’re a curious person, this actually can fill up fast and provides ample material to work with. You’ll then have to actually *answer* those questions though, and that’s where things get difficult. As you refine your work in your field, you’ll come up with strategies and intuition on how to approach different ideas. As for the actual *work* you do, well you basically just stare at a board and write stuff down on it sometimes. It’s like trying to solve a fun puzzle. You just gotta think for a good bit. Sometimes you come up with a really creative idea and it’s really satisfying. Other times you feel like you’ve hit a brick wall and can’t solve some annoying problem. It helps that we have solved so many problems at this point that we have been trained for trying to think through these situations. A math degree is entirely built around the idea of making you struggle and think the whole time to mold your thought process correctly. Then once you’ve got all your ideas and proofs down, you organize your thoughts and make your paper nice and pretty for submission.
Aside problem solving, many mathematicians work with computers.
A computer, in the end, is just a very powerful calculator, it’s able to do tons of simple operations in a short time, but it can’t solve complex problems by itself.
If a company needs to solve a very complex problem, they may need a mathematician with informatics knowledge, which will break down the problem into the lowest number of simple operations, so the computer can solve the problem using less time as possible.
I wake up and immediately calculate the factorial of the time I woke up converted in epoch time. Then I brush my teeth while making sure the motions follow the golden spiral. In the middle of brushing my teeth I get the square root of 7 because I can. Sometimes I like to find the roots of letters too because numbers can get boring. On very rare occasions when I have used up the English alphabet I also find the nth root of greek letters.
My daughter has a Master’s in Math and writes fraud-detection algorithms for a large bank. The algorithms are large and complex to catch as many criminals as possible while also having a low false-positive rate.