Where should society allocate mathematicians? (Grant Sanderson
Вставка
- Опубліковано 10 гру 2023
- Full episode: • Grant Sanderson (3Blue...
Apple Podcasts: podcasts.apple.com/us/podcast...
Spotify: open.spotify.com/episode/0u05...
Transcript: www.dwarkeshpatel.com/p/grant...
Follow me on Twitter: / dwarkesh_sp - Наука та технологія
As a CS major who likes math, this is giving me more reason to start over as a farmer.
The CS -> farming pipeline is real
Sounds like you’re shit at both so you’re coping by not committing to a role in your field
CS and farming are a great fit. With climate change we will need AI to detect and respond to ecosystem changes. Our food sources are in massive peril. There is a deeper need here beyond simple automation and fancy UI.
Stardew Valley pipeline
If you're studying CS and actually want to use advanced math - I'd highly suggest focusing on a job in either academia or scientific research. The vast majority of software development work that exists never uses advanced math and attempting to do so (when it wasn't strictly needed) would be a huge negative. Everyone conflates software development and math, but the factual truth is that they are not related. 99.9% of software development rarely uses anything beyond elementary math and - on the occasions it does - it pulls in existing 3rd party / open source libraries that do all the work. fyi
My room mate recieved an undergraduate in Physics. Top of class and the guy every physics major went to for help. He was married as sophomore and then had child so grad school was out of question. Went to work for his father in law as cement truck driver and later in shop. Moved to union job and bought rental houses and fixed them up. Had wife kids regular hours. Fishing on weekends. Happy life. Better than academia financially. He was smarter than we thought.
couldn't he do the same without a degree?
@@mymoviemania1of course he could! But his experience during academia for sure helped him during his life journey
@@mymoviemania1 maybe, but maybe he wouldnt excel at it without his trainning on really complex and abstract subjects.
@@mymoviemania1I'm currently pursuing a Mathematics major. At the same time, I works as Sales Executive in a SaaS B2B company. The thing is, I started as a Sales Assistant, knowing little to nothing on the matter, yet as I studied Sales Techniques, Workflows, and also the product itself, I recognized patterns with dead ends on my sales. Why I couldnt sell to this type of users? I talked to them, collect data on patterns on their User Flow and when I had an hypothesis, told a friend of mine on Development to work things with me on this matter. We check Google Analytics (which is a basicly a big dashboard with lots of data), and I pointed out a time session problem with this users, as well as a problem with automatic quotation that was given to them. We checked the code (Im able to read code) and we got it. Recently created companies had no data on specific times, the developer had not considered all cases when creating this feature. This was producing the loading problem and also the quotation problem. When we report this to both our Sales Manager and our CTO, they were impressed.
@@lacavernadeyoki1020 Maybe, but working on something closely related helps us improve and excel sooner, and this is a better utilization of time. The reason we don't do this often is because we don't know where we'll end up.
Another good example of the type of "mathematician who decided to shift to something else" is EJ Chichilnisky. He's a neuroscience professor at Stanford who did his undergrad in math and now studies the retina and is looking for a cure for blindness. Neuroscience in particular is a computation heavy field that I think could use more people with backgrounds in math.
As a mathematician who did a PhD in neuroscience, my opinion is that mathematical prowess is likely not the limiting factor of progress in neuroscience. A large fraction of neuroscience professors are ex-physicists, with quite a strong experience in fields like electronics, differential equations, and chaos theory - there is no shortage of such expertise in the field. I have spent a lot of time studying existing theories of the brain, their computer simulations and validation on real-world data. The biggest problem in my opinion is imperfection of experimental techniques. It is very hard to propose any coherent model in the absence of exhaustive understanding of the basic building blocks. Our current understanding of the function of different cells in the brain (neurons, astrocytes, glia) is a vast oversimplification, a well-known fact that is an area of active research.
In summary, I have to conclude that many mathematicians are either too late or too early to the party when it comes to neuroscience. The basic steps have already been done. The hard steps cannot be done yet, at least not before before experimentalists do a few more major steps forward (they are progressing very fast btw). What neuroscience does need is data scientists - people who take burden of statistics and data organization from experimentalists, leaving them with enough time to focus on the experiments. More precisely, it needs better money allocation to increase the number of people per project, which would allow separation of labour, as opposed to cramming all tasks onto one or two researchers. Ultimately, this field would become similar to computer science, with standards for data storage, generalizability over experiments and theories, joint projects over multitude of groups. While there is a lot of progress made, the field still frequently feels like a bunch of scattered labs, where everybody has slightly different experimental designs, different ways to store and process data (frequently re-implemeted from scratch), different questions in mind.
@@ArgumentumAdHominem Maybe what neuroscience needs is the ability to synthetically grow a brain that it can study. This brain, if capable of consciousness, would live a sad existence indeed, not too different from a Boltzmann brain.
@@cryora Indeed, such progress would be associated with great ethical concerns. Another challenge is that of testing. We do not understand what it means to be a functioning brain, so how can we be sure we made one in a petri dish. Yes, we can make it propagate neuronal signals. Yes, we can make it add numbers like a synthetic neuronal network would. We could even make it work periodically by doing computations in a certain phase of a theta-rhythm. So what. Would that be a faithful representation of a real brain? Maybe. Maybe a bunch of neurons would self-organize to actually make a functioning brain according to some magic chaos law. But more likely it will do exactly what we have engineered it to do, and we will learn nothing.
I think that reverse-engineering complex systems is one of the most interesting and most challenging questions of our age. What if reductionism no longer works, because the smallest functional element is already highly non-trivial? What then? I honestly don't know. Maybe mathematicians can indeed propose a way forward. But they don't need neuroscience for that. A demonstration of a statistical approach on surrogate data would surely suffice.
For those interested, I highly recommend an eye-opening and powerful publication by Jonas and Kording, titled "Could a Neuroscientist Understand a Microprocessor?". It is a fun read, give it a go.
Or Stanilas Dehaene, who did pretty much the same thing outside the Anglosphere
All the soft and wet fields could use people who can do math.
While working in a hotel bar one of our infrequent customers was a man who studied maths and computer science at the most prestigious school in Ireland and then went on to study law.
He told me that they gave him very different thought processes to other lawyers and a very unique boolean way of looking at legal cases.
I have a math background, but I landed in manufacturing engineering. I never thought I could (or would enjoy) working on problems as concrete as I do. But a skill I learned that helped me immensely was to take applied concrete problems, abstract them, and use abstract problem solving skills on it, then reapplying the problem
You give me hope as someone who is aimlessly doing cs
Grant not feeling responsible for someone going into math is being way too humble, that guy made a lot of ppl (me included) see math in a new light, his videos are pure art.
As a physics PhD who tried to work out where he could have most impact in the world and ended up becoming a biologist who studies aging-amen to this!
The analytical mindset and problem-solving skills can definitely be deployed in other fields, including into which field to deploy your math skills. :)
Excellent!!! Do you plan on focusing on the biology of aging for the rest of your career? Or do you think you might branch out into other areas, too?
I'm always thinking about new possibilities for math, especially for biology. Medicine, health, fitness, athletics, nutrition, agriculture, economics, ecology, energy, climatology, genetics, development, evolution, social behavior... The possibilities seem endless!
@@surrealistidealist As you’ll see from my channel, very much sticking with aging-specifically, I ended up deciding to write a book and talk about it rather than research it myself because I think raising awareness and using that awareness to boost funding and get more scientists and doctors to work on it is one of the most important challenges of our time!
@@surrealistidealist Huh, UA-cam deleted my reply, I think because I mentioned m y c h a n n e l…where you can find some vidz showing that I decided to carry on with it for the rest of my career, because I think it’s our most important challenge!
Another area I don't ever really hear is using math to ensure world peace and prevent wars like the ones happening in Ukraine and Israel. Math can potentially be used to model populations and their proclivity towards war and means to avoid war through various forms of influence. Perhaps such work is already being done and I am not aware of it. However, the results we see still involve deaths of innocent people and soldiers who were forced by their totalitarian government into their situation. Even though through social and economic pressure, we can tip a war in favor of the side we want to win, the other side still suffers, and it is still not a better solution than peace.
In my opinion, war is a problem humanity has to solve before it can progress in space exploration. Otherwise, space technologies will be used for war between nations on Earth.
Well done and good luck with your new career!
His voice is so calm.
Ideally, "applied mathematicians" should be *anywhere and everywhere* because there's really no predicting when or how the next big applications are going to emerge. But that may not take PhD-level specialization, and even if it does, then specialization itself will probably be inadequate.
The key therefore is to just elevate the mathematical sophistication of as many different people as possible and to combine specialized depth with generalized breadth. This would also make it easier for people with different educational and professional backgrounds to understand each other as they learn from each other. In effect, we may not see many more *applied mathematicians* (defined as PhD-level specialists), but we can instead still see more *applied mathematics.*
Most people who get seriously into advanced math have certain ways of seeing and interacting with the world. You have to be very analytical and precise. That is not a good fit for all professions and activities. Some things would probably be hindered by the mindset of a typical mathematician. As an example, I once know a manager who was extremely good at advanced math. One of the things he oversaw was a quality assurance testing team. He decided to make them more efficient by applying math to their process. Two things happened as a result: 1) team moral went into the toilet and 2) it took 2 to 10 times longer to find and document bugs. From the manager's standpoint it was the most efficient way to do things, and had he personally been doing QA maybe that would have been true for him. But for everyone else, it was a devastatingly poor plan that made everything worse. Don't get me wrong, math is extremely useful and absolutely necessary for many things. But typically those are things that are done very rarely and not applicable to everyday activities. Math and physics were absolutely required to understand and design a CPU for instance. But once its been manufactured, no one needs to know any math to use the CPU. Some perspective to consider.
@@Me__Myself__and__I I see what you mean, regarding most people who get into advanced math typically thinking a certain way that usually isn't widely applicable in everyday settings. I'd say that if we broaden the range of people who get into advanced math, then we might change what's typical at every level. For example, people with more creativity and social skills or people with different everyday experiences might be more commonly found among those who reach advanced levels in math. And they might find less typical applications. Advanced mathematics may be suffering if it's only attracting and holding onto a narrow range of the population who mainly have just a few of the same strengths and weaknesses.
@@surrealistidealistThe sad fact is that there aren't that many people who are ideally suited to the extreme logic, problem solving and rather rigid perspective needed to do advanced math well. The same logic and problem solving ability is required to be a good software developer (though less rigidity and more creativity). But there is a limited pool of humans who are good at such things. More education will not magically make any human excel at these things (sadly). So if more humans who were capable of such things devoted more time to math, what other things would be sacrificed in exchange? The world is full of trade-offs, nothing comes for free.
@Me__Myself__and__I I wouldn't think of pure maths as rigid. In fact, I think it's the opposite the ability to be creative and veiw problems from a different perspective is I think the core skill in analysis and this is a widely applicable skill.
Ok, cool. But do you know, what challenge it is, to not only elevate specialized depth & generalized depth? Often people tend more towards one or the other. People that can do both, are EXTREMELY rare. Most of the guys (not all), who are very good mathematically in one or the other (or both) are people, that you can hardly work with for several reasons: 1. They keep everything to themselves and do not distribute their knowledge and problem-solving routines (a bit like magicians not giving away how their tricks work but different context). 2. They are so invested in the topic that they tend to forget humans. 3. Many of which are arrogant and/or not empathetic because either that's how they are or they don't want to be. 4. People, who are not 1., 2. and 3. who at the same are mathematically extremely gifted are rare and would more often than not have extreme internal problems with "society" due to constant "human expectations" vs. knowing what objectively is "right" or can be done "better" but the context of human interaction does not allow them to utter themselves and on illogical confrontation, they would more often than not retreat although they know that their position on something is probably more suitable for a real world problem. That's why those guys also do not exist in Leadership most of the times. Leaders need to be people who do not get disgusted by illogical arguments and confrontation and deal back the cards and are ok with not producing the most "correct" result/way of solving a real world problem. In our world, solving real world problems needs to be fast. Needless to say: The correct "mathematical/logical" approach is often not exactly the fastest. But people don't care most of the times as long as they don't see the need for more careful approaches. I myself am not a mathematician or very good at maths, but I see this not only from the direction of maths but logic and especially how humans, in theory, would be most efficient when interacting with each other. Seeing on a daily basis, that there is individual segregation, groupies and irrational emotions like jealousy, thirst for revenge etc and actions of violence, I could go out there and tell people how stupid that is and that it sets back humanity in development AND NOONE would CARE. That's sadly just how it is. Similarly, mathematicians will most of the times have analogous problems in smaller environments, e.g. companies. Their solutions might be smarter but if there is no immediate need for it, people will always prefer easier solutions to more complex ones. And with easier I do not mean literally "easier" but easier to think of and execute. More often than not, this easy solution turns out to not be a solution at all but a shifting a problem. Sorry, much text but that's what I feel about this topic. In short. Mathematicians just cannot belong everywhere. They are most fitting in scientific environments, any other is a big challenge for them on a human level and only a select few exist, who can take on this challenge and stay human. That's the reality and I don't think, much is going to change unless we restructure our society and workplaces in a radical way (through urgency potentially).
Real life software engineering has very little do to with math, and even funnier, very little to do with academic style CS
Modern SE is mostly switching between JS frameworks, stackoverflowing and occasionally solving troubles with Git.
Serious answer is try to do almost literally anything else. There are a lot of problems in fields that could benefit from applied mathematical talent but the biggest barrier is that they’re often not the best paying. You could work in a museum, for a local council, for a charity and you will almost certainly be able to find problems that a mathematical mindset would be well positioned to address. It won’t make you famous, or maybe it will but you’ll be able to do a lot of good if you can stay close to where the problems are and where there are not many other people like yourself.
the social sciences such as organisational psychology, have an outsized impact on people's lives via public policy, human resources and management at work, and in other settings such as education. I'd like to see people with math training and more importantly that particular approach to things, in these fields because there is an awful lot of very poor thinking that gets through and into the mainstream and has negative effects on a lot of people
Developing one's ability to think analytically is helpful regardless of where you end up applying it.
yes, but it is not sufficient by itself to make a career.
@@zenmaster1958 sufficient by itself, no. Critical as a foundation for being nimble as to what careers you can step into, absolutely!
What a wonderful and interesting conversation! More please!
I work in aerospace and higher level math people are highly respected. They solve the hardest problems. As a software guy, it’s important to have a math person to go to when the problems get difficult. On the other hand, there might be many software devs to one math expert.
As a maths teacher in a government town I am regularly frustrated by the lack of mathematicians in bureaucracy. Departments that make and administer laws employ lawyers which makes sense but then when faced with complex mathematical questions about those laws they “only” have lawyers to solve those problems. Okay I exaggerate but there isn’t enough mathematicians.
Its upon mathematician to go and populate the administrative posts. There's no other way.
I have found that explaining a business problem to a mathematician can be very difficult. Often, the problem itself is not completely defined, and you need help to formulate it. For some reason, mathematicians abhor messy problems. After trying to get mathematical "help" once or twice, I just gave up and solved it myself after spinning up on the math.
This is a problem with college education in general, not just math. Almost every standardized degree has an "overallocation of talent" that makes it hard to apply to something specific, excepting the *very* applied stuff like medical/law/nursing schools. I don't think the right solution is ever going to involve framing it as a question of "where do mathematicians go", but rather as a question of "part of a college education should be continuously developing and revising a landing plan, how do we get advisors and mentors who are actually capable of helping students do that".
I really like your answer.
Yep, I can tell you that as an engineer, I learned far more technical and math skills in school than I will ever use in my career. And I got only 10% math.
@@Ikbeneengeit I'm saying less that colleges teach students too much, and more that colleges prepare students too little.
Well said
One would be to reduce tuition costs. There’s a reason for this influx and it’s because a lot of people look at CS as a method to secure a high pay and relatively stable employment since the first thing out of college is to pay off loans.
Thank you Conan for your insight.
That's not "playing God", that's "playing USSR". That's exactly how the Soviet system worked.
Btw, an applied mathematician here, had to go into ML to survive.
Man, it's getting harder and harder to find a video that doesn't talk about Georgism!
And I'm here for it
As a Masters student in Biotech i see that the relevance of solving ML and efficiency problems is really huge for protein structures, simulations of all kinds that also transfer to anything from catalysts to materials just by having more accurate models to be able to reduce the incomprehenseble search spaces for chemistry, biology and materials science issues.
To make this very apparent:
im currently working on screening a 14 amino acid peptide, in principle this means a search space of 14^24 ( or more) individual peptides. To put this into perspective this means to be able to do experiemnts i would need an order of magnitude round 10^18 kg of these to screen them all .... for comparison the mass of oceans on earth is round 10^18 kg .... !!!
making sure this complexity can be reduced will allow us to truly do amazing things !
ps ( calculations very hand over foot so i might be of by a bit - but not a relevant amount for the example)
imo Quantum Computing makes more sense long-term since the simulations are non-trivial in classical computing. But yeah, I get where you're coming from the manual vs automated labor.
I got Math and CS degrees in college, but decided to take a chance on an atmospheric science MS. Never realized how much I prefer studying something physically tangible, and in my experience CS skills are still super valuable in Earth sciences.
Atmospheric science is such an interesting topic. I actually started studying civil engineering because I thought the idea of understanding the forces of nature was really cool, but I was quite dissapointed when we didn't go into much depth at all. If my uni offered atmospheric physics I would've studied it most likely.
I wasn't sure about a PhD in theoretical physics, so I did a year in research. I found I preferred writing code and the problems associated with that compared with running it and interpreting results. Everything is so much more tangible. Now I'm a SWE, but farming looks tempting 😉
I did a math degree and am now a machine learning engineer. I strongly considered doing a phd in physics after I graduated but am very happy I chose industry. I think there is a lot of elitism among mathematicians and physicist about doing work that is completely devoid of societal utility. They actually take pride in being useless. I bought into this myself. However, what I have realized now is that many of the useful and important problems out there are actually as fun as pure math or theoretical physics. I think mathematicians and physicists should step out of this academic bubble of proud uselessness and actually try to solve some problems in the real world. You may actually find out you enjoy that.
As a bonus, industry also pays way more.
Please give talks to universities.
Sounds like you had a bad experience, but thinking academics don't do useful research is an insane take
@@HighlyShifty I had a great experience and wouldn’t trade it for anything. I did not mean to imply that I don’t think academics do useful work. They certainly do. I am talking about the cohort of researchers who self-proclaim that their work is useless and view less abstract problems as being beneath them.
I think pure mathematics with no obvious usefulness is awesome. I just think we should also step into the real world and get some exposure into those problems as well.
That's likely true of most academics. In software development typically the more time someone has spent in school for computer science, the worse a software developer they are on a daily basis. The vast majority of the time two intelligent people, one motivated and self taught and the other coming out of the CS department of a university - the self taught person will almost always be significantly better. I don't know about other fields, but college actually teaches many very bad or, at best, useless habits and perspectives when it comes to coding. You end up spending at least as much time (if not more) teaching and correcting the junior developer with a CS degree than you do a self taught junior developer. Plus, the college grad is likely to have higher expectations of pay and see themselves as above others. Software dev is one of those fields that a college degree is not necessary (and certainly not worth the cost), what really matters is knowledge and skill and that can be acquired in other ways.
@@HighlyShiftyThey didn't say "research". Pure, detached non-real world research is what academics excel at. Practical application of anything into the real world (aka outside of academia) is where they are typically terrible. Most academics have spent almost all of their time in school, its all they know. Commercial for-profit ventures require achieving efficient results, often with less than ideal resources. Academics tend to do poorly under those circumstances. I suspect the point @OM-el6oy was trying to make is that it would be an improvment if academics better understood how things work outside of academia.
Honestly, just do what excites you and get good at it. It's the best path to fulfillment. The ideal scenario is bridging a gap b/w different fields you're passionate about.
It's funny because I was terrible at math in school. Later in life I became interested in programming and I was able to get into the industry without a college education. Now improving my math skills are something I do in my spare time because I find the logic of it beautiful and fascinating.
As for mathematics in programming, it depends on the problem space being programmed. I write accounting software now where it's very relevant, but most software projects can be completed without much advanced math. While the big ~5 tech companies have a habit of accumulating more programmers than they know what to do with, the majority of companies are operating on a fraction of the programmers they actually need. I can only speak for my industry though, I'm sure there's other industries who have an even more pressing need of math proficient talent.
My argument is that you were terrible at math at school because that was not real math... it is just some weird bizarre monster that we make pass as math to kids... Programming may have more real math in it though.
Exactly this, I'm much younger but programming made me much more interested in math, and that's why I think it's really beneficial for maybe high schoolers or even middle schoolers to learn programming and math adjacently. The skills you learn from programming really tickle that problem-solving part of the brain and increase your tendency to love math
I did a BSci/BMath with an applied math major and I did a course in my final year I did a course in medical mathematics which was difficult but really interesting. I then switched to medicine and now work as a doctor that has an interest in working mathematics into my job. Jobs for mathematicians are pretty limited in my country, and I definitely wasn't as talented at it as some of my colleagues so I'm really glad that I switched.
I love applied math. If you love applied math joy can be found in almost any topic by seeking out the math. Then the math gives fundamental insight into the rest of the area and you appreciate the field as a whole. It is a nice entry point to many fields. For example getting into EE through figuring out maxwells then circuits then discovering all the neat things integral to daily life which I never paid attention to before
maybe the forcing function should try to expose brilliant mathematicians to industry and to state agencies, not only academics from other departments
elaborate
@3blue1brown suggested NSF grants might oblige mathematicians to collaborate with academics from non-math departments. I wonder if NSF etc might require mathematicians to intern briefly with firms in some different industries, or with public agencies responsible for collecting taxes or purifying water or planning road repairs, for example, to see whether they can help each other @@aaaaaaa4750
@@aaaaaaa4750 I'll add onto what I think they mean.
Most academic issues in other departments are perhaps too subjective for applied maths to help with (as Grant said). Maybe math can help within more objective little things like optimizing businesses, optimizing cash-flow for governments, seeing how the data intersects with spatial information, socio-economic information, etc.
To use an example maybe, the intersection of math and music created harmonic analysis, which in turn was helpful to solve problems in number theory. Maybe there's almost a mutually beneficial socio-mathematical lens to look at the world through that we haven't developed yet.
As an undergrad I had a lot of disparate interests (physics, cognitive science, philosophy) and majored in math simply because it touched all of them. I've worked as a data scientist and software engineer since then because they're the kinds of jobs you can get with a math background but haven't found either to be very fulfilling. I think the "why" behind whatever you do is paramount
In my opinion, mathematics is a very abstract field and is very universal in nature (as in, anyone can understand maths deeply, but for other subjects you need some level of intuition or hands on work). That is why I think math skills are more generalizable.
Physics undergrad in his final year here. I think the 2 main things that put me off from pursuing an academic field is that (a) I just didn't do well enough attainment wise in my first couple of years to even consider it and (b) I realised that if I did truly love physics, it's not something that I would pursue anyways as being surrounded by it my entire life might make me fall out of love with it. There's also the financial strains to factor in
I think actually we need waaaaaaay more cross pollination between all fields, not just maths. Maths does feel a bit isolated at times because of how many people seem like they would rather die than learn calc tho. While many of the concepts you learn in maths would be useful in other fields, it's also extremely difficult to tell exactly where those concepts would be applied in other fields. Meanwhile, it seems to be extremely common that a problem has already been solved in one field but this development has not made its way over to other fields where it would be useful. Mathematicians could help in this and they'd also be very good at creating new solutions but I wouldn't discount the usefulness of cross-pollination between other fields
But on the topic of maths specifically, when I was studying maths at uni, I also took bio as an elective and while there were some situations where maths was used, I felt it was underutilised and the areas where it were used were vastly more advanced. Maybe that's my bias speaking lol but someday I would like to speak to a biologist about some areas where I think maths concepts could be more useful in biology eg maybe you could define ring species topologically? Not sure how useful that would be since I have no idea how complex ring species can get but it would be interesting to discuss
During my MSc in electrical engineering I specialised control theory, a field "discovered" by mathematicians after WWII. They came up with really cool control laws but unfortunately most of them rarely get used in practice. To me, this a field where we don't really need more mathematicians (appart for publishing papers in Automatica).
The new hot machine learning model is based on control theory. It's called HIPPO / state space models.
I appreciate Grant’s humility in saying that he’s not the right person to give an answer to the question, but also recognizing that this allocation game is essentially “playing God”. There are a lot of people out there with suboptimal (or just plain bad) ideas who have no qualms with exercising power over others that isn’t rightfully theirs
I double majored in biochemistry and applied mathemtics. Did research in biomathematics, published then went and worked jn the energy sector as a material scientist, working more in experimentation over theoretical work.
Ive found my applied math degree has helped me see opportunities that people with material science degrees usually cannot see, such as using calc or linear algebra to solve problems while saving money on equipment or i can code more mindless tasks to save time and quantify results that are usually seen as qualitative.
Also, in my free time i enjoy delevopijg models to predict football scores lol
Effectively “fell into” software engineering after graduating in math/cs. Coming closer and closer to switching to something completely different. Pure math was great for me in college. I hate working in a corporation with the skills that I’ve learned (fairly easily). Now that I’m older, I really don’t see the appeal of pure math as much anymore, and I do want to use my skills towards something useful in society - not being a closed off academic, or just making a corporation profit. It’s difficult however to make these choices when society dangles incentives in front of you so that you’re more likely to choose one path vs another.
I'm in a very similar situation. Was very "pure" and academic. Now I need to make money to help my family...
Sounds like you would be interested in Scientific Computing (a.k.a. Computational Science, NOT Computer Science). The IWR in Heidelberg, Germany is all about using these skills (math + cs applied to science) towards something useful in society. They have a good master's program, much cheaper than one might think. Have a look... I'd be happy to answer any questions you might have :)
How do you get into “engineering” without going back for another degree?
@@ianmacpherson6093by doing projects on your own, collaboration with the engineers, getting internships etc
I'm a BS math grad. My degree has no value in the business world. I didn't gain the skillset for much in software and didn't get offers for much beyond 50k/yr analyst jobs. I'm in education now (high school teaching). My earnings are kinda capped below my potential, but my job satisfaction is way higher than it was as an analyst.
I guess the economists answer to that question would be that we don't know generally, but we do already have an allocation system that tries to solve these kind of problems: the market. The players in the market (and lets include the government here) will evaluate whatever skill a mathematician has and how it helps solving their problems and will make them a job offer that pays accordingly.
I know scientists and mathematicians usually don't think that way and are sometimes surprised or even disappointed when they end up in a different domain than what they expected. Sometimes its even a domain that seems to have no connection to math at all, but that does not necessarily mean that their skills are used inefficiently.
Beautiful phrase - "overallocation to talent"
there are different aspects of the problem that need to be considered beyond "where can mathematicians have the most impact?" Infact, I think this should be the near end of the list of functionals needed to describe the allocation of rigorous abstract logical talent. We need to consider what is 1. Just (is it just to push mathematicians to become teachers knowing the crushingly small salary they make? effectively pushing the ones who tried to work hard into poverty?) 2. beneficial (would encouraging a greater degree of math talent into the field actually make a difference?) 3. has the absorption capacity (how many mathematicians do we need to advance AI? do we get diminishing returns on our investment dollars beyond a certain human capital allocation limit), 4. is transferrable (mathematicians do have everything they need to become, say, great physicists, engineers, and in some cases, managers. But the extra education and work requirements of switching fields incur an enormous life and earnings cost which make some directions infeasible). There are others of course, but I submit these are more important than considering where we should allocate mathematicians to make the biggest positive change.
this is a great question, it happens to be what i've been pondering myself - "what impact do i want to have on the world?"
I'm really into the idea of Accelerationism which basically would be to progress as fast as possible. So if you are interested in math, you should give a thought to what technology in your opinion is good to advance and go into that field. Worst case scenario your hard work will make others work harder to compete and the field will develop faster, best case scenario - you brought valuable addition to this process and the field developed even faster.
I was a phd candidate in physical chemistry. My goal since high school. ( yes I was one of those). Before I began dissertation work and began looking around I realized I didn’t want to be a professor. With that epiphany I looked at my study differently and realized I loved the study but not the job future. After discussing with my soon to be wife I quit and went to law school instead. Looking back it was the best decision I ever made.
Same here. My goal in life up to college was to design rockets. So I got a Masters in Mechanical Engineering with an emphasis on thermal fluids, but when I graduated, Rockwell (then parent of Rocketdyne) only hired 8 engineers instead of their usual 200 (this was around 1990). So I went to law school and have had a generally satisfying, if somewhat stressful career as a pant lawyer.
I did a degree in theoretical physics, worked for a data science company for a couple of years, and have just started a PhD in mathematical biology. Being able to apply my skills in a useful way was a real driving factor for this choice
This voice... 😌😌
I’m a cs grad and it’s hard to find jobs right now. Maybe it’s because it’s the holidays and companies don’t want to hire but I wonder if the field is over saturated.
The thumbnail seems a bit like clickbait to me. He never says there are "too many software engineers", but that that's one of the careers people pursue once graduated from Maths. There's a subtle, yet substantial, difference between the two.
I got a CS degree, while i dont regret it Im realising now that Id rather be doing something else.
So many people picked it as a degree not because theu really cared about it but because its was a profitable degree to have.
I think now as time goes on the competition is becoming so crazy and you really need to love it to be able to keep up with all of the technologies and languages.
The wages are starting to normalise as more and more people get into the field
Learn how to program, very few people know how to
Present! From math bachelor to high performance computing engineering master
Standing by to be “allocated”
I am a math major that went into data science for finance. It wasn't at all that I desired to be more impactful; it is simple supply-demand economics. For every job that requires theoretical math skills there are thousands that require software development and practical domain skills. Wall Street is full of mathematicians and physicists. I do agree that mathematicians have generalizable problem solving skills and don't get discouraged by going down one problem solving technique path, failing, and starting over with a different method.
Best comment ever
I was surprise by the comment that CS are hogging the mathematicians. Perhaps Silicon Valley makes it seem so, but most of my former fellow math majors are currently in finance, as were their seniors. Not a small portion are in software but the vast majority are in quant, and we all know why of course.
The answer is obvious - Mathematician-Philosopher-Kings.
Nice
I view it as a spectrum where are one end there's the pure mathematician with clean numbers and on the other the engineer that knows how to build and doesn't need to do formal proofs as long as it works. I find economics, biostatistics and bioinformatics to be somewhere between those two ends. There's many math majors entering those graduate programs that bring with them rigor, but develop skills that demand that rigor. Intro analysis and advanced linear algebra are useful, but baby Rudin and graduate abstract algebra are likely overkill
Do Alan Turing, Charles Babbage, Tim Berners Lee fall in the category of mathematics who turned to practical applications of math? Even J M Keynes the economist
as a computer scientist I'm certain I'd be better than average at anything that requires problem solving skills from week 2.
Ive got 7 of those books on my own bookshelf
This probably counts as data science but the competitiveness of supermarkets here means that they hoover up maths grads to run their ruthlessly efficient logistical networks
This is a great question but it fails to acknowledge the other half of the problem: where is it that applied mathematicians *will be accepted* ?
An awful lot of people and purposes could surely use an analytical approach but have no idea or interest in that assistance. One of the major reasons mathematicians don't apply themselves to other fields is they don't want or know how to sell themselves and their services to other fields where the reception is indifferent or even chilly.
Been on the job hunt since graduation (May 2023) with a master's in applied math. Over 250 applications sent, and I got a grand total of 3 whopping interviews.
Thinking of going to an entirely different field or give teaching a stab.
What kind of job are you looking for
Unpopular opinion: work for the government. Build a better society and don't be a cowardly libertarian about it. Automate taxes, build a universal healthcare system that works efficiently and well, tax better, eliminate poverty. Farming and manufacturing are very dependent on policy, help make those professions thrive.
The quest for purity is a killer. The real world is messy and there are not enough slots where pure maths people can slot in productively.
CS is a possible path, but while there is a shortage of experienced people there is paradoxically a surplus of inexperienced people.
Software engineering requires a 5 to 10 year apprenticeship during which most people are not too productive.
One thing I've been preaching about for over a decade is how bad accountants are at algebra and data handling (involved in determining many values reported in accountancy), so while high level maths is not necessary, in accountancy those skills need a dramatic improvement from the woeful standards among accountants as well as those appraising and assessing work in financial reporting.
As someone who worked 15 years as a computer programmer, cough, I mean software engineer, I found many more converted music majors than math majors. I would also add that in business application programming, I never encountered problems that required math beyond basic algebra.
Important part of coding is interpretability and usually artists have sense of the third persons gaze. One could say that coding is about the "essence" and art is all about aesthetic.
Try Machine Learning
As someone really into math, I felt impotent because of not being able to "execute" or in some way make happen a mathematical process that I know how to do and that I want to do
Like if I know how to specify vertices of a cube in the space, how can I see the cube?
If I know how to create and transform things, how do I manage to make those thoughts a reality?
I felt like math is missing something to make it happen, the only solution I found for this is computer programming, but I feel like it isn't math but telling things to the computer that are math related, I really feel there is a tool that mathematicians are missing that would drastically improve quality of life forever
EDIT: I think all of this is related with mathematicians having to go out into other fields to apply their math, with math not being able to be applied by itself
Math is actually constantly being applied to itself, mainly in the form of new proof technique and generalization/extension of known concepts. its just that it becomes really abstract.
its kind of similar to programming languages. you can write a proof of something in many different ways, groups, sets, etc.
It does actually get to a point where you stop learning methods to do something and start creating something new.
There are a lot of problems that are unsolved, you could try proving them if you want. a solution for the Einstein tiling problem was found by a non-mathematician.
Currently studying AI engineering; I fell in love with pure maths, the axiomatic method, as soon as I finish the engineering I'll pursuit my career in mathematics ❤
falling in love is the best reason to pursue math (or anything really)
Bro I thought I was the only one.
Im in CS right now, but honestly I really dont like CS compared to the math you use in AI stuff.
@@honkhonk8009 Well, It's kind of different, you know, In AI most of the maths are applied maths, e.g. Calculus, linear algebra, probability and statistics. If I had the chance to choose again I'd prefer to start first with computer science because there are some topics of computer science that are simplified on AI or that aren't just covered at all in the field (for terms of simplicity), CS is the perfect grounding for any other of its appendices (I mean, the fields that derive from CS). From the CS base you got there, all the AI stuff will mostly result trivial, you just gotta do some kind of mereological job to find the equivalences, it will not be complicated for you, I promise. Do the best to learn DSA, and the most important thing to do, I'd say, is to develop a good mathematical thinking (I really think CS is better at doing that compared to engineering)
I’m 18 and just finished A levels where I got an A* in further maths but next year I will be going into a psychology degree because I didn’t think I was smart enough to go into maths academia and I saw so much more potential for growth in psychology research than in maths among other reasons. It just so happens that psychology is one of those field that wants more maths minded individuals for things like modelling, neuroscience and statistical analysis. I’ve definitely felt pressure from my peers and teachers to go the traditional route but I think that should change and students should be encouraged to look at other options.
The reason that people encourage the traditional route is that it's generally easier to then go into something where you can start a career. Psychology is probably not a very "easy" route.
I suggest you strongly think about what you want in your future, you may not know. If you take the traditional route, you're probably pretty much guaranteed a solid career, but you may not love it.
It's not about being smart enough, you need to love maths enough to go into academia. If you've gotten an A* in fm you're likely smart enough.
From what you've written it seems like you're more interested in the maths behind neurosciences which there is a lot of! But a psychology degree just won't help you with this. In my opinion, pursue a maths degree and then go for a mathematical neuroscience masters.
There isn’t much useful/scientific stuff going on in psychology outside of psychometry - and that’s mostly about intelligence (inherited, men are smarter, different races have different averages, the environment doesn’t matter much). It’s perfectly possible to do good psychometric research outside of academia (and you are pretty much forced to do it outside of the academic mainstream).
Maybe get a different (better) degree and do psychometric research in your spare time as a “gentleman scientist”?
Oh, and read Gleitman’s book on psychology (NOT any of the abbreviated versions!). That will teach you more than most people with a psychology degree know - and leave you unburdened of most of the field’s “knowledge” ;)
FINALLY someone who talks about how we distribute our most educated people.
As someone in academia, this is a big and difficult question that has a, possibly even a bigger influence on the careers of the graduates than their personal performance..
Where is the discussion of software engineers?
I think it’s less about how society should allocate mathematicians because it’s ultimately the economy that does it. No offense to anyone but the degree is just a piece of paper to people outside academia. Far less people would be choosing STEM fields if the monetary incentives weren’t there. Software engineers with CS degrees can still easily make over 100k within a few years of experience and in some cases starting, and that’s not expected to change soon. It’s all supply and demand, risk and reward. If I woke up tomorrow and some publishing company said they were going to start paying editors $900k like Netflix is starting to pay senior data scientists, I’d be there with my application tomorrow. That’s not the case though, and the jobs that are paying the big bucks are typically looking for ppl with degrees in applied math, data science, stats, CS, software engineering, engineering, and so those are going to be the fields people want to go to because they don’t want $60k in student loans for an English degree and a job that is paying $40k to pay it off. That’s the bottom line.
I had no idea who he was until I heard his voice... then I saw 3blue1brown
I kind of feel the opposite. I feel like everyone around me at school who are all extremely talented mathematicians wish to go into far more practical fields like tech or engineering whether that is for money or for usefulness. While I however wish to go into academia and while I am encouraged by the people around me there is this constant skepticism of my goals and notions that I will want to do something more ‘real’. Although I agree peoples minds change about what they do I feel that most other peoples career desired are not questioned in the same way that mine is.
Sometimes I get so obsessed with some part of math that I feel perfectly content thinking of a future where I attempt a problem for a month straight, and nothing pains me more than knowing that’s not gonna make me money or keep me alive or really contribute to anything (at least not realistically anyway). I’m probably just going to go into engineering because that’s the next most interesting thing, but god I wish I could just fuck around with pure math for the rest of my days.
My own struggle with and approach to this question led me to declare an ad hoc biology and math interdisciplinary major for my undergraduate! In my petition to do so, I specifically emphasized the skill set that abstract mathematics has purely in the distillation and translation of complex problems into articulable, logical terms. Even though day-to-day I’m not using the specific concepts that I learned in say, abstract algebra, I’m exercising very similar mental muscles.
Yes! This part is underrated. The ability to "formalize" any problem by using precise definitions, explicit assumptions, and clear models is something that a lot of fields/industries could use. Especially statistical thinking and modeling.
I think the answer is obviously data science and data analytics for companies/organizations that do good. That's why it's a shame there's such a little emphasis on practicing general purpose modeling in a BSc in math because that is the missing piece that makes a mathematician powerful in the real world.
Got my BS in math at 21. Screwed around for a while in a tough job market. Got a job in an engineering lab. Saw the potential in that field. Got that degree at 29. Am now a licensed civil engineer making great money. Math was a great foundation for my career and sets me apart from my peers. Math was my 'first love', but we don't often end up with those.
Excellent work. If you don’t mind, How did you manage to get a Bachelor’s degree at 21? Albeit an applied mathematics degree, which I am intimidated by but interested in.
I clicked i swore the thumbnail was a picture of Conan lol
Same
Good lord that is a good question.
We don't social engineer hardly at all, but ya, should probably divvy out this precious resource better.
watching this as a software engineer who's fed up with how much software work I find meaningless and overallocated, to put it mildly - adtech, fintech, etc. I have no answer, yet.
I'm probably an outlier because I graduated with a bachelor's in applied math from Cal Poly Pomona (a state university in California) but I work as a self-taught embedded software engineer (extremely, extremely rare and people in my industry don't like non-traditional career paths). In my opinion, society doesn't know how to properly allocate mathematicians because what I've always heard is "actuary, teacher, or academia" (where more career options open up if you pursue graduate degrees). If you have at least a partial background in programming/CS, then you might be accepted for some software engineering jobs. But, in my opinion, a GOOD chunk of the people I've met will view mathematicians as not a useful/helpful set of skills because in the real world, if you are working a normal industry job, ask the engineers, business people, and scientists if they would hire mathematicians for jobs at least adjacent to theirs. I am willing to bet that they would tell you to go screw off or that they would just blatantly say something like "go apply for other jobs" or "i don't know how you would find a job with your set of skills". This is fundamentally the problem I see with society and I also see it in education:
1. We highly value problem solvers who are good at math as a general skill however when it comes to producing results/work in the industry for these math adjacent fields or fields that utilize a lot of math, they tend to not hire mathematicians that just have math degrees. If you have a math degree bundled with another field that heavily utilizes math, then you're highly valued. Its one of those things that are good to see but are not seen as "enough".
2. When I was in college, the professors hardly talked about career prospects or practical applications of math. These math professors always focused on math by itself and while I find that respectable, we really need to put it into the perspective that professors are being paid to do what they love (assuming they enjoy their job) which is solving math problems. Unless they've worked outside of academia, they may not be familiar with the kinds of fields that actually could utilize mathematicians well. This is my gripe with the system and it could just be my anecdotal experience. When I pressed some of them, they could not come up with answers for my questions.
And I do understand that I attended a low-ranking state school so maybe my opinion doesn't weigh as much as someone who attended a better school with a better math program that actually did prepare their students for either transitioning to academia or good careers. I might just be a bitter man rambling about my gripes...
That part about the academics thinking they’re not well-suited for solving problems outside of pure math is probably a mixture of modesty and a sense of comfort that you’re only working on theoretical problems, as opposed to the real world. They very much posses the intelligence/technical knowhow to help, but aren’t psychologically positioned to do so.
I guess this is one of the motivation for having a minor (that uses Math) besides having a Math major, so that you can develop some idea about where your Mathematical knowledge can be useful.
As to the question of "allocation", there is this quote, "Choose own your path or else someone will make that choice for you". Here that someone is the Market (supply and demand). There is just more demand for Math graduates in computational fields.
My mother says software engineers can go clean toilets or farm now
A brilliant example of why this can't be planned is Lyons, a British firm that ran tea shops (and is best known in the UK for ice cream.)
In the late 40's early 50's they hired a Cambridge maths graduate who built the world's first commercial/business computer (there's a brilliant book about it "A computer name LEO".) Unfortunately they failed to commercialise it as they tried to sell business management consulting alongside the computer and that's not what the market wanted.
Great example... perhaps another more modern one was Long Term Capital Management... a hedge fund that prouded itself of being full of academics... they were under catastrophically due to their over reliance of math models... academics (though, to be honest most people) have a tendency to confuse the map with the territory... things that work nicely in paper don't translate well to real life... (non-academic) engineers understand this much better, so they might be reliable than mathematicians in some fields
They commercialized it very well for a while.
There's not too many software engineers lol, there's too many web devs. That is NOT computer science.
Yep too much talent is wasted on software engineering. Especially st companies like Google where they do what exactly? Make people addicted to the internet and optimize ads.
Those who are interested in mathematics and computer science have the option to pursue a career in graphics programming, which involves a significant amount of mathematical computations. There is a substantial demand for computer graphics simulations across various industries, particularly for training purposes.
Based on the comments I've read, it seems that AI will take over many jobs in the future. However, experts in their fields are unlikely to be replaced by AI, since AI is prone to making mistakes and human oversight is necessary to ensure accuracy. Instead, AI will be used as an additional tool by experts to enhance their work. Lower-level jobs will be the most affected and the company hierarchy may also become flatter as a result of this change.
We need more unicorns 🦄 that marry math + CS.
I'm trying to understand what is meant by 'allocating mathematicians'. If you want them to go somewhere, simply pay enough. A lot of mathematicians and physicists went to work on Wall St. for precisely this reason.
As somebody who studied math, I wonder if I would be more satisfied with my career if I had instead studied either electrical or mechanical engineering.
Electrical engineering, maybe. Mechanical engineering, maybe not.
Source: I'm a mechanical engineer.
@@RealGeorg3 curious.
@@EmissaryOfSmeagol I am at risk of going off on an entire thesis here, I'll try to spare you all that (spoiler alert, I did go off on one). You studied mathematics. Electrical engineering is generally considered to be more difficult than mechanical (speaking as a mechanical, they can have the accolade) so I suspect it would be a better fit for a mathematician. As for the actual career of an engineer. I can't speak for electrical but the unfortunate reality is that a lot of the work has already been done in mechanical. It is an old field of engineering. If you look under the bonnet the world is still mostly running on mechanisms that are well over a hundred years old. We've just been slowly, iteratively chipping away at those processes and tacking on improvements from other fields around them; material science, electrical engineering etc. You would be astonished at how little engineering goes on at the big firms. They figured out their business models decades ago, with just the bare minimum of improvement in the subsequent years to keep ticking over. Everyone these days walks out of university into a corporate career at engineering firms rather than an engineering career at engineering firms. Of my peer group I am an outlier. I took a risk and went from a stagnant but outwardly high tech scientific industry into a dirty old niche within heavy industry, long since consigned to semi-irrelevancy. I'm happy with it. I actually do engineering and use maths. However, by current standards this is not the norm. At all.
I am doing my masters in electrical engineering and think the same thing about math 😂
almost every single engineering field has a use for a proficiency in mathematics and basically every single science field has a use for an understanding of statistics, so i don’t think you need to think of the generalization of problem solving for math skills and mathematicians to be useful in applied disciplines
Software is mathematics put to practical use 😊😊😊
Once you understand economics, these kind of questions become very weird to listen to: supple and demand determine prices (and thus wages), and prices allocates resources. So who de ides what mathematicians are doing? Us! Everyone! You and me by our daily decision of buying that bread or this car.
valid theory
It’s pretty funny because my math major friend complained that if they don’t like to work in academic, finance, programming or physics, they have very few choices. It all depends, I guess.
Derivatives trading or energy trader
There's also cybersecurity, developing, data scientists, and IT.
Because I only have a Master in Applied Maths with a physics degreem I cannot manage to find a job. Even in data science, only software developpers are hired.
every technical major is overrun with similar talent, stem shortage was a lie to supply excess applicants for reasonable wages, hr assumes more is better so they require masters and phds to everything. Schools are more than happy to take your money so they promise the world and teach the same topic the profs have been for 30 years. Now everybody gets a masters from the getgo without any application expecting the world. Bachelors in science used to mean you were capable of performing science, and masters/phds were for academics seeking to develop their thesis to further a topic then become a professor to continue research. More people should start businesses and not immediately sell out to the monopoly in the industry.