47 thoughts on “Mathematics – Biology’s New Microscope

  1. I didn't even do math in highschool and am just finishing my degree in biology. The UK lets you do that ._.
    I understand biology more than most (as I better, having looked at it for years) but I'd understand it a lot more if I knew the math. Math is very important but you don't NEED it to do biology, depending on the sub-discipline you go into.You can understand biology to a to a high level without it but it unlocks a much higher understanding as I can tell from all the bits I don't quite grasp

  2. If you can, learn math and it'll give you a great new perspective on biology and the rest of life AND give you prospects others don't have.
    If you can't do math though, don't let that put you off trying to learn the science to the highest level you can with middle school math or whatever you've mastered.
    Get as much math as you can in your skull but don't feel too bad if it isn't your strongest skill.

  3. Good point. I wish I had a better understanding of mathematics but it doesn't limit my enjoyment of science. However, I do feel that advances in biology over the next century will trigger major advances in mathematics and vice versa.

  4. This was a great video. Very encouraging in certain ways.
    To thoroughly understand biology on a mathematical level, we'll probably have to work hard on our understanding of Thermodynamics outside of equilibrium as well as the mid-range of things.
    We already understand what happens in a single moment with one or two particles. We already understand what happens in the long run with almost infinitely many. But what about 100 or 1000 in medium timespans? Those are hard nuts to crack for now.

  5. With the huge amount of data things like the human genome project are compiling, some mathematical tools to wade thought it are definitely needed. We'll also need more math to answer the deep questions that remain (like 'how does this protein lead to this phenotype') than the ones we've answered.

    We're becoming a more math heavy discipline but biology isn't out of reach for people who can only do basic algebra. Still I plan on teaching myself math over the summer for the reasons you give.

  6. One definition of life is thermodynamics outside equilibrium. Practical work like developing lightbulbs led to theoretical advances like Plank's constant, so the practical work on biology will likely be an impetus for theoretical conclusions about non-equilibrium thermodynamics and other fundamental things, as Bozeman says 🙂

  7. indeed. And we really need this. We're incredibly close to (yet still far away from) a "theory of everything" (so far we only have a bunch of promising hypotheses) but that will not be of much use for describing that part of everything that's called life, if we don't advance in non-equilibrium thermodynamics.
    Thermodynamics is kind of a misnomer anyway. It should really be called Thermostatics. While microscopically, things move, macroscopically they don't, so in that sense it's static.

  8. Biology is a parasitic science that needs physics, its not better. I'm a medico and i am embarassed to say how we borrow so much knowledge from other areas of science without deep understanding of any one of them. QM, NMR, Chemistry, Nanotech, Med imaging physics, etc.

  9. Excellent lecture. Thanks for your hard work, these videos are very useful for preparing my own university lectures.

  10. Outstanding video. Patrick is a very cool nerd. I’m guessing that math is becoming ever more important to social sciences as well – detecting patterns in mental health or child abuse or immigration or crime, ect. Once the pattern is detected perhaps a cause can be detected and then perhaps a solution. Math and science will never be able to describe all of existence but I admire the attempt. Loved tis video, Paul.

  11. So… when was the last time a biologist knew what to compute to find out whether time hangs in the vacuoles of intergalactic space-time and map the multidimensional data from a point perspective…

    Because a second ago was the last time every physicist understood the complexity of the entire universe thank you very much 🙂

  12. Mathematics have some wonderful applications. Somewhat similar to the X-Ray example, the diffusion equation with 'backwards time boundary conditions' (ie a condition is specified at some time t and the solution is desired for time less than t). This equation with this boundary conditions allows you to undo diffusion, and these problems arise naturally in image enhancement. Where you a given a blurred, or 'diffused' image if you will, and you want to know what the image looked originally.

  13. Unfortunately though the said boundary conditions tend to be 'badly behaved' and are called 'ill posed'. This is because the solution doesn't vary continuously (in some topological sense on the normed space of continuous functions) with the boundary conditions. Intuitively this is due to the diffusion equation 'smoothing things out' as time increases (eg temperature spreads out to where temperature is low over time) so doing the reverse of diffusion will obviously make the solution less smooth.

  14. European robins may maintain quantum entanglement in their eyes a full 20 microseconds longer than the best laboratory systems, say physicists investigating how birds may use quantum effects to “see” Earth’s magnetic field.(That was what I actually meant)

    Quantum entanglement is a state where electrons are spatially separated, but able to affect one another. It’s been proposed that birds’ eyes contain entanglement-based compasses.

  15. Just another way of how the internet is awesome. I have to write a paper on gene therapy. I check out the paper you linked and what do I see ? A map of >gene expression<. So much win!

  16. I would not go as far to say biology is better more complex then physics, take quantum mechanics for example, it has an effect on all life at the microscopic level and effect how cells function obeying the laws of physics also observation of an experiment can change its result, it is the most counter intuitive theory is science. Very complex mathematics is used to explain, also which one is better is subjective but biology cannot function without physics.

  17. Both of these minds in one place is a testament to the positive effects of technology! As a nursing student, I deal with the task of blending many different disciplines into a global perspective and I often feel the curriculum would benefit from the mixture of art and science. In fact, reading Zen and the Art of Motorcycle Maintenance exposed me to Poincare and his fascinating mathematical genius. This then prompted me to read a book called Poincare's Prize. Am I a living fractal?

  18. So if I wanted to get into a Mathematical Bio Ph.D program how much math should I take? Obviously it'd be all the calcs, Diff Eq, Linear Algebra, and at least 1 Stat class. Is that enough or is there something I'm missing? I know econ majors take topology… Would that be relevant?

  19. Why does one discipline of science have to "better" than another? Physics to Chemistry to Biology and the Math that ties them together.

  20. ur right.. if we can master quantum mechanics we will automatically have many answers to biology and chemistry

  21. This video has helped me to decide what i will take for sixform 😀 Biology, Physics, Psychology and of course maths 😉 Thank you

  22. I'm currently doing a Biology Degree, but find myself frustrated at the lack of mathematics, it's more about remembering a load of facts rather than learning fundamental concepts. Oh yes, and making posters in Biochemistry, what the hell?

  23. Biology is not in anyway like physics nor is it even better. The one problem that will ALWAYS remain with mathematical biology is that, unlike the laws of physics, the fundamental laws of biology (natural selection, homeostasis, etc) are not translatable into mathematical equations. There's no one single equation for natural selection, unlike in the case of three of Newton's laws of motion. Because of this, the mathematics in biology is too context-dependent. There are just simply no UNIFYING mathematical principles that govern biological systems as there are with physical systems. It's because of this that biologists themselves aren't required learn too much mathematics, unlike the physicists. Mathematical biology isn't even a branch of biology to begin with. It's a branch of applied mathematics.

  24. I am uploading a set of short lectures on the mathematical theory of evolution. Have a look at the playlist Mathematical Biology on my channel 🙂

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