lipshits-continuous

[lipshits-continuous]

Right well it seems stupid to go on hiatus just after I got my blog restored but nonetheless I'm taking a break

[lipshits-continuous]

So your argument is that it's good notation for some abstract reasons (type theoretic reasons?). The fact of the matter is, esc was consistently a barrier for me to actually understanding mathematical physics (and still is) and I'm sure I'm not the only one who has the same issue. Good notation should be user friendly and shouldn't rely on having formal knowledge of a completely unrelated field, especially when many physicists aren't even really exposed to formal mathematics (which is a whole other issue). Sure it's a gripe I have that doesn't affect my career because I hardly want anything to do with physics anymore but I can imagine it's turned many people away. You say you're a theoretical physicist in your bio so I imagine you've been working with the notation for a while. My main argument is that it's not friendly for people who aren't surrounded by it constantly

8! Least favorite notation you’ve ever seen

Einstein Summation Convention. I maintain that if you need to add a phrase to the effect of ''where we're using ESC", it is not good notation.

Thanks for the ask!

[lipshits-continuous]

I suppose I should say it's often clarified more than other notation, especially even after it's been stated that something is using it. And I agree, it's not the only thing I dislike about ESC

8! Least favorite notation you’ve ever seen

Einstein Summation Convention. I maintain that if you need to add a phrase to the effect of ''where we're using ESC", it is not good notation.

Thanks for the ask!

[lipshits-continuous]

8! Least favorite notation you’ve ever seen

Einstein Summation Convention. I maintain that if you need to add a phrase to the effect of ''where we're using ESC", it is not good notation.

Thanks for the ask!

[lipshits-continuous]

That's the general approach taken in Lee but the fact you have to distinguish either case is a negative because good notation shouldn't be ambiguous.

Don't get me wrong, having tonnes of indices can get super messy and I appreciate the need for a notation but I don't believe it's necessarily the best solution

8! Least favorite notation you’ve ever seen

Einstein Summation Convention. I maintain that if you need to add a phrase to the effect of ''where we're using ESC", it is not good notation.

Thanks for the ask!

[lipshits-continuous]

8! Least favorite notation you’ve ever seen

Einstein Summation Convention. I maintain that if you need to add a phrase to the effect of ''where we're using ESC", it is not good notation.

Thanks for the ask!

[lipshits-continuous]

real numbers? nah they're fake

chain complex? i find it quite simple

five lemma? that's a few

concrete category? uh this one is self-consolidating

halting problem? i think that's called an addiction

common factor? idk i'd say 97 is pretty rare

field extension? how many acres?

total order? what conspiracy is that?

[lipshits-continuous]

Also bonus question if you feel like it. What are you currently learning (in math)?

[lipshits-continuous]

commuting to the bit. yeah ill be there in about 40 minutes just keep stalling

[lipshits-continuous]

A surgery that preserves G-structure is G-surgery. A surgery along a (k-1)-sphere is k-surgery.* But a G-surgery that is also a k-surgery is ... what? A G-k-surgery? Like a chemist??

*Yeah I know this is possibly non-standard, I might change it, but it's slightly more convenient for me.

[lipshits-continuous]

Haven't done a poll in aaaages (said in the same tone of voice as a cat who ate 7 minutes ago)

[lipshits-continuous]

I think it's pretty neat that I was able to use the rank-nullity theorem in my dissertation

[lipshits-continuous]

"homo""top"y theory, what are we studying here, gay sex??

[lipshits-continuous]

Do you know who Leonhard Euler is?

[lipshits-continuous]

answer all the primes on the real's mathblr ask post!

Hopefully I don't miss any, here goes! I'll put it under a cut cause my answer to 2. is already long oops

2. What math classes did you do best in?

I got 93% in my differential geometry exam last year which is my best grade. It was definitely the easiest module relative to the difficulty of other third year modules.

It also helped that one of the lecturers refused a question from the past exam that we were given solutions to

I also got 91% in the analysis module I took last year which was half measure theory and half an intro to functional analysis. And I got 90% in complex analysis, multivariable calculus, and pdes. It may come as a surprise that topology wasn't my best but do to a mix of personal circumstances, the exam being at the very end of a long exam season and the exam having a more combinatorial flavour in the second half all played against me (not that I did badly, I still got 83% but was my second lowest grade last year)

3. What math classes did you like the most?

In first year linear algebra was my favourite and being able to give tutorials in it this year I still think it's one of my favourites.

Complex analysis is also still high up there and is probably what spawned my love of topology (the topological stuff was definitely more present than in real analysis).

Obviously topology is also one of my favourites, though as alluded to in the previous question there was a more combinatorial approach to some things which I wasn't as much of a fan of (they did change the course significantly for this year though and it seems much better). Differential geometry was also very enjoyable.

This year, algebraic topology has obviously been one of my favourites, even if the second term lecturer wasn't the most organised person. I enjoyed representation theory a lot more than I thought I would and was probably my second favourite module this year. Riemannian geometry was also really good, especially since the lecturer was lovely!

5. Are there areas of math that you enjoy? What are they?

Topology first and foremost! I'm quite interested in differential topology and homotopy theory at the moment. The former is what my dissertation is about and there are things I'd like to read more about relating to it! Homotopy theory is more of a curiosity since I've not had much chance to read about it yet but that's one of my summer plans!

I also enjoy group theory and homological algebra a lot!

7. What do you like about math?

It's inherent exploratory nature as well as how everything connects. One big thing in maths is we have structures and we see what happens when we play with them or alter them. Another is realising connections between different areas. Like for example, my friend who has the same advisor as me for his diss is writing his about Kähler manifolds and Dolbeault cohomology and there's a proof of the Hodge decomposition theorem (I think that's the theorem) that involves the representation theory of sl_{2,C} (as in the lie algebra). Like the fact there's a connection at all is really interesting to me. I suppose that relates to my interest in when algebraic structures sort of arise naturally when looking at certain things in topology.

11. Tell me a funny math story.

13. Do you have any stories of Mathematical failure you’d like to share?

My real analysis lecturer was giving an example of a sequence that didn't converge uniformly and I realised how to alter the example slightly to make it converge uniformly. Turns out that was his next example and he was so happy that I'd preempted it that he jokingly proposed to me.

17. Are there any great female Mathematicians (living or dead) you would give a shout-out to?

None that have come to mind, and I've been thinking a while /lh

Emmy Noether is an obvious one but she literally started homology theory as we know it! I think the story is she attended combinatorial topology lectures and realised she could reframe the language of Betti numbers etc in terms of what we know as simplicial homology.

There are a few living female mathematicians I could shout out but it I do not wish to be doxxed.

19. How did you solve it?

I'm not exactly sure what this question is referring to so I will just give one piece of advise for solving problems. Sometimes a problem is hard because you just haven't had enough experience to solve it yet. Obviously this is isn't helpful is you're trying to solve a homework/exam problem but more generally about learning mathematics. Sometimes you haven't got the tools or the experience to think about it in the right way and that's okay. And the best part about it is that one day you'll come back to the problem and realise that it's easy/easier for you to solve. I think everyone studying maths would benefit from being able to experience this once in a while because it serves as an excellent reminder that you're growing as a mathematician.

23. Will P=NP? Why or why not?

Probably not, though I'm not well-versed enough in it that I could recall well the explanations given for why people think not.

29. You’re at the club and Grigori Perlman brushes his gorgeous locks of hair to the side and then proves your girl’s conjecture. WYD?

Asking him to join the polycule obviously

31. Can you share a math pickup line?

This one is courtesy of me in first year: Are you a subset of a vector space whose elements are of the form ax+b because you're looking (af)fine

37. Have you ever used math in a novel or entertaining way?

Certainly not novel but I have dabbled in how train timetabling works a bit because I have what is essentially a model railway in (heavily modded) Minecraft!

41. What’s the silliest Mathematical mistake you’ve ever made?

I remember in secondary school we did these tests every so often that tested your "essential mathematical skills". I once made the very silly error of writing 3×8=18. Perhaps not the silliest mistake ever but it's one that's stuck with me

43. Did you ever fail a math class?

Not as of yet

47. Just how big is a big number?

As my friend would say: at least 3

53. Do you collect anything that is math-related?

Currently only textbooks, of which I have quite a few now!

59. Can you reccomend any online resources for math?

For algebraic topology I can recommend Friedl's lecture notes. It's a massive several thousand pages. I have currently only used it as a reference document/supplementary material. But from what I've used of it it's clearly written (though trying to use the search function is an uphill battle with how large the document is)

61. Does 6 really *deserve* to be called a perfect number? What the h*ck did it ever do?

It's perfect insofar as its equal to the sum of its proper divisors but it's certainly not free of sin

67. Do you have any math tatoos?

The statement "every tattoo that I have is a maths tattoo" is vacuously true.

71. 👀

👀

73. Can you program? What languages do you know?

Yes but I am very rusty. I used to know java decently well and I knew a bit of python. But I'd probably have to refresh myself a bit before being able to program again

Thanks for the ask!!

[lipshits-continuous]

"homo""top"y theory, what are we studying here, gay sex??

[lipshits-continuous]

Real’s Math Ask Meme

What math classes have you taken?

What math classes did you do best in?

What math classes did you like the most?

What math classes did you do worst in?

Are there areas of math that you enjoy? What are they?

Why do you learn math?

What do you like about math?

Least favorite notation you’ve ever seen?

Do you have any favorite theorems?

Better yet, do you have any least favorite theorems?

Tell me a funny math story.

Who actually invented calculus?

Do you have any stories of Mathematical failure you’d like to share?

Do you think you’re good at math? Do you expect more from yourself?

Do other people think you’re good at math?

Do you know anyone who doesn’t think they’re good at math but you look up to anyway? Do you think they are?

Are there any great female Mathematicians (living or dead) you would give a shout-out to?

Can you share a good math problem you’ve solved recently?

How did you solve it?

Can you share any problem solving tips?

Have you ever taken a competitive exam?

Do you have any friends on Tumblr that also do math?

Will P=NP? Why or why not?

Do you feel the riemann zeta function has any non-trivial zeroes off the ½ line?

Who is your favorite Mathematician?

Who is your least favorite Mathematician?

Do you know any good math jokes?

You’re at the club and Andrew Wiles proves your girl’s last theorem. WYD?

You’re at the club and Grigori Perlman brushes his gorgeous locks of hair to the side and then proves your girl’s conjecture. WYD?

Who is/was the most attractive Mathematician, living or dead? (And why is it Grigori Perlman?)

Can you share a math pickup line?

Can you share many math pickup lines?

Can you keep delivering math pickup lines until my pants dissapear?

Have you ever dated a Mathematician?

Would you date someone who dislikes math?

Would you date someone who’s better than you at math?

Have you ever used math in a novel or entertaining way?

Have you learned any math on your own recently?

When’s the last time you computed something without a calculator?

What’s the silliest Mathematical mistake you’ve ever made?

Which is better named? The Chicken McNugget theorem? Or the Hairy Ball theorem?

Is it really the answer to life, the universe, and everything? Was it the answer on an exam ever? If not, did you put it down anyway to be a wise-ass?

Did you ever fail a math class?

Is math a challenge for you?

Are you a Formalist, Logicist, or Platonist?

Are you close with a math professor?

Just how big is a big number?

Has math changed you?

What’s your favorite number system? Integers? Reals? Rationals? Hyper-reals? Surreals? Complex? Natural numbers?

How do you feel about Norman Wildberger?

Favorite casual math book?

Do you have favorite math textbooks? If so, what are they?

Do you collect anything that is math-related?

Do you have a shrine Terence Tao in your bedroom? If not, where is it?

Where is your most favorite place to do math?

Do you have a favorite sequence? Is it in the OEIS?

What inspired you to do math?

Do you have any favorite/cool math websites you’d like to share?

Can you reccomend any online resources for math?

What’s you favorite number? (Wise-ass answers allowed)

Does 6 really *deserve* to be called a perfect number? What the h*ck did it ever do?

Are there any non-interesting numbers?

How many grains of sand are in a heap of sand?

What’s something your followers don’t know that you’d be willing to share?

Have you ever tried to figure out the prime factors of your phone number?

If yes to 65, what are they? If no, will you let me figure them out for you? 😉

Do you have any math tatoos?

Do you want any math tatoos?

Wanna test my theory that symmetry makes everything more fun?

Do you like Mathematical paradoxes?

👀

Are you a fan of algorithms? If so, which are your favorite?

Can you program? What languages do you know?