BR Maths Corner-1

[Amber G.]

The above ad was 4th ... after Mike Myers and Dr Evil in the super bowl ..
THE BEST COMMERCIALS OF SUPER BOWL LVI

(I found use of the word 'equation' (instead of 'inequality') little strange - turns out Prof Ken did suggested the same but the the script writers kept the word 'equation' (as in "help with this equation")..

[Amber G.]

President Kovind presented Nari Shakti Puraskar to Neena Gupta for her excellence in Mathematics. A professor at Indian Statistical Institute, Kolkata, she has solved 70 years old Zariski Cancellation Problem. She is also the winner of 'Ramanujan Prize' for Young Mathematicians..

[Amber G.]

Congratulations for winning 3 bronzes! Well done.
(After a gap of two years, the Indian team was happy to represent onsite at the 11th European Girls’ Mathematical Olympiad be held in Eger, Hungary. (April 6-12, 2022)
(photo - team departing from Mumbai a few days ago with well wishes from many).


(Congratulation to US Team too - 3 Gold, 1 Silver - overall 1st)

[Amber G.]

^^^ Special shoutout to Jessica Wan, (USA) who placed first in the entire competition with the only perfect score.

[Amber G.]

Sharing a gem of a twitter thread...(Written by grand son of this great Mathematician.
Shri PK Srinivasan should be much better known.

https://threadreaderapp.com/thread/1519 ... 72480.html

26/04 - the Remembrance Day of one of the brightest minds India gave the world - #SrinivasaRamanujan. Today, however I ended up remembering another man - who was born 4 years after Ramanujan died, but whose life was inextricably entwined with Ramanujan’s.
Image...
This man was born on 04.11.1924 (Avittam) as the eldest son of a humble clerk in Madras’s police dept. Quickly mastering the languages of Tamil, Telugu, Sanskrit & English at a very young age - he shifted his focus to Mathematics. For a young lad, he was supremely disciplined..
“A nation that celebrates its creative geniuses, is a nation that progresses” he wrote in the biography of Srinivasa Ramanujan.

His name was P.K. Srinivasan.

And he also happens to be my grandfather. My Cheenu Thatha

[Vayutuvan]

Nice. One of the people who visited is Prof. Bruce Berendt. I can recognize him in the picture where he is shaking hands with Shree P. K. Srinivasan.

[Amber G.]

Happy Friday! Just for fun - One (relatively) easy problem:.. Enjoy

[Yayavar]

Happy Friday! Just for fun - One (relatively) easy problem:.. Enjoy

Approx 1.2

[Amber G.]

^^^ Answer is correct.. (FYI: In the above - calculators are not allowed - the tournament is open to middle/high_school students)..
Edited later - some may use a different form -- see the next post. ..

[Yayavar]

^^In that case - no calculator or any mathematical expertise used. Just staring the image for a while to get 'sixth root of 3' .

[Amber G.]

^^^ ... Nice.
Another one from the same contest..
Interesting to see this (very similar) problem was posted in this math dhaga 10 years before it was posted in this tournament (HMMT)


(Note: HMMT is a nice competition - open to all (global but mainly USA students) middle and high schoolers)

Added later : just saw- The problem is the *first* problem I posted in my *first* post in this dhaga.. ....

[Amber G.]

Happy Tau (ताऊ) Day for all the ताऊ's of in Brf !
(For those who are not fluent in Mathematics or Hindi - Tau is two times Pi (2*3.14=6.28) and is celebrated on 6/28. Tau (ताऊजी) is an elder brother of you father.

[Vayutuvan]

^^In that case - no calculator or any mathematical expertise used. Just staring the image for a while to get 'sixth root of 3' .

I stared for a lot of time even after the answer. Then got it. Very nice. Now for the generalization of that.

x^(ax^b) = b/a

To make the underlying field real, b > a > 0, impose b > a > 0. Strictly greater than zero or we end up 0^0 (which is undefined. Proof of why 0^0 is undefined is left as an exercise )

For the original problem, I initially thought to use newton's method of finding zeros of f(x) = x^(2x^6) - 3. Start with 1.5. 2 is clearly too big and x = 1 is too small. It might be better to start with something closer to 1 as x=2 is very from a zero.

[Amber G.]

^^^ FWIW - for problems like (x^(2x^6)=...), one of the technique I teach my students is to notice that the function is *continuously* increasing and thus if one find one solution (even by trial or error), there is *only* one solution. (If one does not explicitly state such argument in answer, they may not get the full credit).

Here, of course, if one takes y = x^6 (or x=y^(1/6)) ==> the equation reduces to (y^(1/6)^2y = y^(y/3) = 3 ==> y^y = 3^3 so obviously y=3 is a solution. (By logic of previous paragraph - the *ONLY* solution) y=3 ==> x= 3^(1/6).

----
BTW HMMT is a nice competition for 9-12 grade students.

[Amber G.]

IMU 2022 is coming. The famous event comes every fourth year and Fields Medals (== Nobel prize in math). Here is live feed of the Fields medal (and other IMU prizes) prize ceremony. 4:00am EST on July 5th.
Link: https://www.youtube.com/watch?v=6I0siVD7RBI


( The awards will be given at an in person ceremony at Aalto University in Helsinki on July 5th. The prize winner lectures will open the virtual ICM that begins the next day on July 6th

(My sources tell me that there are four Fields Medals this time. I hope Bhargav Bhatt is one of them)

[Amber G.]

USA will host next IMC (2026).
Also by this time tomorrow we will know who the Field Medalists are.

[Vayutuvan]

@Amber G. ji, thanks. Any predictions?

[Amber G.]

The Medalist are:
Number Theorists Maryna Viazovska(Swiss Federal Institute of Technology in Lausanne)
and James Maynard (Oxford)!
( Packing of eight-dimensional spheres and research in prime numbers.)
and Hugo Duminil-Copin ( Institut des Hautes Études Scientifiques)
June Huh (Princeton University)


Mark Braverman, Princeton University received the Abacus Medal, a newer award that was modeled after the Fields for young computer scientists.

Dr. Viazovska is just the second woman to receive a Fields Medal. She is from Ukraine and many of us have predicted and are happy -- this ought to make big news.

[Amber G.]

Also prof. Barry Mazur is awarded the 2022 Chern Medal for his profound discoveries in topology, arithmetic geometry and number theory, and his leadership and generosity in forming the next generation of Mathematicians.

[Amber G.]

One of the interesting thing for me is that *both* Maryna Viazovska and James Maynard were honored with Ramanujan Awards in past - Ramanujan Award is given by SASTRA in Thanjavur and it spots future Fields Medallists. The award recognizes very young mathematicians, under the age of 32 (Ramnujan's age).

Remarkable that I can count the following successes.. (In our math dhaga - i have covered a few of them in my posts).

Manjul Bhargava (RA 2005, FM 2014)
Terence Tao (RA 2006, FM 2006)
Akshay Venkatesh (RA 2008, FM 2018)
Peter Scholze (RA 2013, FM 2018)
James Maynard (RA 2014, FM 2022)
Maryna Viazovska (RA 2019, FM 2022).

---
Prof. Vidyasagar (of Sutra fame - which I have mentioned many times here in BRF) facilates SASTRA for instituting the award. Prof. Krishnaswami Alladi conceptualized it and I think does the administering.
Kudos for spotting young talent. Impressive record.

[Amber G.]

Wishing all the best to the Indian Team participating in International Mathematical Olympiad (#IMO2022) being held at Oslo, Norway from Jul 9-16, 2022.
Members include: Pranjal, Atul, Arjun, Adhitya, Vedant, Kaustav (Contestants) and Prof. Laishram & Spandan (Leaders).

[Vayutuvan]

Mark Braverman, Princeton University received the Abacus Medal, a newer award that was modeled after the Fields for young computer scientists.

Amber G. ji,

Nevanlinna Prize. The very first one went to Robert Andre Tarjan. Two Indian origin people also received the award - Prof. Madhu Sudan, MIT and Prof. Subhash Khot (he was at Georgia Tech then but I think he is at UCLA or USC NYU now).

PS: You are right. Nevanlinna Prize has been renamed. I remember the following. But didn't realize that OMU changed the name of the prize.

Alexander Soifer, president of the World Federation of National Mathematics Competitions, complained about the prize's honouring of Nevanlinna, as he was a supporter of Hitler and had acted as a representative for the Finnish Volunteer Battalion of the Waffen-SS during World War II. Soifer discussed Nevanlinna's wartime activities in a 2015 book, and forwarded his personal and his organization’s requests to the Executive Committee of IMU to change the Prize's name.[5][6] In July 2018, the 18th General Assembly of the IMU decided to remove the name of Rolf Nevanlinna from the prize.[7] It was later announced that the prize would be named the IMU Abacus Medal.

[Amber G.]

^^^ Thanks. Yes The IMU Abacus Medal is a continuation of the Rolf Nevanlinna Prize that was awarded from 1982 to 2018
---
People here may enjoy listening- there are many popular articles/You-tube production by a few of the other prize winners in this IMC 2022.

Barry Mazur( 2022 Chern Medal) - Inspired many - perhaps a next generation of Mathematicians with his fun math.

Nikolai Andreev (2022 Leelavati ): "For his contribution to the art of mathematical animation and of mathematical model-building, in a style which inspires the young and the old alike, and which mathematicians around the world can adapt to their varied uses-as well as for his indefatigable efforts to popularize genuine mathematics among the public via videos, lectures, and a prize-winning book."

(As Many know Leelavati Award is "an award for outstanding contribution to public outreach in mathematics. It is named after the 12th-century mathematical treatise "Leeavati" devoted to arithmetic and algebra written by the Indian mathematician Bhaskara Achārya." In the book the author posed, in verse form, a series of problems in (elementary) arithmetic to one Leelavati ( his daughter) and followed them up with hints to solutions -- Not unlike some problems/solutions posted in this dhaga

[Amber G.]

Wishing all the best to the Indian Team participating in International Mathematical Olympiad (#IMO2022) being held at Oslo, Norway from Jul 9-16, 2022.
Members include: Pranjal, Atul, Arjun, Adhitya, Vedant, Kaustav (Contestants) and Prof. Laishram & Spandan (Leaders).

The Indian Team for the 2022 IMO--
Pranjal Srivastava
Arjun Gupta
Vedant Saini
Adhitya Venkata Ganesh Mangudy
Atul Shatavart Nadig
Kaustav Mishra.

Congrats to everyone who made the team and best wishes!
---
Day 1 of the contest is over.

[Vayutuvan]

A very nice video Leelavati Prize 2022 Nikolai Andreev

[Vayutuvan]

Category Theory gone wild.

[Amber G.]

International Math Olympiad 2022 . Official scores are not posted (may be posted tomorrow)
Indian Team Scores ( from the last information I have) are (about0 34 28 28 27 24 24 (Perfect score = 42)
(***Not** official results - )
(Note: The grading/marks for all problems is not known - some guess-work is based from report from student(s) -- how well he think he did on the problem where grading is still not known)

Added later: This scoresheet is more accurate. (The final scores may still change - official announcement tomorrow)
(India (6 contestants , perfect score 42)
34, 28, 28,27,24, 24

Impressive from Team India. The 34 might get gold but rest might get silver/bronze

Since it seems that this years IMO was one of easier one (people scoring high marks), The cut-off for medal is difficult to estimate. (Officially they have not made all the scores of all the teams available)

it seems we have a Gold or two (Pranjal) and a few silvers (and/or Bronze)
(My estimation)

IMO site is https://www.imo2022.org/imo/Home When results are up I will post/update the results.


****
Meanwhile China seems to have done extremely well (all 6 golds - with perfect or near perfect scores). US may be 5 (or 6) Golds.. Pakistan one person may get score in double digit.
***
If you want to try, here is one problem (which I found interesting) (and, at least looks easy):

Find all triples (a,b,p) of positive integers with p prime that satisfy:
a^p=b!+p

[Amber G.]

^^^Impressive from Team India.
Unofficial Scores (Perfect score 42)

Pranjal Srivastava -34
Arjun Gupta - 28
Adhitya Venkata Ganesh Mangudy - 28
Vedant Saini 27
Atul Shatavart Nadig 24
Kaustav Mishra 24

(All will receive a medal!).

---
China - Very impressive, all six perfect scores!
USA:
Derek Liu - 40
Luke Rabitaille - 37
Kevin Cong - 36
Eric Shen - 36
Andrew Gu - 33
Ram Goel - 25
---
Official scores will be announced tomorrow.
Gold Medal cutoff I believe will be around 32 (my guess) so Pranjal is most likely a Gold.
Silver Cut-off may be around 27 (my guess)
All others will at least get a Bronze.
Will post the results tomorrow,

[Amber G.]

I am also happy to notice : Derek Liu and Luke Robitaille who won the Gold for USA also won Spirit of Ramanujan Fellowships in 2018 (as middle-schooler). Also,Ram Goel who won a bronze medal also won 2021 SOR Fellowship.
Congratulations Derek, Luke and Ram!!!!

Someone informed me that cut-off points are .. 34, 29, 23 for gold, silver and bronze.

So India team has only 1 Gold and 5 Bronze.
USA 4 Gold, 1 Silver, I bronze.

Official results have been posted.

[Amber G.]

Have not seen any news item in Indian Newspapers... perhaps they will put something now after Brf post.

[Shwetank]

Do you think India does bad in IMO comparitive to China/US because it doesn't have the prestige or be future prospects in the country (like doing well on IIT-JEE does)? Or are Chinese just inherently better at math tests? (Was there something to having to learn the structure of the their written language making them better suited?)

[Vayutuvan]

As much as we love pure math, it is not all that important in the overall scheme of things. Very few (but many) Fields medalists would have had IMO medals of any kind. It is similar to not many winning Nobel literature after winning a spelling bee championship. It is very very very hard to be a Fields medalist. Many things have to perfectly line up on top of individual effort, natural talent, and the academic pedigree. IN the end, it all boils down to what is usually known as "luck". This is no different from what makes Bill Gates/Steve Jobs/Elon Musk vs. the also-rans - Mitch Kapur, Xerox PARC, and many EV startups.

[Vayutuvan]

(Was there something to having to learn the structure of the their written language making them better suited?)

Russians used to do well in IMO and pure maths at the research level. The US had been doing well. Both Russian and American (English) use the Roman alphabet. Indic languages are no different. Algebraic vs. Chinese (geometric.) written system.

To excel in maths, one needs a judicious mixture of algebraic and geometric intuituition.

Mathematicians are good musicians because they excel in pattern recognition. Vice ve5rsa is not always true.

[Amber G.]

SASTRA Ramanujan Prize for 2022 goes to Yunqing Tang

[gakakkad]

^^^Impressive from Team India.
Unofficial Scores (Perfect score 42)

Pranjal Srivastava -34
Arjun Gupta - 28
Adhitya Venkata Ganesh Mangudy - 28
Vedant Saini 27
Atul Shatavart Nadig 24
Kaustav Mishra 24

(All will receive a medal!).

---
China - Very impressive, all six perfect scores!
USA:
Derek Liu - 40
Luke Rabitaille - 37
Kevin Cong - 36
Eric Shen - 36
Andrew Gu - 33
Ram Goel - 25
---
Official scores will be announced tomorrow.
Gold Medal cutoff I believe will be around 32 (my guess) so Pranjal is most likely a Gold.
Silver Cut-off may be around 27 (my guess)
All others will at least get a Bronze.
Will post the results tomorrow,

i think the AOPS group is really helping the yankee team do well. During my year at least in INPHO , the chinese had sent college students was the whisper.

[Amber G.]

Wonder how many brfites are now active in mastodon. In a very short time-frame, since Musk took-over Twitter, *most* (*very* large % of people I follow on Twitter) have migrated to this platform. I like the fact that I can use LaTeX, and people like Terrence Tao are posting there. He is beginning to post some really good stuff! And he is not alone. Looks like a migration to this place from Twitter is quite big. Good place to hangout while people talk about math physics and such stuff.


(For those who may not know - Terry Tao is widely regarded as one of the greatest living mathematicians and is referred as the "Mozart of mathematics" - who is also extremely generous with his time as a great teacher and prolific with popular articles and social media presence)

[Vayutuvan]

Amber G. ji, thanks for the above link to Mastodon. The best course of action is to register at mathsodon server as a Mastodon user.

I am @[email protected]

[Amber G.]

Okay... just for fun for Tuesday..
What are the values of (x,y,z) if:
1/x + y + z = 3
x + 1/y +z = 3
x + y + 1/z = 3

[hgupta]

Okay... just for fun for Tuesday..
What are the values of (x,y,z) if:
1/x + y + z = 3
x + 1/y +z = 3
x + y + 1/z = 3

X = 1, Y = 1, Z = 1.

[Prem Kumar]

Amber G: I plugged your question into ChatGPT, the latest release by OpenAI, that's got everyone super-excited. This is what it wrote back. You can see that it kind of gets into a "a = a" type of situation. But then eventually figures out at least 1 correct answer

****************

To solve this system of equations, we can start by multiplying the first equation by x, the second equation by y, and the third equation by z to eliminate the fractions. This gives us the equations:

x^2 + y + z = 3x
xy + y^2 + z = 3y
xz + yz + z^2 = 3z

Next, we can add these equations together to get:

x^2 + 2xy + y^2 + 2xz + 2yz + z^2 = 3x + 3y + 3z

We can then use the original equations to eliminate x, y, and z from this equation, giving us:

(1/x + y + z) + (x + 1/y + z) + (x + y + 1/z) = 3 + 3 + 3

Substituting the values from the original equations, we get:

3 + 3 + 3 = 9

This means that the values of x, y, and z must satisfy the equations 1/x + y + z = 3, x + 1/y + z = 3, and x + y + 1/z = 3. However, since we have not been given specific values for these variables, there could be multiple sets of values that satisfy these equations. For example, one possible solution is x = 1, y = 1, and z = 1, which would give us 1/1 + 1 + 1 = 3, 1 + 1/1 + 1 = 3, and 1 + 1 + 1/1 = 3. However, there could be other solutions as well.