Does mathematics really "exist"?

Mike Rugnetta asks “Is Math a Feature of the Universe or a Feature of Human Creation?”.

Math is invisible. Unlike physics, chemistry, and biology we can’t see it, smell it, or even directly observe it in the universe. And so that has made a lot of really smart people ask, does it actually even EXIST?!?! Similar to the tree falling in the forest, there are people who believe that if no person existed to count, math wouldn’t be around . .at ALL!!!! But is this true? Do we live in a mathless universe? Or if math is a real entity that exists, are there formulas and mathematical concepts out there in the universe that are undiscovered? Or is it all fiction? Whew!! So many questions, so many theories… watch the episode and let us know what you think!

Mike Rugnetta of PBS’ Idea Channel

The discussion is rather philosophical…

ul. Sniadeckich

impan

impan The Institute of Mathematics of the Polish Academy of Sciences at Warsaw is located on ul. Śniadeckich. I decided to have a quick look into the naming of the street. I discovered that it is named after two brothers, both of whom were outstanding Polish scholars end of the eighteenth and the first half of the nineteenth century.

Jan Śniadecki

Jan Śniadecki (August 29, 1756– November 9, 1830) was a Polish mathematician, philosopher and astronomer. He published works on his observations of the then recently discovered planetoids.

His O rachunku losów (On the Calculation of Chance, 1817) was a pioneering work in probability theory.

Jan
(1823 painting by Jan Rustem)

Jędrzej Śniadecki

Jed
(1843 painting by Aleksander Sleńdziński)
Jędrzej Śniadecki (30 November 1768 – 12 May 1838) was a Polish physician, chemist and biologist.

He is best known for important book Początki chemii (The Beginnings of Chemistry), the first Polish-language chemistry textbook.

Opportunity Physics; fundraising campaign

physics The Institute of Physics will start a fundraising campaign Opportunity Physics which aims to raise £10m over 5 years. The money will be used to continue and extend the activities of the Institute both in the UK and abroad.

The official launch of the campaign, will be hosted by Professor Brian Cox and IOP president Professor Sir Peter Knight, on Monday 23 September 2013.

Why raise funds?

At the point where increased funding is needed to scale up our work, there are uncertainties about the sustainability of our main revenue stream which has come from IOP Publishing. It is prudent to plan for the change in funding landscape by raising funds now.

IOP

The campaign aims
In short there are four areas the IOP wants to focus on; discovery, society, economy and education.

The campaign aims can be found here (opens pdf)

Links
Fundraising campaign, IOP website.

Professor Jeff Forshaw wins Kelvin medal and prize

jeff Professor Jeff Forshaw of the University of Manchester has won the 2013 Kelvin medal and prize awarded by the Institute of Physics. The medal is for Prof. Forshaw’s wide-reaching work aimed at helping the general public to understand complex ideas in physics.

Prof. Forshaw has written two popular science books; “The quantum universe” and “Why does E=mc^2”, both with Brian Cox.

Links

2013 Kelvin medal and prize, IOP website

Jeff Forshaw’s homepage

Professor Copeland wins Rayleigh Medal and Prize

ED Professor Edmund Copeland of the University of Nottingham has won the 2013 Rayleigh Medal and Prize as awarded by the Institute of Physics.

Professor Copeland was awarded the prize for his work on particle/string cosmology from the evolution of cosmic superstrings, to the determination of the nature of Inflation in string cosmology and to constraining dynamical models of dark energy and modified gravity.

A personal note
I first met Professor Copeland back in 2005 when was at the University of Sussex. I was there studying for my masters degree. He then, in the same year moved to Nottingham to establish the Particle Theory Group.

Link
2013 Rayleigh Medal and Prize, IOP website.

Prof. Copeland’s homepage

Policja Robots

polish police The Policja (Polish police) were in plac Zamkowy on Saturday showing off some of their equipment including cars, motorbikes and two of their bomb squad robots.

Here are some photos of the said robots…

robot1

This was quite an impressive robot and the largest of the two on display.

robot2
Here is the same robot with one of its operators.

robot3
This is the smaller of the two robots. One of the operators was demonstrating the use of this robot in picking up small packages.

robot4
The smaller of the robots again.

bomb suit
This is one of the police’s bomb suits.

Controversial topics in Wikipedia

wiki Yasseri, Spoerri, Graham and Kertèsz [1] have analysed page edits of Wikipedia entries to find the most controversial entries. Many entries in the open encyclopedia are only locally debated, for example in Romania the Universit­atea Craiova football team is a hot topic!

The researchers concentrated on finding the entries which editors scrapped about in order to find controversial subjects. This is believed to be more reliable than simply concentrating on those that have changed a lot

There are of course things that are more universally controversial and receive lots of edits. The top 10 “touchy” subjects according to the research are;

  1. George W Bush
  2. Anarchism
  3. The Prophet Muhammad
  4. World Wrestling Entertainment employees
  5. Global warming
  6. Circumcision
  7. The United States
  8. Jesus
  9. Race and intelligence
  10. Christianity

The most controversial
Millions of articles from 10 different language versions of Wikipedia were analysed. English, Spanish, Persian, Arabic and Czech editions were among those studied. Across all the languages the most controversial entries were found to be;

  1. Israel
  2. Adolf Hitler
  3. The Holocaust
  4. God

I would say no real surprises here.

Reference
[1]Yasseri T., Spoerri A., Graham M., and Kertèsz J., The most controversial topics in Wikipedia: A multilingual and geographical analysis. In: Fichman P., Hara N., editors, Global Wikipedia:International and cross-cultural issues in online collaboration. Scarecrow Press (2014). (arXiv:1305.5566v2 [physics.soc-ph] )

Do all useful mathematical ideas really come from physics?

maths

Image by Saeed.Veradi

Some one once remarked to me that all the important ideas in mathematics come from physics. After a little thought I tend to agree, and for sure many important topics in mathematics have their roots in physics or at least quickly found applications in physics.

Below are some examples of the branches of mathematics that have clear physical applications as well as being of independent interest. The list is by no means complete, in no particular order and will reflect my own interests. Also I will not be at all technical here.

The theory of partial differential equations
This is just so encompassing, I was not sure how to include it! A partial differential equation (PDE) is a differential equation in unknown multivariable functions and their partial derivatives. PDEs are used to model a huge range of phenomena such as sound, heat flow, electromagnetic waves, fluids, the vibrating string, classical fields, superconductivity and so on.

As many branches of mathematics employ tools from differential calculus just about every mathematician will come across a PDE of some kind in his work. I cannot begin to list where the theory PDEs come in useful.

What should be remarked is that not all PDEs have nice solutions that can be expressed in terms of elementary functions. One will often need to turn to numerical methods to solve PDEs.

All the other branches listed below have some interface with PDEs as they are so universal.

Symplectic geometry and classical mechanics
Symplectic and Poisson geometry is essentially the study of manifolds equipped with Poisson brackets; that is a particular kind Lie algebra structure with a Leibniz rule. The study of such structures is fundamental in understanding the Hamiltonian formulation of classical mechanics; classical phase spaces carry such Poisson brackets.

Such geometries have become a large subject of study and also have found applications in diverse areas of mathematics. For example, geometric representation theory, non-commutative geometry, integrable systems and the theory of Lie algebroids have found much use for ideas found in Poisson geometry.

Riemannian geometry
This is loosely the study of spaces, that is manifolds, with the local notion of the length of a path as well as areas and volumes. One should think of Riemannian geometry as a very broad generalisation of the geometry of surfaces in \(\mathbb{R}^{3}\).

Although Bernhard Riemann’s initial work on the subject predates Einstein’s special and general relativity, Riemannian geometry is fundamental in the formulation of relativity. Indeed general relativity, that is Einstein’s theory of gravity as the local geometry of space-time, remains a large motivator for the study of Riemannian geometry.

One should also note that Riemannian geometry has proved useful in group theory, representation theory, algebraic topology and so on.

Functional analysis
Here we have the study of vector spaces equipped with some extra structure such as an inner product or a norm, and operators on such vector spaces. Such structure allows one to think about limits. Functional analysis has its roots in the study of function spaces and transformations on them like the Fourier transform. The main focus of functional analysis is the extension of the theory of integration and probability to infinite dimensional spaces.

The notion of a Hilbert space, which is an infinite dimensional vector space with an inner product, if fundamental in non-relativistic quantum mechanics. Spectral theory of operators on Hilbert spaces, which is part of functional analysis is very important in quantum physics. In particular the algebras of operators on such spaces is deeply linked with physics…

Operator algebras
Really this too can be seen as part of functional analysis. An operator algebra is (loosely) an algebra of linear operators on an infinite dimensional vector space. From a physics point of view operator algebras are found behind the quantum statistical mechanics, axiomatic quantum field theory and non-commutative generalisations of space-time.

Group theory
Group theory can be thought of as the abstract study of symmetry. Many physical systems exhibit symmetries, such as crystal lattices, molecules as well as the much more complicated symmetries that can be found behind electromagnetic theory. The representation theory of groups, “representing groups by linear operators on a vector space”, has fundamental applications in physics and chemistry. For example, all the fundamental particles in nature are classified by the representations of the Poincare group, which is the group describing the symmetries of flat space-time.

Group theory itself is a huge subject, which applications throughout pure and applied mathematics. For example, group theory has been very influential on the development of differential geometry and abstract algebra.

Combinatorics
Combinatorics is the study of finite or countable discrete structures. Loosely combinatorics is about counting the number of elements of some structure. The Fibonacci numbers are a classical example here.

Combinatorics has strong applications in algebra, probability theory, number theory and topology. From the physics side of things we see combinatorics appearing in statistical mechanics and quantum field theory.

Białowieża

sign I have just returned from the XXXII Workshop on Geometric Methods in Physics. The work shop was a great experience and I enjoyed myself very much; maybe all the Polish Vodka helped!

The village of Białowieża is located in north-east of Poland in the Podlaskie Voivodeship, very close to the border with Belarus. The village is located in the middle of the Białowieża Forest.

Here are some photos that I took…

gates
Here are the main gates to the park. They lead to a small bridge across the small river and the lake.

tree
When on an afternoon excursion we visited the forest itself. Here is one of the few remaining old oak trees left.

creepy tree
This tree is to be found just out side the guest house I was staying at. I think it looks rather creepy and reminiscent of Iron Maiden’s “fear of the dark” album cover.

The wildlife
The area is known for it’s wildlife including bison. I did not see any bison, but I did see plenty of mosquitoes! I also found plenty of common frogs in the forest.

frog
The common frog, Rana temporaria.

Also very common are the white storks.

stork
This stork was searching for food in the back garden of the guesthouse I was staying at.

stork2
They can be found nesting during the summer on top of houses and telegraph poles. The birds are encouraged by the local to nest and they seem largely appreciated. The storks are not exactly shy birds, but they are easily spooked.

Science and the Chancellor’s Spending Round 2015-2016

osborne

George Gideon Oliver Osborne MP, Chancellor of the Exchequer and Second Lord of the Treasury of the United Kingdom

On the 26th of July the Chancellor George Osborne announced in his spending review for 2015-2016 that public funding of science would remain flat at about £4.6bn per year. This figure has been held flat since 2011.

Scientific discovery is first and foremost an expression of the relentless human search to know more about our world, but it’s also an enormous strength for a modern economy,

George Osborne, Chancellor of the Exchequer

The science minister said the following;

This settlement reflects the vital contribution that science, innovation and higher education make to the UK economy. Increasing capital funding for science and universities will underpin our ambitious industrial strategy, ensure our brightest minds can commercialise their ideas and support the knowledge that drives growth.

The science minister David Willetts

At a glance

  • Day-to-day science spend to remain at £4.6bn
  • Capital investment to rise from £0.6bn to £1.1bn
  • Capital increase to rise with inflation to 2020-21
  • Additional £185m for Technology Strategy Board
  • £100m/yr available to partner with private industry
  • £100m/yr to support innovative UK businesses

Some responses

The announcement that the current science budget will be maintained at £4.6 billion is a welcome recognition of the importance of science as an engine for future growth, but it needs to be noted that inflation has already substantially eroded the value of funding for science in the UK, by 2-3% per annum since 2010’s flat cash settlement.

Professor Sir Peter Knight, President IOP

You can read the full response from the Institute of Physics by following the link below.

In recent years science has suffered, as maintaining investment means a real terms cut due to inflation, but in the context of cuts elsewhere, science has been relatively protected Today’s announcement should be seen as a foundation for a long term strategy of increased investment. At present our economic competitors are outspending us in science but are not outperforming us.

Prof. Paul Nurse, President of the Royal Society

You can read the full response from the Royal Society by following the link below.

Links
UK science spending to remain ‘flat’, BBC NEWS


Response to Spending Round 2015-16
, The Institute of Physics

Chancellor champions science The Royal Society

Random thoughts on mathematics, physics and more…