Comment: It is really a shame that the article tells us so much about British scientists and the revolutionary concept of toposes, but do not even mention the French mathematician, Grothendieck, who against the mainstream mathematicians invented and developed the theory of toposes. Is it because Grothendieck is being considered as "weird"? Look at the entry from Wikipedia:

Alexander Grothendieck (born March 28, 1928 in Berlin, Germany) is one of the most important mathematicians of the 20th century. He is also one of its most extreme scientific personalities, with achievements over a short span of years which are still astounding in their broad scope and sheer bulk, and a lifestyle later in his career which alienated even close followers. He made major contributions to algebraic geometry, homological algebra, and functional analysis. He was awarded the Fields Medal in 1966, and co-awarded the Crafoord Prize with Pierre Deligne in 1988. He declined the latter prize on ethical grounds in a letter to the media.[4]

He is noted for his mastery of abstract approaches to mathematics, and his perfectionism in matters of formulation and presentation. In particular, his ability to derive concrete results using only very general methods is considered to be unique amongst mathematicians. Relatively little of his work after 1960 was published by the conventional route of the learned journal, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal, on French mathematics and the Zariski school at Harvard University.

He is the subject of many stories and some misleading rumors concerning his work habits and politics, confrontations with other mathematicians and the French authorities, his withdrawal from mathematics at age 42, his retirement, and his subsequent lengthy writings.

What were these "misleading rumours", one may like to know. This is mentioned in the Wikipedia article as follows:

"Grothendieck's political views were considered to be radical left wing and pacifist. He gave lectures on category theory in the forests surrounding Hanoi while the city was being bombed, to protest against the Vietnam war.

He retired from scientific life around 1970, after having discovered the partly military funding of IHES (see pp. xii and xiii of SGA1, S pringer Lecture Notes 224). He returned to academia a few years later as a professor at the University of Montpellier, where he stayed until his retirement in 1988. His criticisms of the scientific community are also contained in a letter written in 1988, in which he states the reasons for his refusal of the Crafoord Prize."

Grothendieck also declined his 1966 award in Moscow in protest against the Soviet Union's military intervention in Eastern Europe, though he later accepted.

Many interesting historical facts can be found in Grothendieck's autobiographical essays, partly translated from French to English:

Unfortunately the translation which was free for downloading a year or so ago is no more free. The essays are still free in French and in Russian. Here is just one excerpt that tells us what kind of a unusual person Grothendieck is (he lives in seclusion in the French Pyrenees):

"The Universe, the World, let alone the Cosmos, are basically very strange and distant entities. They don't really concern us. It is not towards them that the deepest part of ourselves is drawn. What attracts us is an immediate and tangible Incarnation of them, that which is close, "physical", imbued with profound resonances and rich in mystery- that which is conflated with the origins of our being in the flesh, and of our species - and of That which at all times awaits us, silently and ever welcoming, "at the end of the road". It is She, the Mother, She who gives us birth as she gives birth to the World, She who subdues the urges or opens the floodgates of desire, carrying us to our encounter with Her, thrusting us forwards towards Her, to a ceaseless return and immersion in Her.

Thus, digressing from the road on this unanticipated "promenade", I found, quite by accident, a parable with which I was familiar, which I'd almost forgotten - the parable of The Child and the Mother. One might look upon it as a parable of "Life in Search of Itself" . Or, at the simple level of personal existence, a parable of "Being, in its quests for things " .

It's a parable, and it's also the expression of an ancestral experience, deeply implanted in the psyche - the most powerful of the original symbols that give nourishment to the deepest levels of creativity. I believe I recognize in it , as expressed in the timeless language of archetypal images, the very breath of the creative power in man, animating flesh and spirit, from their most humble and most ephemerable manifestations to those which are most startling and indestructible.

This "breath", even like the carnal image that incarnates it, is the most unassuming of all things in existence. It is also that which is most fragile, the most neglected and the most despised ...

And the history of the vicissitudes of this breath over the course of its existence is nothing other than your adventure, the "adventure of knowledge" in your life. The wordless parable that gives it expression is that of the child and the mother.

You are the child, issued from the Mother, sheltered in Her, nourished by her power. And the child rushes towards the Mother, the Ever-Close, the Well-Understood - towards the encounter with Her, the Unlimited, yet forever Unknowable and full of mystery ...."

But back to the article that states "Isham and his colleagues at Imperial College London and elsewhere believe they can glimpse the answers to these profound questions."

The article, as it is usual for popular articles, is completely misleading. It does not mention at all the achievements of many other people in the field who proposed and developed much more efficient ways of solving the quantum dilemmas. It takes a piece of an undeveloped idea that can be easily criticised by other experts as totally useless, and it blows it up out of proportion. The public wants sensational news, and here is a sensation, served on the plate. You don't have to think.

Comment: That is a very confident statement, which normally is a sure sigh of ignorance. But then again traditional science is built on linear time, so one shouldn't expect to much.