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Author: Donal O'Shea

Duration: 200 pages – and an additional 92 pages of notes, terminologies, bibliographies, and index.

There’s been quite a lot of misunderstanding in regards to this subject and usually highly informed reporting has indeed come unstuck on the clarity of this matter.

Writing about dimensions no reader can visually grasp without confidence makes this ‘Readers Digest’ styled book, somewhat an enigma. Professor Donal O’Shea whose name sounds like a character from the TV hit show ‘Father Ted’; has earnestly tried to educate his readership the wonders of Topology and how it shapes everything that exists – indeed, this is quite a vast subject. Such vastness cannot be put to paper effectively. It would be more at home it the book was read on a satellite whereby the gargantuan expansion could be witness as you peer at Earth’s aura, from 240 miles high – and beyond. The Poincaré Conjecture (PC) delves into the notion of 4D and beyond from a 3D sphere, for whatever that means and harder still explaining it on rectangle leafs of paper, is a mean feat in itself. Herewith the PC has been orbiting British libraries since its theoretical conception in 1904 by Henri Poincaré (1854 – 1912). Part of his theories derived from mathematician Enrico Betti (1823 – 1892) studies of homology. Since the pioneering days of Poincaré’s work, it seemed the (PC) had perished with Henri Poincaré earlier in the twentieth century – until that was, the day of April 7th 2003 arrived in Cambridge, Massachusetts - when guest speaker Russian mathematician, Grigory Perelman, mimicked bearded professor, looking older than his 37 years, announced the ‘Ricci Flow Equation’
had proved the (PC) is indeed credible. The curvature of space via the ‘Ricci Flow Equation’ simulates a complex heat theory evident in space that works in kinship with molten and lava – conformation Henri Poincaré’s theory was viable. Perelman’s interpreted the universe as being a myriad of mathematical equations that interlock together, changing as the equation creates geometrics, synchronized in unison harmoniously. The closest thing I could fathom it out to be like is a musical composition; perfect geometrics, where a hierarchal form of intelligence must be evident to conduct it.

O’Shea initiated in the ‘Preface’ – readers requires a little High School knowledge of geometrics to get the gist of the book’s complex mathematical conundrums - to say it mildly; O’Shea may’ve overestimated the High School curriculum. And on that note makes professor O’Shea appear misinformed, a fundamental weakness to the book. Curious minds will find nourishment as O’Shea adopts a reader friendly narrative coming to the conclusion, a refreshing breather from the brain drain ‘fig drawings’ of warped dumb bells and netted skittles. O’Shea’s lecture reiterates the importance of mathematical understanding in education and uses Perelman as an example of human mathematical endeavour. He covertly hopes this book may’ve created a generation of sublime mathematicians to go beyond the equation complexities derived from the ground breaking studies of Perelman. O’Shea reaches his beleaguered audience eventually; he warms up little by little as you progress through the lineage minefields of diagrams and math jargon, which you can look-up at the back of the book. Too much jargon is one of the pitfalls of writing about subjects that depend so much on ‘so-called’ theories and of the unknown - the (PC) analogy doesn’t engage a readership, via subject alone. It needs an engaging author to humanize the data, to enthuse an audience just to lighten the subject load. Donal O’Shea had a message that superseded any witticisms or lightening data analysis. It was a message that education is key for progression – what do you expect from a lecturer, who facially looked like Rasputin as a younger man?

Interesting factors included the Jacobean era when the masters of intellect dithered on the shape of the spherical Earth – Columbus went on the notion planet Earth was pear shaped; that you could travel around it without coming to an edge. He wasn’t far wrong, albeit the North and South poles flatten greatly - not too dissimilar to a ‘Terry’s Chocolate Orange’. Joan’s Blaue’s; ‘Atlas Major’, was published initially in four languages in 1662 – 63 – they’re best described as a work of art, rather than a credible geographer’s research tool; even in the Jacobean era. Maps became a relevant source of information towards the end of the nineteenth century. O’Shea’s book knits a patchwork of material mainly designed to fill out to the ‘piece de resistance’ The Poincare Conjecture, the crux of the book. Due to this irritation, O’Shea’s structure will not suit most readerships; but indefinitely be a resourceful aid for research. Don’t expect a euphoric moment that’ll captivate an audience, just because you’re fascinated by the universe. The statistics available won’t mean much to the non mathematician, but still they’re well sourced out so, O’Shea certainly has done his homework, probably suffered from a smidgeon of overkill in data, as it is an imbalance to the book’s readability. O’Shea obviously aimed it for the John Nash’s of this world, who was incredibly depicted by Russell Crowe in the 2001 film ‘A Beautiful Mind’ – instead of coded digits O’Shea uses Pythagoras theory to determine the shape of the universe – imagine a collection of rectangle shapes, make it an Aquarian or a transparent shoe box, he exclaims (a pathetic bid to humanize the premise) visualize clear liquid crystals with yellow spots, they’re stars, solar systems. Every now and then O’Shea will introduce ‘Blue Peter’ styled practices to deliver an ideology; not that it makes sense, although it embodies O’Shea’s eccentricities. He has a hunch the universe is finite, apparently - basically means the universe has an ending, not that we know how to define it yet. O’Shea’s quest in putting universe diagram figs in a shoe box doesn’t necessary help visual aid – but it serves a purpose to O’Shea’s message; ‘mathematical education is vital to understanding the universe’. I suppose the fact that most view mathematics and topology equations with a confused eye – goes hand in hand with the unknown (fourth dimension and beyond); Hence, space is the fourth dimension; we see it on a 3D sphere with the Polaris (North Star) as a guide to where we are in regards to what is out there - so instead of ignoring it, it should be embraced.

O’Shea didn’t delve into the ‘big bang theory’; he naturally skits around the theory, and instead cleverly tinkers with mathematical comrades resources from the past and present. Like an extended relay team, O’Shea manages to fit in theories from Poincaré to Reimann, to Perelman, to Whitehead - and back to Poincaré. A story begins laced with an extra strong cup of coffee; Henri Poincaré’s written documents conclude he discovered new material contrary to his initial comprehensions – a large class of functions. The next stage was how he should present these findings. That is another ‘kettle of fish’; in which one hundred years on, we’re still figuring it out.