If you're only casually into photography the only names on the list you'll really know are HCB, St Ansel and Arbus. I do sympathize with what the author is trying to say. If I ask a photog about their favorite artists and they don't mention anyone outside of the holy Tri-X trifectorate or the Flickr all-stars I assume the rest of the conversation will be about gear and technique rather than photography itself. That may be just me being an art photography snob but I believe that all photographers from the enthusiast to the highest paid professional must know some basic art photography history.
The truism that if you don't know your history you're doomed to repeat it applies to photographers just as much as it is true for anyone else. In the modern world we are surrounded by photographs: billboards, advertising, the interwebs is full of photography. Some of it is good, some is bad, but, if you're a visual person, you can't help but be influenced by it. It will also leak out in your photography. The trouble with that influence is that it is second or third-hand so it is weak and diluted. You have to go back to the original source. That's the only way to know what you're really trying to emulate or the cliche's you should try to avoid. If you're a young musician and you love Green Day, and you want to start your own punk band you will just be a hollow imitation of punk if you don't go back to Green Day's own influences. You'd have to go back to The Sex Pistols and The Clash and understand why punk came about to be relevant today.
At the risk of putting words into Mr Formals' mouth it seems to me he was saying you have to know these influential photographers so that you can avoid their influence in your own work: "don’t ignore [their] work. Absorb it, absorb it all, marvel in [their] genius and grace." In most cases the authors didn't seem to be deriding the source but those that mindlessly emulate them. Whatever the intention, after I'd read the piece and stopped sniggering it did feel a little elitist and negative. In in effort to address this with a more positive list here are 10 photographers (in no particular order) who I think you ignore at your peril:
Martin Parr
It is hard to overstate Martin Parr's influence on the modern art photography scene. He literally wrote the book (actually 2) on art photography books. His best known work is luridly saturated and has been accused of looking down on his blue-color or tasteless, nouveau riche subjects but he has, over recent decades, fearlessly described a change in society towards a bland, commercial globalization of our world. His work is full of truth and an uncomfortable humor.If you don't know where to start, start at The Last Resort and work forwards.
William Eggleston
William Eggleston was the punk in photography. He was the first color photographer exhibitted at MoMA and it's hard to appreciate the controversy it created in its day (Ansel Adams hated it so much he wrote to the museum's board) but this work not only legitimized color work but it heralded a new snapshot aesthetic that is still hugely influential today. I know Eggleston was in the list of photographers to ignore but you do so at your peril.If you don't know where to start, start with Eggleston's Guide and see how many album covers you spot in it's pages.
Helen Levitt
According to the negative list HCB 'narrowed the path of street photography'. If this is true Levitt walked that path and humanized it. Of course all street photography is a product of the time and place it was created and the appeal of Levitt's work is partly being transported back to another time. Contemporary street photography always seems to be fighting between the aesthetic laid out by HCB and modern subjects. Event though Levitt's work is decades old she shows that street work should be contemporary to the time you live in and doesn't need to prematurely nostalgic.If you don't know where to start, Crosstown is just about the most perfect monograph I have come across. As it's out of print hunt it down in secondhand books stores and treasure it when you find it.
Robert Frank
Another photographer from the ignore list but if Jack Kerouac writes the forward to your book you know it is something special. Frank was as much an influential part of the beat generation as Kerouac. His work is the equivalent of The Road and he was one of the first photographers that tried to describe who and what America was.If you don't know where to start, start with The Americans: it can be a little underwhelming to modern eyes but let is sit a while - it is not such an influential book without a reason.
Andreas Gursky
We know the headlines: Gursky's Rhein II sold for more than 4 million dollars to become the most expensive photography ever sold. So what do deap pocketed collectors know that you don't? In a world dominated by an instant snapshot aesthetic Gursky shows that there is room for something more slow and considered. His large format process and huge prints show the power and impact that photography can have but they also show big prints have to be big for a reason not just to cover square inches. His work can seem dispassionate and deadpan but it is unrepentantly modern and relevant.
If you don't know where to start Gursky's work should be seen in the flesh not reduced down for publication. Many modern art museums display his work (MoMA, SF MoMA, Centre Pompidou, Tate Modern, etc.)
Richard Avedon
If you attempt fashion or portrait photography it is impossible to avoid the influence of Richard Avedon. Any black and white picture shot against a plain white background is going to draw comparisons. There is so much of his own personality in his portraiture that he sometimes is criticized for it but he understood the relationship between art and (that dirty word) money better than any other photographer of his day and his influence is still felt today. His pictures look so contemporary because many photographers have followed in his deceptively simple style and his influence and popularity show no sign of waning.
If you don't know where to start, start with his Magnum Opus, In The American West. It is, however, a poor substitute for seeing this show for real. If it ever tours again you must make time to see it. It shows an understanding of the use of drama and stagecraft in a gallery setting.
Jeff Wall
When thinking of a photo-conceptualist to include here I was torn between Jeff Wall and the slightly more mainstream Gregory Crewdson. To me they represent the same idea of describing a fully formed narrative in a single image and an antidote to the misconception that modern photography is just about snapping pictures of what you encounter. Every inch of the frame is carefully considered and nothing you see there is an accident. Jeff Wall's images are carefully constructed and the results are often displayed back-lit which heightens the cinematic experience.
If you don't know where to start, Jeff Wall is another photographer who should be seen in person but he is a thinking person's photographer so his Selected Essays and Interviews are a rich source document.
Sebastiao Salgado
The sheer scope of Salgado's work is massive. His two largest projects are to be found in Migrations and Workers which contain hundreds of images describing the big picture issue in each. Salgado is concerned with world wide issues which can't easily be described in a single image. These two works can both be overwhelming which is appropriate in that the issues he depicts are overwhelmingly huge too. Yet Salgado, even at this point in his career, believes that his work can change the world. In a cynical world his images can sometimes be hard to stomach and yet his message is hopeful.
If you don't know where to start, you have to get hold of both Migrations and Workers and keep going back to them.
Bernd and Hilla Becher
The Bechers invented the form sometimes called typology. Their deceptively straightforward aesthetic and uniform approach to every subject lend a scientific air to their work. Subjects were generally industrial architecture with prints being arranged deliberately to demonstrate differences and similarities between subjects. Their influence is found on many documentary and conceptual photographers today and, although it can be argued that typology has been done to death, a view at the Bechers oeuvre shows the power in the form.
If you don't know where to start, any of their typologies are worth seeing: Typologies of Industrial Buildings is a good example.
Elliot Erwitt
In case we take ourselves too seriously and forget that photography should be fun, I include Elliot Erwitt here. If you think he just takes images of dogs you must revisit his work. He has a visual wit that is unmatched. His catalog is huge and he still continues to make images and exhibit his work today. In case there is a danger that we do take him too seriously he has created an alter ego, André S. Solido, in order to "satirise the kooky excesses of contemporary photography".
If you don't know where to start, start with Snaps.